Self-assembled Magnetic Nanostructures: Synthesis and ...

Self-assembled Magnetic Nanostructures: Synthesis and

Characterization

DISSERTATION

zur

Erlangung des Grades

“Doktor der Naturwissenschaften”

an der Fakultät für Physik und Astronomie der Ruhr-Universität Bochum

von

María José Benítez Romero

aus

Quito (Ecuador)

Bochum 2009

1. Gutachter Prof. Dr. Dr. h.c. Hartmut Zabel 2. Gutachter Prof. Dr. Ferdi Schüth

Datum der Disputation 14.12.2009

“There's Plenty of Room at the Bottom”

Richard P. Feynman

Dedico esta thesis a mi familia

por su constante apoyo y su amor incondicional.

Los amo mucho.

i

List of Abbreviations

AF Antiferromagnetic

BET Brunauer-Emmett-Teller

BJH Barrett-Joyner-Halenda

BSE Back Scattered Electrons

CMC Critical Micelle Concentration

DAFF Diluted Antiferromagnetic in a Field

dc direct current

DS Domain State

dw wires diameter

EASG Edwards-Anderson Ising Sping Glass

EBL Electron Beam Lithography

EDX Energy Dispersive X-Ray Spectroscopy

FC Field-Cooled

FM Ferromagnetic

FiM Ferrimagnetic

FORC First Order Reversal Curve

GMR Giant Magneto-Resistance

IPA Isopropanol

IRM Isothermo-Remanent Magnetization

IUPAC International Union of Pure and Applied Chemistry

HRSEM High Resolution Scanning Electron Microscope

HRTEM High Resolution Transmission Electron Microscope

LRO Long Range Order

MF Molecular Field

MIBK Methylisobutylketon

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NP Nanoparticle

NW Nanowire

PEO Poly(ethylene oxide)

PPO Poly(propylene oxide)

PM Paramagnetic

PMMA Polymethylmethacrylat

RF Random Field

RIE Reactive Ion Etching

RFIM Random Field Ising Model

RKKY Ruderman-Kittel-Kasuya-Yosida

SDA Structure Directing Agent

SE Secondary Electrons

SEM Scanning Electron Microscope

SG Spin Glass

SPM Superparamagnetic

SQUID Superconducting Quantum Interference Device

STP Standard Temperature and Pressure

SW Stoner-Wohlfarth

TEM Transmission Electron Microscope

TEOS Tetraethoxysilane

TRM Thermo-Remanent Magnetization

XRD X-Ray Diffraction

ZFC Zero-Field-Cooled

List of Figures

2.1 Schematic representation of a paramagnetic system under an applied field. 6

2.2 Temperature dependence of spontaneous magnetization. . . . . . . . . . . 10

2.3 Schematic representation of the two equivalent interpenetrating sublattices. 13

2.4 Spin rotation in an antiferromagnetic material. . . . . . . . . . . . . . . . 16

2.5 The temperature dependence of the susceptibility of antiferromagnets. . . 16

2.6 Spin-flop transition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.7 Schematic phase diagram of a three-dimensional DAFF. . . . . . . . . . . 18

2.8 Schematic spin configuration illustrating the Imry-Ma argument. . . . . . 19

2.9 Spin arrangement of inverse spinel ferrite. . . . . . . . . . . . . . . . . . 21

2.10 Spinel structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.11 Coordinate system for magnetization reversal process in a single-domain

particles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.12 Angular dependence of the magnetization hysteresis in the S-W model. . 26

2.13 φ dependence of the total energy for a SPM system. . . . . . . . . . . . . 27

2.14 The dependence of the relaxation time τ as a function of T . . . . . . . . 28

2.15 Schematic illustration of ZFC and FC magnetization curves for SPM systems. 30

2.16 Possible cases of ’uncompensated’ surface spins according to Néel. . . . . 31

3.1 Examples of magnetic nanostructures. . . . . . . . . . . . . . . . . . . . . 33

3.2 Examples of self-assembly. . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.3 Examples of the combination of top-down and bottom-up processes. . . . 35

3.4 Schematic of nanocasting method. . . . . . . . . . . . . . . . . . . . . . . 36

3.5 Different aggregate morphologies predicted by the packing parameter g. . 37

3.6 Mechanism of template formation. . . . . . . . . . . . . . . . . . . . . . . 39

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3.7 Schematic of an electron-beam lithography. . . . . . . . . . . . . . . . . . 43

3.8 Schematic of an electron-beam exposure system. . . . . . . . . . . . . . . 44

3.9 Expression of dose for area, line and dots. . . . . . . . . . . . . . . . . . 45

3.10 Mechanism of radiation-induced chain scission in PMMA. . . . . . . . . . 46

3.11 Schematic of possible dry etching techniques. . . . . . . . . . . . . . . . . 48

3.12 Schematic of an ion beam milling system. . . . . . . . . . . . . . . . . . . 49

4.1 Types of gas adsorption - desoportion isotherms. . . . . . . . . . . . . . . 52

4.2 Types of adsorption-desorption hysteresis loops. . . . . . . . . . . . . . . 54

4.3 Scattering of radiation from two particles. . . . . . . . . . . . . . . . . . 57

4.4 Example of experimental and calculated powder XRD diffraction pattern

of mesoporous materials. . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.5 The principle set-up of a TEM. . . . . . . . . . . . . . . . . . . . . . . . 61

4.6 The principle set-up of a SEM. . . . . . . . . . . . . . . . . . . . . . . . 63

4.7 Schematic of specimen-electron beam interaction. . . . . . . . . . . . . . 64

4.8 Schematic of a dc SQUID. . . . . . . . . . . . . . . . . . . . . . . . . . . 67

4.9 Critical current of a dc SQUID as a function of the applied flux. . . . . . 68

4.10 Schematic representation of commercial SQUID-magnetometer (MPMS-

5S, Quantum Design). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

4.11 Schematic representation of ZFC and FC magnetization curves. . . . . . 70

4.12 Schematic representation of hysteresis loops. . . . . . . . . . . . . . . . . 71

5.1 Schematic illustration of the synthesis of mesoporous SBA-15. . . . . . . 75

5.2 Small-angle XRD patterns of SBA-15-100 with different connectivities. . 76

5.3 N2 sorption isotherm and pore size distribution of SBA-15-100-50. . . . . 77

5.4 N2 sorption isotherm of SBA-15-100 with different conectivities. . . . . . 78

5.5 Schematic illustration of the synthesis of mesoporous KIT-6. . . . . . . . 79

5.6 Small-angle XRD pattern of KIT-6. . . . . . . . . . . . . . . . . . . . . . 80

5.7 N2 sorption isotherm and pore size distribution of KIT-6-100 . . . . . . . 81

5.8 N2 sorption isotherm of KIT-6 synthesized at different hydrothermal treat-

ment temperatures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

5.9 Schematic illustration of the synthesis of Co3O4 NWs. . . . . . . . . . . . 83

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5.10 Small-angle XRD pattern of Co3O4 NWs with different connectivities. . . 84

5.11 High-angle XRD pattern of Co3O4 NWs. . . . . . . . . . . . . . . . . . . 85

5.12 TEM, HRSEM and HRTEM images of the Co3O4 NWs. . . . . . . . . . . 86

5.13 HRSEM images of Co3O4 NWs with different diameter sizes. . . . . . . . 87

5.14 N2 sorption isotherm and pore size distribution of Co3O4 NWs. . . . . . . 88

5.15 High-angle XRD pattern of Co3O4 and Co2SiO4. . . . . . . . . . . . . . . 89

5.16 Schematic illustration of the synthesis of cubic Co3O4 nanostructures. . . 90

5.17 Small-angle XRD pattern of cubic Co3O4 nanostructures. . . . . . . . . . 91

5.18 High-angle XRD pattern of cubic Co3O4 nanostructures. . . . . . . . . . 91

5.19 N2 sorption isotherm and pore size distribution of Co3O4-Cubic-100. . . . 92

5.20 N2 sorption isotherms and pore size distribution of cubic Co3O4 nanos-

tructures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

5.21 Schematic of how one or two pore sizes in mesoporous materials can occur. 94

5.22 HRSEM and TEM images of cubic Co3O4 nanostructures with different

diameter sizes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

5.23 HRSEM image of cubic ordered mesoporous CoO. . . . . . . . . . . . . . 95

5.24 HRSEM image of cubic ordered mesoporous Cr2O3. . . . . . . . . . . . . 96

6.1 Defect structure of wüstite. . . . . . . . . . . . . . . . . . . . . . . . . . 98

6.2 Crystal structure of magnetite. . . . . . . . . . . . . . . . . . . . . . . . 99

6.3 Synthesis of monodispersed nanocrystals. . . . . . . . . . . . . . . . . . . 100

6.4 TEM images of 20 nm monodisperse iron oxide nanoparticles. . . . . . . 101

6.5 Schematic illustration of NPs self-assembly on a solid substrate. . . . . . 102

6.6 SEM image of iron oxide NPs on Si(100). . . . . . . . . . . . . . . . . . . 103

6.7 SEM image of one monolayer of iron oxide NPs. . . . . . . . . . . . . . . 104

6.8 SEM image of iron oxide NPs annealed at 170 ◦C . . . . . . . . . . . . . 104

6.9 XRD patterns of iron oxide NPs. . . . . . . . . . . . . . . . . . . . . . . 105

6.10 Schematic illustration of deposition of iron oxide NPs into patterned lines. 107

6.11 SEM image of parallel arrays of NPs in patterned lines. . . . . . . . . . . 108

6.12 SEM image of self-assembled NPs in patterned circles. . . . . . . . . . . 109

6.13 SEM image of NPs in patterned lines of 130 nm width dried at 80 ◦C. . . 109

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6.14 SEM image of NPs in patterned lines of 130 nm width dried at 170 ◦C. . 110

7.1 Crystal structure of Co3O4. . . . . . . . . . . . . . . . . . . . . . . . . . 112

7.2 Level configuration for Co2+ and Co3+ ions in Co3O4. . . . . . . . . . . . 113

7.3 M vs. T curves of Co3O4 NWs. . . . . . . . . . . . . . . . . . . . . . . . 114

7.4 ΔM vs. T of Co3O4 NWs. . . . . . . . . . . . . . . . . . . . . . . . . . . 115

7.5 Memory effect of Co3O4 NWs. . . . . . . . . . . . . . . . . . . . . . . . . 116

7.6 M vs. T curves of Co3O4 NWs with different connectivities. . . . . . . . 117

7.7 M vs. T curves of Co3O4 with different diameter sizes. . . . . . . . . . . 119

7.8 M vs. T curves of 6nm Co3O4 NWs. . . . . . . . . . . . . . . . . . . . . 120

7.9 Dependence of T1 and T2 as a function of dw. . . . . . . . . . . . . . . . . 121

7.10 HRSEM image and schematic diagram of Co3O4 NWs showing the AF core

and a 2d DAFF shell. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

7.11 M vs. H hysteresis curves of Co3O4 NWs. . . . . . . . . . . . . . . . . . 123

7.12 M vs. H hysteresis curves of Co3O4 with different diameter sizes. . . . . 124

7.13 The experimetal procedure to measure TRM and IRM vs. H . . . . . . . 126

7.14 TRM and IRM vs. H of 8 nm Co3O4 NWs. . . . . . . . . . . . . . . . . 127

7.15 TRM and IRM vs. H of magnetic systems. . . . . . . . . . . . . . . . . . 128

7.16 TRM and IRM vs. H for different diameters of Co3O4 NWs. . . . . . . . 130

7.17 TRM and IRM vs. T of 6 nm Co3O4 NWs. . . . . . . . . . . . . . . . . . 131

7.18 M vs. T curves of cubic Co3O4 nanostructures. . . . . . . . . . . . . . . 133

7.19 M vs. T curves of different diameters of cubic Co3O4 nanostructures. . . 134

7.20 M vs. H curves of cubic Co3O4 nanostructures. . . . . . . . . . . . . . . 135

7.21 TRM and IRM vs. H of cubic Co3O4 nanostructures. . . . . . . . . . . . 136

7.22 TRM vs. T of cubic Co3O4 nanostructures. . . . . . . . . . . . . . . . . . 137

7.23 M vs. T curves of cubic CoO nanostructures. . . . . . . . . . . . . . . . 138

7.24 M vs. H hysteresis curves of cubic CoO nanostructures. . . . . . . . . . 139

7.25 TRM and IRM vs. H of cubic CoO nanostructures. . . . . . . . . . . . . 140

7.26 TRM vs. T of cubic CoO nanostructures. . . . . . . . . . . . . . . . . . . 140

7.27 The magnetic structure of Cr2O3. . . . . . . . . . . . . . . . . . . . . . . 141

7.28 M vs. T curves of cubic Cr2O3 nanostructures. . . . . . . . . . . . . . . 142

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7.29 M vs. H curves of cubic Cr2O3 nanostructures. . . . . . . . . . . . . . . 143

7.30 M vs. H curves of cubic Cr2O3 nanostructures. . . . . . . . . . . . . . . 144

7.31 TRM and IRM vs. H of cubic Cr2O3 nanostructures. . . . . . . . . . . . 145

7.32 TRM vs. T of cubic Cr2O3 nanostructures. . . . . . . . . . . . . . . . . . 146

7.33 M vs. T curves of Co2SiO4. . . . . . . . . . . . . . . . . . . . . . . . . . 147

7.34 M vs. H hysteresis curves of Co2SiO4. . . . . . . . . . . . . . . . . . . . 148

7.35 TRM and IRM vs. H of Co2SiO4. . . . . . . . . . . . . . . . . . . . . . 149

7.36 TRM vs. T of Co2SiO4. . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

8.1 Antiferromagnetic structure of wüstite. . . . . . . . . . . . . . . . . . . . 152

8.2 Electron transfer between Fe2+ and Fe3+ states in magnetite. . . . . . . . 153

8.3 M vs. T curves of iron oxide NPs dried at 80 ◦C. . . . . . . . . . . . . . 155

8.4 Schematic representation of mechanical rotation of NP in toluene matrix. 156

8.5 M vs. T curves of iron oxide NPs dissolved in benzene and on top of PMMA.157

8.6 M vs. T curves of iron oxide NP dried at 80 ◦C. . . . . . . . . . . . . . . 158

8.7 M vs. T curves of iron oxide NP dried at 80 ◦C. . . . . . . . . . . . . . . 159

8.8 M vs. T curves of iron oxide NP annealed at 170 ◦C. . . . . . . . . . . . 160

8.9 M vs. T curves of iron oxide NP annealed at 170 ◦C. . . . . . . . . . . . 161

8.10 M vs. H hysteresis curves of iron oxide nanoparticles dried at 80 ◦C. . . 162

8.11 M vs. H hysteresis curves of iron oxide NP annealed at 170 ◦C. . . . . . 163

8.12 M vs. T curves of iron oxide NPs. . . . . . . . . . . . . . . . . . . . . . . 164

8.13 M vs. T curves of iron oxide NPs trenches annealed at 170 ◦C. . . . . . . 165

8.14 M vs. H curves of iron oxide NPs trenches annealed at 170 ◦C. . . . . . 165

9.1 HRSEM image and schematic diagram of Co3O4 NWs showing the AF core

and a 2d DAFF shell. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

9.2 TRM and IRM vs. H of magnetic systems. . . . . . . . . . . . . . . . . . 168

9.3 SEM image of self-assembled nanoparticles into patterned structures. . . 169

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List of Tables

2.1 Examples of ferromagnetic materials. . . . . . . . . . . . . . . . . . . . . 12

2.2 Examples of antiferromagnetic materials. . . . . . . . . . . . . . . . . . . 18

2.3 Examples of ferrimagnetic materials. . . . . . . . . . . . . . . . . . . . . 23

2.4 Critical single-domain radius for different magnetic materials. . . . . . . 24

2.5 The experimental measuring time for some experimental techniques. . . . 29

3.1 Relation between g of cationic surfactant and mesostructure. . . . . . . . 38

3.2 Synthesis routes to mesoporous materials focous on silicates. . . . . . . . 40

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Contents

1 Introduction 1

2 Basic concepts in magnetism 3

2.1 Basic bulk properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1.1 Ferromagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.1.2 Antiferromagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.1.3 Diluted antiferromagnets in a uniform field . . . . . . . . . . . . . 17

2.1.4 Ferrimagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.2 Small particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.2.1 Stoner-Wohlfarth model . . . . . . . . . . . . . . . . . . . . . . . 24

2.2.2 Superparamagnetism . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.2.3 Nanoscale antiferromagnetism . . . . . . . . . . . . . . . . . . . . 30

3 Fabrication of magnetic nanostructures 33

3.1 Nanocasting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.2 Electron beam lithography . . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.2.1 EBL with positive resist and lift-off . . . . . . . . . . . . . . . . . 43

3.2.2 EBL with negative resist and etching . . . . . . . . . . . . . . . . 47

4 Characterization techniques of magnetic nanostructures 51

4.1 Gas adsorption-desorption techniques . . . . . . . . . . . . . . . . . . . . 51

4.1.1 Classification of the gas adsorption isotherms . . . . . . . . . . . 52

4.1.2 Types of adsorption-desorption hysteresis loops . . . . . . . . . . 53

4.1.3 Determination of surface area . . . . . . . . . . . . . . . . . . . . 54

xi

4.1.4 Determination of pore volume . . . . . . . . . . . . . . . . . . . . 55

4.1.5 Determination of pore size distribution . . . . . . . . . . . . . . . 55

4.2 X-ray diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

4.3 Microscopy techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.3.1 Transmission electron microscopy . . . . . . . . . . . . . . . . . . 60

4.3.2 Scanning electron microscopy . . . . . . . . . . . . . . . . . . . . 63

4.4 The superconducting quantum interference device: SQUID . . . . . . . . 65

4.4.1 SQUID magnetometer . . . . . . . . . . . . . . . . . . . . . . . . 68

4.4.2 Applications of SQUID magnetometers . . . . . . . . . . . . . . . 70

5 Synthesis and structural characterization of antiferromagnetic nanos-

tructures 73

5.1 Synthesis of mesoporous SBA-15 . . . . . . . . . . . . . . . . . . . . . . . 74

5.2 Synthesis of mesoporous KIT-6 . . . . . . . . . . . . . . . . . . . . . . . 79

5.3 Synthesis and structural characterization of Co3O4 nanowires . . . . . . . 82

5.4 Synthesis and structural characterization of cubic Co3O4 nanostructures . 89

5.5 Synthesis of cubic CoO and Cr2O3 nanostructures . . . . . . . . . . . . . 95

5.6 Summary and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 96

6 Synthesis and structural characterization of iron oxide nanoparticles 97

6.1 Crystal structures of bulk iron oxides . . . . . . . . . . . . . . . . . . . . 98

6.2 Synthesis of iron oxide nanoparticles . . . . . . . . . . . . . . . . . . . . 100

6.3 Self-assembly of three and two dimensional arrays of iron oxide nanoparticles102

6.4 Templated self-assembly of iron oxide nanoparticles in lithographical patterns106


7 Magnetic characterization of antiferromagnetic nanostructures 111

7.1 Magnetic properties of bulk Co3O4 . . . . . . . . . . . . . . . . . . . . . 112

7.2 Magnetic properties of Co3O4 nanowires . . . . . . . . . . . . . . . . . . 114

7.2.1 Magnetization vs. temperature curves . . . . . . . . . . . . . . . . 114

7.2.2 Hysteresis loops . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

7.2.3 Remanent magnetization curves . . . . . . . . . . . . . . . . . . . 125

xii

7.3 Magnetic properties of cubic Co3O4 . . . . . . . . . . . . . . . . . . . . 132




7.4 Magnetic properties of cubic CoO . . . . . . . . . . . . . . . . . . . . . . 137




7.5 Magnetic properties of cubic Cr2O3 . . . . . . . . . . . . . . . . . . . . . 140




7.6 Magnetic properties of Co2SiO4 . . . . . . . . . . . . . . . . . . . . . . . 146





8 Magnetic characterization of iron oxide nanoparticles 151

8.1 Magnetic structure of bulk iron oxides . . . . . . . . . . . . . . . . . . . 152

8.2 Magnetic characterization of two dimensional arrays of iron oxide nanopar-

ticles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

8.3 Magnetic characterization of iron oxide nanoparticles in lithographical pat-

terns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

8.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

9 Summary and Final Remarks 167

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Chapter 1

Introduction

Today, nearly three thousand years since the first discovery of magnetism, scientists

around the world are working on new findings that bring us closer to its understanding.

Bulk magnetic materials exhibit exiting magnetic properties, and what happens when we

get to the very, very small scales?

In the annual meeting of the American Physical Society in 1959, Richard Feymann

raised several questions regarding the very small world [1]. Can we write the entire 24

volumes of the Encyclopedia Brittanica on the head of a pin? Can we arrange the atoms

in the way that we want? Can we make smaller computers? How do we write small? He

believed that there is a positive answer to all of these questions. Nowadays, we know that

he was right. The Giant Magneto-Resistance (GMR) effect discovered by A. Fert and P.

Grünberg is an impressive example of what we can do [2,3]. The GMR effect opened the

way to an efficient control of the motion of electrons by acting on their spin through the

orientation of a magnetization.

The magnetic properties on a very small scale are not the same as on a large scale.

They do not simply scale down in proportion. Upon decreasing the size, nanosized fer-

romagnetic structures enter so-called superparamagnetism, i.e. a thermally activated

single-domain state. However, antiferromagnetic nanosystems are governed by core-shell

behavior. In this case the surface plays a particularly important role for the magnetic

behavior. This dissertation presents an exciting experimental study on antiferromagnetic

nanostructures. This study does not only reveal a completely different view on the surface

1

2 Introduction

behavior of these antiferromagnetic nanosystems, but it also shows a surprising decou-

pling scenario of the shell of these systems and its core. Furthermore, this dissertation

presents an easy approach to fabricate sub-100-nm arrangements of iron oxide nanopar-

ticles. Studies on the self-assembled nanoparticle films as well as on the nanoparticle

arrays show a strong dependence of the magnetic properties on a thermal treatment.

The contents of this dissertation are divided in nine Chapters. Chapter 2 provides the

basic concepts in magnetism focusing on the basic bulk properties and small particles. In

Chapter 3 two fabrication methods of magnetic nanostructures, i.e. nanocasting and e-

beam lithography are discussed. The experimental techniques required to characterize the

systems are described in Chapter 4. Chapter 5 and 6 are concerned with the synthesis

of magnetic nanostructures. Chapter 7 and Chapter 8 are devoted to discussions of

magnetic characterization of the synthesized magnetic nanostructures. The summary

and final remarks are presented in Chapter 9.

Chapter 2

Basic concepts in magnetism

2.1 Basic bulk properties

Magnetism in solids arises from the magnetic moments of the electrons. The origin of

the orbital magnetic moment can be understood by considering the model of an orbiting

electron around its nucleus [4, 5]. In a classical approach, where the electron motion is

modeled as a ring current I, around the enclosed are A with normal vector n, the magnetic

moment μ is then given by

μ = IAn, (2.1)

Taking into account that the current is given by I = −e(ω/2π) where ω is the angular

frequency with which the charge e moves around the current loop, and the area of the

loop is A = πr2, where r is the orbital radius, Eqn. 2.1 can be written as

μ = −e

2r2ω, (2.2)

By considering the classical angular momentum, l, of an orbiting electron with mass

me,

l = mer2ω (2.3)

Eqn. 2.2 can be written as

3

4 Basic concepts in magnetism

μ = − e

2me

l = γl (2.4)

where γ is the gyromagnetic ratio [6]. In the quantum mechanical approach, however,

one has to consider expectation values of operators [4]. The component of the expectation

value of l along the quantization axis, z, usually that of the applied magnetic field, is 〈lz〉.The eigenvalues of the operator l̂z are ml�, with ml = −l, −l + 1, ..., l [5]. The quantum

mechanical expression for the measured magnetic moment along z can then be written

as

〈μz〉 = − e

2me

ml� = −μB

�〈lz〉 (2.5)

where μB = e�

2me= 0.927 × 10−23[Am2] is the Bohr magneton1.

Eqn. 2.5 gives only the orbital magnetic moment. In addition, the electron has a

characteristic intrinsic angular momentum, the spin. Electrons have a half-integer spin

quantum number s=1/2 and projections 〈sz〉 = ms� = ±�/2. The spin magnetic moment

〈μzs〉 is

〈μzs〉 = −gs

μB

�〈sz〉 (2.6)

with gs ≈ 2 being the spin Landé-factor2.

The total magnetic moment is obtained by the sum of the orbital and spin magnetic

moments, thus

〈μztotal〉 = −μB

�(2 〈sz〉 + 〈lz〉) (2.7)

Let us consider the behavior of magnetic moments in a field. An important mea-

surement value is the magnetization M. It is defined as the total magnetic moment per

volume,

1Two system of units are particular useful in magnetism, i.e. the Gauss CGS and the InternationalSystem of Units (SI) [6]. The system employed throughout this chapter is the SI system of units. Thereader can find summarized conversions between both systems of units in the Ref. [7]

2In a full QED description one finds gs=2.0023 [8].

2.1 Basic bulk properties 5

M =1

V

∑i

μi (2.8)

In matter the magnetic field H and the magnetic induction B are related by

B = μ0(H+M) (2.9)

where μ0 = 4π × 10−7 Hm−1 is the permeability of free space [4, 7, 9].

The magnetic susceptibility, χ, per unit of volume is defined as

M = χH (2.10)

From Eqns. 2.9 and 2.10, one can write

B = μ0(1 + χ)H = μ0μrH (2.11)

The relation is only valid if the medium is isotropic and no hysteresis occurs [9].

Let us consider first isolated magnetic moments, viz. non-interacting magnetic mo-

ments. If the susceptibility given by Eqn. 2.10 is small and negative (χ < 0), the material

is called diamagnetic [5]. The negative susceptibility arises from the fact that the applied

field induces a magnetic moment which is proportional to the applied field and is always

in the opposite direction to it. Let us consider a solid composed of N atoms per unit

of volume V . If 〈r2i 〉 is the mean square distance from the nucleus, and on average the

distribution is spherically symmetrical, the diamagnetic susceptibility is given by [5, 6]

χ = −Ne2μ0

V 6me

Z∑i=1

⟨r2i

⟩(2.12)

Eqn. 2.12 is the Langevin formula for diamagnetism. Note that diamagnetism is inde-

pendent of the temperature. Next, let us consider paramagnetism, which is characterized

by a positive susceptibility, χ > 0. It can be understood in a model of non-interacting

magnetic moments, where their orientations are determined by a competition between an

external field and thermal fluctuations. That is, in absence of a magnetic field, thermal

fluctuations cause a random orientation of the individual magnetic moments, giving zero


net magnetization. When a magnetic field is applied, the magnetic moments tend to be

oriented in direction of the field (Fig. 2.1). The potential energy of a single moment in

a field is equal to −μ ·B [4, 6].

Fig. 2.1: Schematic representation of a paramagnetic (PM) system under an applied field [10]. Themagnetic field is assumed to be along the z axis.

The total magnetic moment of an atom is characterized by the quantum number J ,

which measures the magnitude of its total angular momentum, |J|2 = J(J + 1)�2 [11].

That is, J is the sum of the orbital angular momentum and the spin angular momentum,

J = L + S [11]. If one considers the semiclassical treatment of paramagnetism, i. e.

J = ∞, the magnetic moments are free to point in any direction. However, if one

considers a quantum mechanical system, the magnetic moments can point only along

certain directions because of the quantization [6]. Let us consider a general case where J

can take any integer or half integer value. The magnetization is given by [6]

M = MsBJ(y) (2.13)

where Ms (Eqn. 2.14) is the saturation magnetization, i. e. the maximum magneti-

zation obtained when all the magnetic moments are aligned [5, 6],

Ms = ngJμBJ (2.14)


where n is the number of magnetic moments per unit of volume. The Brillouin

function, BJ(y), is given by [6]

BJ(y) =2J + 1

2Jcoth

(2J + 1

2Jy

)− 1

2Jcoth

y

2J(2.15)

with

y =gJμBμ0JH

kBT(2.16)

kB is the Boltzmann’s constant. The constant gJ is called the Landé g-value and is

given by

gJ =3

2+

S(S + 1) − L(L + 1)

2J(J + 1)(2.17)

In the limit when J → ∞ one obtains the Langevin function [4, 6]

B∞(y) = L(y) = coth y − 1

y(2.18)

When J = 12

only two states are possible, corresponding to mJ = ±12, the Brillouin

function is simply the tanh y, and thus the magnetization is

M = Ms tanh y (2.19)

where y = μBμ0H/kBT .

For small values of y the susceptibility is given by

χ =M

H∝ μ0M

B=

nμ0μ2eff

3kBT=

C

T(2.20)

where C is the Curie constant given by

C =nμ0μ

2eff

3kB

(2.21)

and μeff is the effective moment


μeff = gJμB

√J(J + 1) (2.22)

The temperature dependence of the susceptibility in Eqn. 2.20 is known as the Curie

law. Note that in paramagnetism the magnetic moments interact only with an external

magnetic field and not with each other. When interactions between the moments are

present, one may add an appropriately chosen effective field to the applied external field,

as it will be shown in the next sections.

2.1.1 Ferromagnetism

A ferromagnetic (FM) material is characterized by a saturation or spontaneous mag-

netization Ms even without any applied field. Above a critical temperature, the Curie

temperature TC , the spontaneous magnetization vanishes [5,11,12]. The material is then

paramagnetic with a susceptibility given by the Curie-Weiss law. Below TC , the interac-

tion of the single magnetic moments leads to a collective alignment and thus a magneti-

zation which is non-zero integrating over the volume. A strong interaction field favors the

collective alignment of the moments along a common direction. Weiss proposed that the

interaction field, called molecular field Hm, is proportional to the magnetization [5,8,11],

i. e.

Hm = λM (2.23)

where λ is a constant thus parametrizing the strength of the molecular field as a

function of temperature. In a ferromagnet, the total magnetic field that each moment

experiences consists of the applied field (Ha) and the molecular field, i. e.

Ht = Ha + λM (2.24)

In the previous discussion of paramagnetism, the relation between the magnetization

and the applied field was given by (Eqn. 2.13).

M = MsBJ

(gJμ0μBJH

kBT

)(2.25)


For a FM material, the field H can be replaced by the total field [5, 11, 13], i. e.

M = MsBJ(y) (2.26)

and

y =

(gJμ0μBJ(Ha + λM)

kBT

)(2.27)

To obtain solutions to the Weiss model, it is required that Eqn. 2.26 and Eqn. 2.27 are

satisfied simultaneously. The spontaneous magnetization can be obtained by considering

the limit where Ha → 0. The magnetization then follows the law

M = MsBJ

(gJμ0μBJ(λM)

kBT

)(2.28)

The solutions can be found graphically by plotting both functions at various T and

determining the points at which the curves intersect [5, 6, 9, 11, 13]. The case when the

straight line is tangent to the Brillouin function at the origin corresponds to the critical

temperature. This critical temperature at which Ms falls to zero is the Curie temperature,

TC . Its value in terms of the molecular field parameters is determined from the slope of

the Brillouin function at the origin which is (J + 1)/3J [5, 11]. Thus,

TC =gJμB(J + 1)λMs

3kB

(2.29)

The solution for J = 1/2, 1, 3/2 and ∞ is plotted in Fig. 2.2.

Above the Curie temperature, T > TC , the FM material behaves paramagnetically.

When Ms falls to zero at TC , the internal field also falls to zero and remains zero above

TC unless a magnetic field is applied. The susceptibility is given by

χ ∝ 1

T − TC

(2.30)

which is the Curie-Weiss law. The Eqn. 2.30 indicates that a graph of 1/χ versus

temperature should give a straight line with an intercept at TC .

A quantum mechanical description of the Weiss molecular field can be derived from


Fig. 2.2: Temperature dependence of spontaneous magnetization at H=0 and for different values ofJ . [6].

the Heisenberg Hamiltonian [4, 5, 9]. Let us consider two atoms, i and j, each of them

having one electron. The exchange Hamiltonian is

Hij = −2Jijsi · sj (2.31)

where Jij is the exchange integral of the two electrons. For two atoms, each of them

having more than one electron with an unpaired spin, the exchange Hamiltonian is

Hij = −2JijSi · Sj (2.32)

where Si =∑si and Sj =

∑sj. It was considered here, that all the electrons have

the same exchange integral Jij, and that the exchange integral between the electrons of

the same atom is constant, and therefore can be omitted3.

If the exchange integral is isotropic and if only nearest neighbors interact, then the

exchange Hamiltonian for spin i can be written as

Hi = −2∑

j

JeSi · Sj (2.33)

3The first considerations is valid if the angular momentum is quenched. The second one is valid ifthe spin angular momentum is not quenched. In this case, J = S, which works for most 3d ions.


where the summation is over the nearest neighbors of atom i.

Considering by simplicity the Ising model, one has

Hi = −2Je

∑j

Szi S

zj (2.34)

The connection of Je to the Weiss field is seen by taking into account the magnetiza-

tion, assumed along the z-direction, which is given by M = ngμB

∑j

⟨Sz

j

⟩. Here one re-

places the summation by a time average as an approximation, i. e. Hi = −2Je

∑Sz

i Szj ≈

−2JeSzi

∑j

⟨Sz

j

⟩neglecting fluctuations [5]. Thus, for the z nearest neighbors, Eqn. 2.34

can be written in terms of the magnetization as

Hi = −2zSz

i JeM

ngμB

(2.35)

where z is .The Hamiltonian in term of the Weiss field is then

Hi = −gSzi μBλM (2.36)

From Eqn. 2.35 and 2.36 one obtains the molecular field constant, λ,

λ =2zJe

ng2μ2B

(2.37)

A positive Je favors parallel alignment of the spins, which is the case for a ferromag-

netic interaction [12].

Using Eqn. 2.29 [5, 6], one finds that the Curie temperature is

TC =2zJeS(S + 1)

3kB

(2.38)

Examples of ferromagnetic materials are shown in Table 2.1.

2.1.2 Antiferromagnetism

It has been discussed that when the exchange interaction is positive, the spins tend

to be aligned parallel to each other. However, a negative exchange interaction tends

to align the neighboring spins antiparallel [5, 12]. In the ordered state, which sets in


Tab. 2.1: Examples of ferromagnetic materials taken from Ref. [6].Material Tc (K) magnetic moment

(μB/formula unit)Fe 1043 2.22Co 1394 1.1715Ni 631 0.605Gd 289 7.5

MnSb 587 3.5EuO 70 6.9EuS 16.5 6.9

below a critical temperature, the magnetic moments are aligned forming two or more

spontaneously magnetized and interpenetrating sublattices. Since the magnetizations

are differently oriented, the resultant magnetization is zero at zero applied field. This

kind of order is known as antiferromagnetism [5, 8, 11, 14]. Let us consider the case of

two interpenetrating sublattices, A and B, on one of which the spins point up and on the

other down as shown in Figure 2.3. The theory considers that the exchange interaction

between the nearest neighbors favors antiparallel alignment of the magnetic moments [14].

In that case, it is expected that a close approximation to the magnetically ordered state

at absolute zero is the alignment of all A ions in one direction and of all B ions in

the opposite direction. This consideration involves short-range interactions between first

neighbor atoms and negligible interactions beyond the second or third neighbors. In this

situation, the sublattice A exerts a molecular field HA on the sublattice B, whereas the

sublattice B exerts a molecular field HB on the sublattice A [14]. Then the molecular

field acting on sublattice A and B is given by

HA = −λAAMA − λABMB,

HB = −λBAMA − λBBMB. (2.39)

where MA = μA/VA and MB = μB/VB are the total magnetization of the A and B

sublattices, respectively. The constants λAB and λAA measure the interaction between

the nearest-neighbors and the next-nearest-neighbors, respectively, for an atom in the A


Fig. 2.3: Schematic representation of the two equivalent interpenetrating sublattices A and B.

site. Similar, the constants λBA and λBB measure the interactions between the nearest-

neighbors and the next-nearest-neighbors, respectively, for an atom in the B site [11].

Since the atoms occupying the sites A and B are of the same type, one has

λAA = λBB,

λAB = λBA. (2.40)

Since the interactions between the next-nearest-neighbors favor the antiparallel align-

ment, λAB is positive [5, 11].

The expressions for spontaneous magnetizations, MA and MB, as a function of tem-

perature, T , can be derived using the Eqn. 2.13. The latter describes the magnetization

induced by an external magnetic field H in a system of noninteracting ions. According

to the mean field hypothesis, the magnetization MA and MB are given directly by Eqn.

2.13, when HA and HB are replaced respectively for H. Thus, one can express the total

sublattice magnetization under the molecular field HA or HB as

MA = MsBJ

(−gJμ0μBJ(λAB − λAA)MB

kBT

)

MB = MsBJ

(−gJμ0μBJ(λAB − λAA)MA

kBT

)(2.41)

Ms is the saturation magnetization corresponding to a complete alignment of the ions,


and J is the total quantum number of the ion4. The two sublattices are exactly equivalent

in the absence of an external applied field, therefore MA will be equal in magnitude to

MB and with λAB (favoring antiparallel alignment) much greater than λAA. Consequently

MA = MB = M and the total sublattice magnetization can be written as

M = MsBJ

(gJμ0μBJ(λAB − λAA)M

kBT

), H = 0 (2.42)

The expression in Eqn. 2.42 is similar to the corresponding equation derived for

ferromagnetism (Eqn. 2.28), but in this case (λAB − λAA) is the molecular field constant

which replace to λ in the case of expression 2.28. At absolute zero MA and MB are equal

to Ms. The two sublattices acquire spontaneous magnetization (H = 0) in opposite

directions with increasing temperature and vanishing for temperatures T greater than

the Néel temperature TN [14]. TN is given by

TN =gJμB(J + 1)(λAB − λAA)Ms

3kB

=1

2C(λAB − λAA) (2.43)

Thus the Néel temperature is defined as the temperature at which the spontaneous

magnetization of one of the sublattices vanishes. For T > TN the material becomes

regularly paramagnetic [5, 8, 11].

The existence of antiferromagnetism is observed experimentally using neutron diffrac-

tion, nuclear magnetic resonance, Mössbauer effect, specific heat and magnetic suscepti-

bility. In this section the magnetic susceptibility will be described.

For temperatures greater than TN and in a sufficiently small applied field, one can

derive the expression for the susceptibility using the Eqn. 2.13. MA and MB are induced

only in the presence of an external applied field Ha. One can use the limiting behavior of

the Brillouin function for small values of its argument. One considers that above TN , MA

and MB are both parallel to Ha and therefore to each other. This assumption is valid if

λABMA and λABMB are much smaller than Ha. The magnetic susceptibility is given by

χ =C

T − Θ(2.44)

4Often in the literature, the orbital momentum is neglected in the description of antiferromagnetismbecause in most AF the crystal fields almost completely quench the orbital moments.


where Θ is the Curie-Weiss temperature. Note that in contrast to the case of ferro-

magnetism, Θ is not equal to the critical temperature. In this case, Θ is negative. If

Θ = 0, the material is paramagnetic.

Taking into account magnetocrystalline anisotropy, below TN one finds two suscepti-

bilities depending on whether the magnetic field is applied along the easy axis (longitudi-

nal susceptibility) or perpendicular to it (transverse susceptibility). For a magnetic field

applied parallel to the anisotropy easy axis one can write

MA =M+ δMA (2.45)

MB = −M+ δMB (2.46)

The parallel susceptibility is

χ|| =δMA + δMB

H(2.47)

χ|| is maximal at the transition temperature TN and decreases as the temperature

decreases (Fig. 2.5 ). For T → 0, χ|| → 0, because sublatticesMA andMB are completely

long-range ordered and cancel exactly [11]. Thus the field does not exert any torque on

the moments, resulting in a zero susceptibility. When the field is applied perpendicular

to the magnetization direction of one of the spin axis, both sublattice magnetizations tilt

in the direction of the magnetic field (Figure 2.4), therefore χ⊥ �= 0. The perpendicular

susceptibility is

χ⊥ =C

2TN

(2.48)

which shows that χ⊥ is constant independent of temperature, as illustrated in Fig.

2.5. At the Néel temperature, the three susceptibilities, χ, χ|| and χ⊥ have the same value.

Figure 2.5 shows the magnetic susceptibility of an AF system. The characteristic feature

is the derivative of the temperature dependence of susceptibility. Thus, any average or

combination of the susceptibilities will show a discontinuity which corresponds to the

Néel temperature. Above TN the Curie-Weiss law is followed.


Fig. 2.4: Spin rotation in an antiferromagnetic material for the case when the field is applied perpen-dicular to the easy axis [15].

Fig. 2.5: The temperature dependence of the susceptibility of antiferromagnets.

The susceptibility for a polycrystalline sample is obtained by averaging the suscepti-

bility over the angle θ between the spins axis and the magnetic field [7]. For example for

a cubic material χ is

χp = χ||⟨cos2 θ

⟩+ χ⊥

⟨sin2 θ

⟩=

1

3(χ|| + 2χ⊥) (2.49)

Considering the case of uniaxial anisotropy, the energy per unit volume is

Ea

V= K sin θ (2.50)

where K is the anisotropy constant and θ the angle between the sublattice magneti-

zation and the easy axis.


Fig. 2.6: Spin-flop transition taken from Ref. [6].

A strong magnetic field applied in AF will overcome any internal molecular field

saturating the entire system [6–8,16]. If the magnetic field is applied parallel to the easy

axis there are two cases. (i) Systems exhibiting a ’metamagnetic’ transition. At a critical

field the AF switches into a saturated state. The strong applied parallel field provokes

that one sublattice completely reverses. This is called spin-flip transition. (ii) The system

shows a spin-flop phase. In this case, there is a critical field in which the system ”flops” in

a different configuration as depicted in Figure 2.6. MA andMB lie at an angle θ and φ to

the magnetic field, respectively, with θ = −π/2 and φ = π/2 at the spin-flop transition.

The critical value of HSF , at which the spontaneous magnetization ”flop” from parallel

to transverse direction is

HSF =

(2K

χ|| − χ⊥

)1/2

(2.51)

Examples of materials with AF order are transition metal oxides, e. g. MnO, FeO,

CoO, Co3O4 and NiO. Table 2.2 shows the Néel and Curie-Weiss temperature of few AF

materials.

2.1.3 Diluted antiferromagnets in a uniform field

A diluted antiferromagnet in a uniform field (DAFF) is a physical realization of the

random-field Ising model (RFIM) [18–20]. In a DAFF system magnetic ions are randomly

substituted by nonmagnetic ones. The most prominent example of DAFF systems is

FexZn1−xF2, under not too large fields [18, 21, 22]. Other examples are MnxZn1−xF2 and


Tab. 2.2: Examples of antiferromagnetic materials.Material TN (K) Θ (K)MnF2 67 -80 [6]MnO 122 -610 [6, 15]CoO 293 -280 [15]Co3O4 40 -53 [17]FeO 198 -570 [15]Cr2O3 307 -485 [6]FeF2 79 -117 [15]

CoxZn1−xF2 [18].

The phase diagram of a three dimensional DAFF is shown in Figure 2.7. A DAFF

system exhibits a long-range order (LRO) if it is cooled from above TN in zero magnetic

field (ZFC). At Tc(H = 0) which is dilution-dependent, the system undergoes a phase

transition from the disordered paramagnetic phase to the long-range-ordered antiferro-

magnetic phase. However, if the DAFF system is cooled in the presence of a magnetic

field, a metastable domain state without long range order is obtained below a certain tem-

perature Ti(H). This is due to the extremely slow dynamics involved, which avoid that

the system reach LRO. The system approaches to LRO state with a domain size growing

logarithmically in time [18]. The metastable domain survives even after switching off the

field leading to a remanent magnetization which decays extremely slowly.

Fig. 2.7: Schematic phase diagram of a three-dimensional DAFF [21].

The domain formation was originally investigated by Imry and Ma for the RFIM.

By using the argument of Imry and Ma for a DAFF system one finds that the driving

force for the domain formation is a statistical imbalance of the number of impurities of


the two antiferromagnetic sublattices within any finite region of the DAFF. Figure 2.8

shows a schematic spin configuration illustrating the Imry-Ma argument [21]. The black

dots represent the nonmagnetic ions or vacancies. The solid line surrounds a domain in

which the staggered magnetization is reversed with respect to the background staggered

magnetization outside this domain.

Fig. 2.8: Schematic spin configuration illustrating the Imry-Ma argument [21].

The characteristic size of the domain depends on the random field (RF) present when

the sample is cooled through TN [23]. The reduced mean square value of the random field

for the site-diluted AF is proportional to the uniform field H according to

H2RF =

x(x − y)[TMFN (1)/T ]2(gμBSH/kBT )2

[1 + ΘMF (x)/T ]2(2.52)

where x is the concentration, TMF is the pure system mean field transition tempera-

ture and ΘMF is the Curie-Weiss susceptibility parameter.

DAFF systems show irreversible behavior for T < Ti(H). During field cooling from the

paramagnetic state the DAFF develops a domain state (DS) with higher magnetization

as compared to the long-range-ordered. Note that Tc(H) and Ti(H) are field dependent

and that Tc(H) < Ti(H). For small magnetic fields, both temperatures approach the

Néel temperature.

The Hamiltonian of the DAFF can be expressed as


H = −∑ij

JijεiεjSiSj − μμ0H∑

i

εiSi (2.53)

where Jij < 0 is the antiferromagnetic nearest-neighbor exchange constant and H is

the magnetic field. Si = ±1 are normalized Ising spin variables representing spins with

an atomic moment μ. A fraction p of sites is left without a magnetic moment (εi = 0)

while the other sites carry a moment ( εi = 1) [21].

A 2d DAFF does not show a phase transition and hence no critical behavior in a

field [24]. This is in contrast to the 3d case, where a sharp phase transition at Tc(H)

is present as explained above. However, in 2d DAFF systems it is possible to observe

a peak that becomes rounder and decreases in amplitude with increasing field [25]. It

marks the (non-critical) transition from the paramagnetic state to a metastable domain-

state with short-range AF order [26]. The domain-state is characterized by an irreversible

(non-ergodic) behavior. An example of 2d DAFF is Rb2Co0.85Mg0.15F4 [27, 28].

2.1.4 Ferrimagnetism

A ferrimagnetic (FiM) material possesses a spontaneous magnetization without applied

field, similar to a ferromagnet. In order to understand ferrimagnetism, let us consider

two sublattices denoted by A and B as in the case of antiferromagnetism. When the

sublattices magnetizations, MA and MB are not equal, there will be a non-zero net

magnetic moment [12, 15]. Therefore, it is expected that the magnetizations MA amd

MB do not cancel each other out. This is the case when the atoms occupying the A

and B sites are from different elements or when the ions are not the same. Examples

are ferrites in which Fe3+ ions are found in one sublattice whereas divalent metal ions

M such as Mn2+, Co2+, Ni2+, Zn2+ or Fe2+ are in the other sublattice (Fig. 2.9) [15].

The most typical ferrimagnets are the spinel ferrites (Figure 2.10). The white circles in

the Figure 2.10 represent the oxygen ions which are forming a close-packed face centered

cubic lattice. The pink and purple circles represent the metal ions. The spinel structure

contains two types of lattice sites, i. e. tetrahedral (A or 8a) and octahedral (B or 16d)

sites. In the former, the metal ions are surrounded by four oxygen atoms whereas in the

latter the metal ions are surrounded by six oxygen atoms.


Fig. 2.9: Spin arrangement of inverse spinel ferrite. Filled circles represent the divalent metal ion M2+.Open circles represent the Fe3+ [15].

Fig. 2.10: Spinel structure. Ions are not to scale.

In normal spinels the M2+ occupies the A sites whereas the Fe3+ occupies the B sites

such as in Zn ferrite. In inverse spinels Fe3+ occupies all the A sites and half of the B

sites and the other half of the B sites are occupied by the M2+, i. e. Fe3O4 which contains

an equal mixture of Fe2+ and Fe3+ in the octahedral sites [6].

In a ferrimagnet, the molecular field acting on sublattice A and B are formally the

same as those for AF, that is

HA = −λAAMA − λABMB,

HB = −λBAMA − λBBMB. (2.54)

At equilibrium, λAB = λBA, however, λAA �= λBB due to the sublattices are crystallo-


graphically inequivalent. The magnitudes of MA and MB can be determined as a function

of the temperature as proceeding in a similar way that in the case of antiferromagnetism.

In order to obtain the sublattice magnetization, one uses the Eqn. 2.13. In this case the

field H can be replaced by the molecular field. Thus,

MA = MsABJA

(gJA

μBμ0JAHA

KBT

),

MB = MsBBJB

(gJB

μBμ0JBHB

KBT

). (2.55)

MsB and MsB are the magnetizations of the A and B sublattices if all the moments

were aligned. The magnetizations in Eqns. 2.55 are obtained by assuming that the

magnetization of the A and B sublattices are aligned antiparallel5. This is valid when

λAB is large compared to λAA and λAB. Eqns. 2.55 can be solved graphically [29]. The

spontaneous magnetization of a ferrite Ms is the resultant of MA and MB, that is

Ms = |MA − MB| (2.56)

The form of the spontaneous magnetization as a function of temperature, can vary

widely. As one sees in Eqn. 2.56, Ms is the difference of two varying terms [5, 11].

The molecular field theory leads to an expression for the PM susceptibility above the

FiM Curie temperature, TFiM6. The expression can be obtained by taking the limiting

behavior of the Brillouin function at very small arguments7. Thus,

MA =CA

THA,

MB =CB

THB. (2.57)

5Even for a two sublattices system, there are several schemes that can lead to FiM. For example atriangular configuration. Various possible FiM arrangements for two sublattices can be found in Ref. [5].

6In literature the critical temperature above which the spontaneous magnetization vanishes is calledCurie or Néel temperature. Here, it is called ferrimagnetic Curie temperature, TFiC , in order to reducethe danger of ambiguity, due to the fact that some materials could exhibit both FM and FiM phases orFM and AFM phases.

7This is possible because the magnetization of each sublattice and therefore their respective molecularfields are small above the TFiC .

2.2 Small particles 23

Tab. 2.3: Examples of ferrimagnetic materials taken from Ref. [6].Material Tc (K) magnetic moment

(μB/formula unit)Fe3O4 858 4.1

CoFe2O4 793 3.7NiFe2O4 858 2.3CuFe2O4 728 1.3Y3Fe5O12 560 5.0

where

CA =NAg2

JAμ2

BJA(JA + 1)

3kB

,

CB =NBg2

JBμ2

BJB(JB + 1)

3kB

. (2.58)

The susceptibily is then

χ =MA + MB

Ha

(2.59)

and the ferrimagnetic Curie temperature, T = TFiC is [5],

TFiC = −1

2(CAλAA + CBλBB) +

1

2[(CAλAA − CBλBB)2 + 4CACBλ2

AB]1/2 (2.60)

Below TFiC there is a spontaneous magnetization in zero applied field which is similar

to a ferromagnet. Above TFiC the magnetization is zero in zero applied field. Further

examples of FiM are garnets and certain rare earth-transition metal alloys. Table 2.3

shows the properties of some common ferrimagnets.

2.2 Small particles

The formation of magnetic domains is dominated by the minimization of magnetostatic

energy. By reducing the size of the magnetic material one finds that for a critical diameter


it is energetically favorable to form only one magnetic domain (single domain state) and

to avoid domain walls. The latter depends on the spontaneous magnetization, anisotropy

energy and exchange interactions between individual spins. Typical values for the critical

radius of magnetic nanoparticles are between 10-800 nm (Table 2.4) [30]. It is given

by [16]

Rc =36

√AK1

μ0M2s

(2.61)

where Ms is the saturation magnetization, A is the exchange stiffness constant, and

K1 is the crystalline anisotropy constant [16].

Tab. 2.4: Critical single-domain radius for different magnetic materials [16].Compound Rc (nm)

Fe 6Co 34Ni 16

BaFe12O19 290SmCo5 764

Nd2Fe14B 107

The reduction in size of a magnetic material changes its bulk magnetic properties

which has attracted much interest among magnetism researchers for decades. Magnetic

nanoparticles and nanowires exhibit huge potential in technological applications either in

purely magnetic areas as recording technology [31], but also in other disciplines such as

in biology and medicine [32]. In fundamental research they usually serve as ideal model

systems, mentioning e.g. the Stoner-Wohlfarth and the Néel-Brown model [30] or to

study the finite size effect [33]. In this section the fundamental aspects of fine magnetic

particles will be introduced.

2.2.1 Stoner-Wohlfarth model

The Stoner-Wohlfahrt model (SW) or coherent rotation model proposes a description of

magnetization reversal of noninteracting single-domain particles with shape anisotropy

[12]. The model assumes constant magnetization throughout the magnet [16, 34]. The


consequences of this assumption is that the exchange energy is constant during magne-

tization reversal and the energy of the particle is equal to the anisotropy and Zeeman

energy [16].

Fig. 2.11: Coordinate system for magnetization reversal process in a single-domain particles [35].

The ideal SW particles are single domain prolate particles sufficiently separated from

each other so that the interactions between them can be neglected. The crystalline

anisotropy axis is assumed to coincide with the particle long axis. If an external mag-

netic field H is applied at an angle θ of the easy axis of the anisotropy of the particle,

the magnetization rotates homogeneously and behaves like a rigid macroscopic magnetic

moment. The total energy of the system is

E = KV sin2 φ − μ0HMsV cos(θ − φ) (2.62)

where the first term corresponds to the effective anisotropy and the second to the

Zeeman contribution. K is the effective anisotropy constant, V is the particle volume

and Ms is the saturation magnetization. φ is the angle between the anisotropy easy axis

and the magnetization unit vector (Figure 2.11).

The magnetization will choose to lie at an angle φ which minimizes the energy given

in Eqn. 2.64 [16]. Thus,

∂E

∂φ= 2K sin φ cos φ − μ0HMsV sin(θ − φ) = 0. (2.63)


The equilibrium energy states are stable when ∂2E∂2φ

is positive,

∂2E

∂2φ= 2K(cos2 φ − sin2 φ) − μ0HMsV cos(θ − φ) > 0 (2.64)

If the magnetic field H is applied at an angle θ = 0 of the easy axis of the anisotropy

of the particle, a perfectly square hysteresis loop is obtained. In this case, the model

predicts that the coercivity is equal to the anisotropy field 2K/μ0Ms [16].

If the magnetic field H is applied perpendicular to the the easy axis of the anisotropy

of the particle (θ = 90◦), no anisotropy is obtained. The loop is a straight line with no

hysteresis and zero coercivity and slope dM/dH = 2K/μ0M2s [16].

By solving numerically the Eqn. 2.64 one obtains the variation of the coercivity with

different angles. Figure 2.12 shows the magnetization in field direction for various angles

of φ. The nucleation field HN decreases with the angle φ and reaches its minimum for

φ = 45◦ and increases again. For angles φ > 45◦ the coercivity Hc is smaller than the

nucleation field. In Figure 2.12 one can see that for φ = 60◦ the magnetization is zero for

a field value smaller than the nucleation field. Note that the alignment increases both

the value of Hc and the remanent magnetization Mr.

Fig. 2.12: Angular dependence of the magnetization hysteresis in the Stoner-Wohlfarth model [16].


2.2.2 Superparamagnetism

In the previous section the concept of coherent rotation was introduced. The SW model

explains the hysteretic rotation of the magnetization over the magnetic-anisotropy energy

barrier under the influence of an applied field. Let us now consider a spherical single

domain particle with uniaxial anisotropy and the applied field lying on the easy axis. In

a first approximation the anisotropy energy is proportional to its volume V . Thus, the

total magnetic anisotropy is given by

E(φ) = KV sin2 φ (2.65)

where φ is the angle between the easy axis and the magnetization vector. In zero

applied field (Eqn. 2.65) there are two minima for φ = 0 and φ = π separated by the

energy barrier EB = KV . The latter is the maximun energy value for φ = π/2. Figure

2.13 (a) shows φ dependence of the total energy.

Fig. 2.13: φ dependence of the total energy (a) for zero applied field and (b) when a field is appliedalong the easy axis.

For a finite temperature it is possible that the moments switch over the energy barrier

EB by means of thermal fluctuations, i.e. the magnetic moment of the particle can

thermally fluctuate like a single spin in a paramagnetic material. However, in contrast to

PM systems the magnetic moments are much larger than a single spin. This phenomenon

is called superparamagnetism (SPM) [36].

The magnetic behavior of fine particles depends on the measuring time (τm) of the

specific experimental technique with respect to the relaxation time (τ) associated with the


overcoming of an energy barrier [30]. This relaxation process was proposed and studied

by Néel in 1949 [37] and further developed by Brown in 1963 [38]. The characteristic

time of thermal fluctuation of the magnetization of a particle with uniaxial anisotropy is

τ = τ0exp

(EB

kBT

)(2.66)

where τ0 ≈ 10−9 s (elementary spin flip time) [6,35]. Figure 2.14 shows the relaxation

time τ as a function of the temperature T .

Fig. 2.14: The dependence of the relaxation time τ as a function of T [6].

If τm >> τ , the relaxation appears fast during the time of the experiment. The

magnetization flips back and forth and in zero applied field the measured value will be

zero. If τm << τ , no change of the magnetization can be observed during the time of

the measurement. The relaxation appears so slow that the magnetic moment appears

blocked in one of its two minima [6,39]. The temperature that separates the two states is

called blocking temperature (TB) and it is defined as the temperature for which τm = τ .

Therefore (TB) is not unique and neither indicates a phase transition as in the case of

TC or TN . Note that the blocking temperature TB depends on the time scale of the

experimental technique. Furthermore, TB decreases as the particle size decreases and for

a given size it decreases as the measuring time increases. Table 2.5 shows the measuring

time for some experimental techniques commonly used to study SPM systems.

If a magnetic field is applied along the easy axis the energy of the particle is


Tab. 2.5: The experimental measuring time for some experimental techniques taken from Ref. [6, 30].Experimental technique τm (s)

dc susceptibility ≈ 10-100ac susceptibility 10−5-104

Mössbauer spectroscopy 10−7 -10−9

Ferromagnetic resonance 10−9

Neutron diffraction 10−8-10−12

E(θ) = KV sin2 φ + HMs cos φ (2.67)

where Ms is the spontaneous magnetization of the particle. Figure 2.13 (b) shows

Eqn. 2.68 vs. φ. In this case there are also two minima at φ = 0 and φ = π, however

they are not equivalent as in the case of zero applied field. When the field is applied in

opposite direction to the magnetization, the energy barrier that separates the unstable

minimum from the stable one can be approximated to [33]

EB(H) = E0B

(1 − H

H0sw

)2

(2.68)

where H0sw is the minimum value of the field at zero temperature. M irreversably

rotates at zero temperature when H = H0sw = Ha = 2K/Ms, where Ha is the anisotropy

field.

Employing field cooled (FC) and zero field cooled (ZFC) magnetization experiments

at low fields the SPM properties can be evidenced [30,35]. The measuring procedure is ex-

plained in chapter 3. Figure 2.15 taken from Ref. [35,40] shows a schematic representation

of typical ZFC and FC curves for a superparamagnetic system. At higher temperatures

T > TB the superspin-flips back and forth and in zero applied field the measured value

of the magnetization is zero (1). After cooling the system in zero field the superspins

are blocked and the overall magnetization is still zero (2). If a magnetic field is applied

at this stage, there is a slight rotation of the spins and a small mangetization (M > 0)

is observed (3). By increasing the temperature, the superspins become more and more

unblocked and the magnetization increases with temperature (4). At τ = τm the applied

field still maintains the net alignment and a peak at TB in the ZFC curve is observed (5).


For T > TB the thermal fluctuations destroy the alignment and the magnetization de-

creases with increasing T (6). In the case of FC the superspins are frozen in net aligment

in H > 0. The magnetization increases as the temperature decreases (7).

Fig. 2.15: Schematic illustration of ZFC and FC magnetization curves for SPM systems. Red arrowsmark ’blocked’ moments, green arrows mark ’free’ moments [35,40].

The above discussion only holds when the particles are separated far enough that no

interparticle interactions exist between the particles, i. e. the SPM regime. As pointed

out before, the time dependence of the total magnetization is governed by the thermal

activation over the individual energy barriers of each particle. If one considers magnetic

interactions between particles the magnetic behavior is modified and even collective states

can occur [41]. The main types of interactions in magnetic small particles are: a) dipole-

dipole interactions, b) exchange interactions (direct / indirect / superexchange) and c)

RKKY (Ruderman-Kittel-Kasuya-Yosida) interactions [33,35, 42].

2.2.3 Nanoscale antiferromagnetism

In the previous section it has been explained that nanosized ferromagnetic structures enter

so-called superparamagnetism, i.e. a thermally activated single-domain state. However,

antiferromagnetic nanosystems are governed by core-shell behavior. In this case the


surface plays a particularly important role for the magnetic behavior. As the size of

a magnetic system decreases the significance of the surface spins increases. Since an

antiferromagnet usually has two mutually compensating sublattices, the surface always

leads to a breaking of the sublattice pairing and thus leading to ’uncompensated’ surface

spins. This effect was already discussed by Luis Néel for the explanation of a net magnetic

moment in AF nanoparticles [43]. Néel proposed that μ depends on the incomplete

magnetic compensation between the atoms in the two sublattices, A and B. He considered

three possible cases, i. e. (i) random distribution, (ii) randomness only in the surface, or

(iii) the top and the bottom layer belongs to the same sublattice (Figure 2.16).

Fig. 2.16: Possible cases of ’uncompensated’ surface spins according to Néel [44].

After this pioneering work of Néel in the 1940s, several experimental studies followed

suggesting various scenarios for the magnetic properties found in AF nanosystems, e.g.

spin-glass or cluster-glass-like behavior of the surface spins [45–48], thermal excitation of

spin-precession modes [49], finite-size induced multi-sublattice ordering [50], core-shell in-

teractions [46,47,51], or weak ferromagnetism [52,53]. However, the precise identification

of the nature of the surface contribution has remained unclear. Terms like ’disordered

surface state’, ’loose surface spins’, ’uncoupled spins’, ’spin-glass-like behavior’, etc. ex-

press the uncertainty in the description of the shell contribution. One of the core subjects

of this thesis has been to achieve a better understanding of the shell contribution. This


is discussed in Chapter 7 in detail.

Chapter 3

Fabrication of magnetic nanostructures

Exciting novel phenomena are introduced once the dimensionality of the magnetic struc-

tures are on length scales between 1 nm and 100 nm. Examples are the giant magnetore-

sistance (GMR) effect in magnetic-nonmagnetic multilayers [2,3,54], oscillatory exchange

coupling between magnetic thin films [55] and enhancement of the energy product in two-

phase nanostructured systems composed of an aligned hard phase and a soft phase [56].

Thus, magnetic nanostructures are a fascinating topic with increasing interest on both

fundamental and applied level in physics, chemistry, material science and engineering.

Fig. 3.1: Examples of magnetic nanostructures. (a) Iron oxide nanoparticles prepared by thermaldecomposition of metal-oleate precursors [57]. (b) Magnetic nanowire prepared by focused ion beammilling [58]. (c) Fe islands placed between the nodes of kagome lattice produced by e-beam lithography[59]. (d) Cubic ordered mesoporous Co3O4 prepared by nanocasting method.

33

34 Fabrication of magnetic nanostructures

Fig. 3.2: Examples of self-assembly. (A) Crystal structure of a ribosome. (B) Self-assembled pep-tideamphiphile nanofibers. (C) An array of millimetersized polymeric plates assembled at a water/perflu-orodecalin interface by capillary interactions. (D) Thin film of a nematic liquid crystal on an isotropic sub-strate. (E) Micrometersized metallic polyhedra folded from planar substrates. (F) A three-dimensionalaggregate of micrometer plates assembled by capillary forces. [60]

Magnetic nanostructures can be fabricated in a variety of shapes, such as nanoparti-

cles, nanowires, dots, nanotubes, thin films and nanorings (Figure 3.1). There are two

main efficient and versatile approaches to create nanostructures, i. e. ’top-down’ and

’bottom-up’. The former uses fabrication methods based on focused ion beam milling

(FIB), electron beam (ion beam) induced deposition (EBID, IBID), scanning probe nanos-

tructuring (SPN), electron beam lithography (EBL), UV lithography (UVL), interference

lithography (IL) and nanoimprint lithography (NIL). Generally these methods impose a

structure on the substrate. In contrast, bottom-up approaches guide the assembly of

atomic and molecular components into organized structures by processes inherent in the

3.1 Nanocasting 35

manipulated system [61]. Examples of bottom-up are self-assembled structures such as

atomic, ionic and molecular crystals, liquid crystals and lipid bilayers. Figure 3.2 shows

some examples of self-assembly [60]. The structure is usually determined by van-der-

Waals, hydrogen bonding, and electromagnetic dipolar interactions.

Fig. 3.3: Examples of the combination of top-down and bottom-up processes. SEM images of 2D arraysof monodispersed polystyrene beads (A, C and D) and monodispersed silica colloids (B) assembled ontemplated Si(100) substrates. [62]

Furthermore, by combining ’top-down’ and ’bottom-up’ techniques, it is possible to

overcome the current limitations that each approach presents (Figure 3.3). E.g. e-beam

lithography can not create structures smaller than 10 nm whereas in self-assembly systems

it is difficult to obtain a precise control over the geometrical arrangement of the materials.

This chapter is focused on two fabrication methods of magnetic nanostructures, i.e.

nanocasting and e-beam lithography.

3.1 Nanocasting

Nanocasting is a templating process for preparation of novel mesostructured materi-

als such as metal, metal oxide, metal sulfide and polymer replica mesostructures. The

nanocasting process involves three main steps, i. e. formation of the template, the cast-


ing step and the removal of the template [63] (Figure 3.4). The main advantages of the

nanocasting method is the possibility to obtain nanowire arrays with a diameter smaller

than 10 nm, with high surface area and narrow size distribution.

Fig. 3.4: Schematic of nanocasting method taken from Ref. [63].

Since the discovery of mesoporous materials in the early nineties tremendous work

has been carried out to understand the synthesis and the mechanism of the formation of

these materials [64–68]. Nanocasting of carbon from ordered mesoporous silica was first

obtained by Ryoo’s group in 1999 [69] and later on this approach has been successfully

employed giving high quality oxide materials [70–79].

The first step in the nanocasting method consists in the formation of the template.

Organic surfactant molecules act as structure directing motifs by self-assembling to central

mesostructured materials around which networks form. Therefore the shape and size of

the organic aggregates correlate directly with the final geometry and pore size in the

mesoporous material. The synthesis of a mesoporous template consists of 5 elemental

steps: 1) Dissolving the structure directing agents (SDA’s) in water under acidic or

basic conditions. 2) Addition of an inorganic precursor. 3) Hydrolysis and condensation

of the inorganic precursors around the templates catalyzed by an acid or a base. 4)

Hydrothermal treatment. 5) Removal of the template.

In the first step SDA’s are dissolved in water under acidic or basic conditions. SDA’s

are organic molecules with amphiphilic behavior due to their hydrophilic head and hy-

drophobic tail. When these compounds are dissolved in a solvent, they self-assemble in a

way that hydrophilic and hydrophobic interactions are energetically optimized. Thereby

the surfactants may form micellar or lamellar structures in solution, for instance [81]. An

important factor that influences the formation and shape of micelles and their aggrega-

3.1 Nanocasting 37

Fig. 3.5: Different aggregate morphologies predicted by the packing parameter g taken from Ref. [80].

tion into liquid crystals is the surfactant concentration. At very low concentrations single

surfactant molecules are separated from each other in the solution. At slightly higher

concentrations the individual molecules assemble to small spherical micellar aggregates.

This concentration is called critical micelle concentration, CMC. As the concentration

increases the micelles form firstly micellar rods (CMC2) which further assemble to liquid

crystalline phases, e.g. to hexagonal close-packed arrays, cubic or lamellar phases [81–83].

In order to predict and to explain the geometry of mesostructured materials based on

the used surfactants, Israelachvili introduced the so-called packing parameter g [84–86].

The packing parameter is defined by g = V/(a0l), where V is the total volume of the hy-

drophobic chains plus any co-surfactant between the chains, a0 is the effective hydrophilic

headgroup area at the aqueous-micelle surface and l is the length of the hydrophobic tail.

In other words, the geometry of the mesostructure depends on the number of carbons

in the hydrophobic chain, the degree of chain saturation and the size and charge of the

polar head group. Besides the type of surfactant, several other factors like the pH, the

temperature, the ionic strength of the solution and co-surfactant effects influence the

forming structure and can be thus included in V , a0 and l [87]. By increasing the g value

one can observe a transition from cubic (Pm-3n, etc.) and 3D hexagonal (P63/mmc)

mesophases (g < 1/3), over 2D hexagonal (p6mm) (1/3 < g < 1/2) and cubic (Ia-3d)


Tab. 3.1: Relation between g of cationic surfactant and mesostructure taken form Ref. [65]

(1/2 < g < 2/3) structures to lamellar phases (g ≈ 1) whereas for g > 1 reversed micelles

are expected [86, 88, 89] (Table 3.1). Figure 3.5 shows different aggregate morphologies

predicted by the packing parameter g.

The structure directing agents can be classified in cationic, anionic and non-ionic

compounds. Examples of cationic surfactants are quaternary ammonium cationic com-

pounds CnH2n+1N(CH3)3Br (n = 8-22) [90–92], such as cetyltrimethylammonium bro-

mide (C16H33N(CH3), CTAB). Their advantages are the commercial availability, the

good solubility and their robustness towards acidic and basic reaction conditions. A

big disadvantage is the toxicity of cationic surfactants. Some examples of anionic surfac-

tants are carboxylates, sulfates, sulfonates or phosphates [93]. An example of non-ionic

surfactants is the family of the so-called block copolymers. One member of this fam-

ily are Pluronic triblock copolymers which exhibit alternating blocks of poly(ethylene

oxide)-b-poly(propylene oxide)-b-poly(ethylene oxide) (PEO-PPO-PEO) units [94–96].

The non-ionic surfactants offer numerous advantages, because they are non-toxic, com-

3.1 Nanocasting 39

mercially available and economically viable. Furthermore they are stable in basic and

acidic reaction media.

In the second step of the synthesis of a mesoporous material an inorganic precursor

is added, which yield to the corresponding composite material by condensation on the

surfactant surface. In the past 15 years much effort has been made in understanding the

manner of interaction between the inorganic precursors and the organic surfactants. Two

major mechanisms are discussed in literature, i.e. a true liquid crystal templating [95]

and a cooperative surfactant-inorganic self assembly mechanism [90,97] (Figure 3.6).

Fig. 3.6: Two mechanism of template formation (A) cooperative self-assembly and (B) ”true” liquid-crystal templating taken from Ref. [65].

In the true liquid crystal templating mechanism, the structure is determined by self-

assembly of the surfactant molecules into liquid crystals. The first step in this pathway

includes the formation of a liquid crystalline phase, e.g. consisting of hexagonal arrange-

ment of micellar rods which are formed by surfactant micelles. Next, the inorganic pre-

cursor is added and an incorporation of an inorganic array (silica, silica-alumina) around

the rodlike structures occurs forming rigid frameworks [95].

In the cooperative surfactant-inorganic self assembly mechanism the inorganic pre-

cursor is dissolved simultaneously together with the surfactant. Next, the interactions

between the inorganic precursor and the surfactant lead to an ordering of the surfactants,

e.g. into a hexagonal arrangement. Note, that in contrast to the true liquid crystal mech-

anism a liquid-crystalline state prior to mixing of the precursors is not present. Hence,

the composite material forms cooperatively from the organic surfactants and the inor-


Tab. 3.2: Synthesis routes to mesoporous materials focous on silicates taken form Ref. [65]

ganic precursors. The driving force of this mechanism is provided by weak noncovalent

bonds such as hydrogen bonds, van-der-Waals forces, and electrovalent bonds between

the surfactants and inorganic species. Stucky et al. suggested a general mechanism

for the cooperative self-assembly pathway which is based on the interaction of charged

species [90,97]. Thereby one can find four different types of interactions between charged

species which finally determine the structure and properties of each system, i.e. S+I−,

S−I+, S+X−I+ and S−M+I− (S+ = surfactant cations, S− = surfactant anions, I− = in-

organic precursor anion, I+ = inorganic precursor cation, X− = anionic counterion, X+

= metal counterion) (Table 3.2).

Cationic surfactants (S+) can be used for structuring anionic inorganic precursors

(I−) (S+I− mesostructures), whereas anionic surfactants (S−) structure cationic inorganic

3.1 Nanocasting 41

species (I+) (S−I+ mesostructures). Furthermore also a combination of identically charged

species is possible, but then countercharged ions are necessary for the formation of the

mesostructure (S+X−I+, and S−M+I− mesostructures). In the case of neutral amines or

nonionic polyethylene oxide surfactants which can also act as structure directing agents,

one has to consider that the surfactant species are probably partially protonated or

charged. However, the cooperative surfactant-inorganic self-assembly mechanism has

been extended to pathways using neutral (S0) or non-ionic surfactants (N0). The main

driving force for the formation of the mesophase in these neutral templating routes is

considered to be a hydrogen-bonding interaction at the S0I0 [98] or N0I0 [99] interface.

During this step, microphase separation and condensation of the inorganic precursor

occur. For instance, in the case of silicate precursor, e.g. tetraethoxysilane (TEOS) the

condensation and the subsequent precipitation is rapid in cationic solutions whereas the

formation of mesostructures is slow if nonionic surfactants are used as templates [65].

In order to cause a complete condensation and to improve the organization, i.e. the

mesoscopic regularity of the mesostructured material, a hydrothermal treatment follows

[86,100]. The hydrothermal treatment leads to a reorganization, growth, and -sometimes-

crystallization of the mesostructures. Due to a degradation of ordering and decomposition

of the organic surfactants the temperature during the hydrothermal treatment is relatively

low (80 - 150 ◦C). Once the hydrothermal treatment is finished the product is cooled

down to room temperature where the mesostructured material is easily separated from

the mother liquor by filtering. In the case of small particles a centrifugation might be

also necessary in the workup. Further purification includes several washing steps, mostly

by water. In order to maintain the mesoscopic regularity the drying is usually carried out

at room temperature. The last step in the synthesis of a mesoporous material requires

a removal of the organic template from the inorganic-organic mesostructures. In the

case of mesoporous silicates, aluminosilicates, metal oxides, and phosphates the template

is easily removable by calcination, i.e. by heating of the inorganic-organic composite

material up to temperatures in which the organic part completely decomposes or oxidizes

under oxygen or air atmosphere [101, 102]. An alternative, in fact milder, method to

remove the template is extraction with common organic solvents, e.g. ethanol or THF.

In that case an addition of a small amount of hydrochloric acid leads to an improvement


of the extraction procedure and of the final product [103,104].

Mesoporous silica is the most suitable template for the nanocasting process. The

main advantage in usage of ordered mesoporous silica is the easy controllability of the

structure and morphology. Furthermore, it possesses large surface areas and large pore

volumes and can be prepared in diverse shapes such as spheres, fibers, rods and chiral

morphologies. The synthesis temperature is rather low, from room temperature to 130◦C.

The second step of the nanocasting method is the casting step. Here, the target

material is incorporated into the channels of the mesoporous template in the form of a

precursor (generally molecular) and later it is converted to the desired material by calci-

nation under air or inert atmosphere. The precursors are incorporated in the pore system

of mesoporous silica by sorption, phase transition or ion exchange. In order to be easily

infiltrated into the pore system, the precursor has to be either gaseous, highly soluble

or liquid. The interaction between the silica walls and the precursors are determined

by hydrogen bonding, coordination bonding, coulombic interactions and van-der-Waals

forces. Once inside the pore system, the precursor is then thermally decomposed. Note

that the conversion of the precursor to the final material should proceed with low volume

shrinkage and without a reaction with the template in order to get a high quality replica.

The byproducts usually leave the channels in the gas phase. Some examples of convenient

precursors are metal chlorides, metal nitrates and metal acetates.

The final step in the nanocasting method consist of the removal of the template using

chemical treatments, combustion or treatment with other highly reactive gases. For

example, silica templates can be easily removed by dissolution in NaOH or HF solutions.

Therefore, the obtained replica material using silica template must be stable not only

during thermal treatments but also towards chemical agents. Carbon templates offer an

alternative to nanocast materials that are attacked by NaOH or HF. The carbon template

is removable by combustion or treatment with highly reactive gases.

3.2 Electron beam lithography 43

3.2 Electron beam lithography

Electron beam lithography (EBL) is an attractive technique to create nanostructures

on substrates in a controlled manner. There are two different basic methods to create

nanostructures by EBL, i. e. EBL with positive resist and lift-off and EBL with negative

resist and etching. Each of them consist generally of 5 steps [105,106]. Figure 3.7 shows

the schematic illustration of nanofabrication using EBL.

Fig. 3.7: Schematic of an electron-beam lithography.

3.2.1 EBL with positive resist and lift-off

The first step in EBL with positive resist consists in spin-coating the resist on a cleaned

substrate. The most used substrate is polished single crystal silicon, with natural SiO2

layer. However other materials can be used as substrate, such as GaAs, MgO, Al2O3 and

MgF2. Before depositing the resist the substrate must be sonicated in acetone, washed

in isopropanol and finally dried with pure N2 stream.

The resist is generally a polymer or co-polymer sensitive to the radiation used. The

irradiation causes de-polymerization (chain-scission) in the polymer. The most used


resist is a 1-5 % solution of polymethylmethacrylat (PMMA) with certain molecular

weight (50 K-950K). The spinning speed and the resist viscosity will determine the final

resist thickness. Next, the resist is baked (5-30 min at 60-170 ◦C) [107] to evaporate the

solvent and improve the adhesion. Subsequently, the sample is exposed to the electron

beam source.

A remote control of the scanning coils is used in order to write pre-defined structures.

Thus, computer control is responsible to the design, exposure rhythm, adjustment of the

exposure field and stage positioning. Figure 3.8 shows a schematic of the SEM with

the lithography unit. In order to reproduce the desired designs, the lithography can be

performed by scanning the whole field line by line or each element is exposed individually

by the electron beam. In the former the beam blanker switches the beam on and off to

illuminate the desired structure (scanning technique). In the latter the beam is blanked

and the electron-optic is adjusted to the next element of the design fields and the beam

gets un-blanked again (vectorial technique).

Fig. 3.8: Schematic of an electron-beam exposure system [108].

The resist can be exposed using three different options, i.e. single spot, single pixel line

or by area of exposure. Single spot (point by point) address each point individually. Single


pixel line defines the start and end point of a line. The beam moves quasi-continuously

and the blanker blanks the beam only between two lines. In the area of exposure, the

designed areas are subdivided into polygons, in which the beam can write long lines. The

blanker operates between two polygons. Exposure parameters that one should consider in

the writing process are dose, acceleration voltage U , beam current Ib, stepsize (distance

between the exposure points) and working distance (distance between the final condenser

lens and the specimen). The mentioned parameters influence the resolution, the exposure

time and the quality of the result.

The exposure dose Do is the number of electrons per unit of area that receives the

resist. Do depends on the acceleration voltage, the size and the distance between exposed

areas. Figure 3.9 shows the expression of dose for area, line and dots.

Fig. 3.9: Expression of dose for area, line and dots, where τ is the exposure time per point and s thespot size [109].

The acceleration voltage U determines the kinetic energy. i.e.,

Wkin = 12mev

2e = eUacc

At lower energies, the charging effects are reduced but the resolution is lower. At

high acceleration voltage, the resolution is higher but damage in the crystalline structure

increases. The beam current determines the throughput and the resolution. Higher

current enables faster delivering of electron dose, whereas smaller currents enable to

control more precisely the quantity and the position of the delivered dose. Therefore,

higher currents are suitable for bigger structures, whereas smaller current is the best

option for smallest structures where maximum resolution is pursued.


The performance of a resist is mainly defined by the tone, sensitivity, resolution and

contrast. The tone determines the areas that will be removed in the developing process.

The sensitivity quantifies the dose that is required to reach the desired development.

The resolution defines the smallest distance between two patterns that can be resolved.

Finally, the contrast γ is a measurement for the sharpness of the transition between the

exposed and the unexposed areas of the sample after developing.

The resist can be synthesized in a variety of polymeric materials, therefore tone,

sensitivity, resolution and contrast can be adjusted for specific applications. As mentioned

above, in positive resist the electron beam irradiation will break the backbone bonds,

causing the fragmentation of the polymer. Once in the developer, the irradiated areas are

easily dissolved. Figure 3.10 shows generic reaction paths caused by EBL on PMMA [110].

Fig. 3.10: Mechanism of radiation-induced chain scission in PMMA [110].

The third step in the lithography process is the development which is a chemical mul-

tistep process. First, the sample is immersed in the developer which generally is methyl

isobutyl ketone (MIBK) when working with PMMA. MIBK mixed with isopropanol (IPA)

in a ratio of 1:3 shows low sensitivity but high contrast. Second, the sample is bathed in

stopper, i.e. IPA for 30 s and finally dried with pure N2 stream.


In the fourth step of EBL with positive resist, a single material layer or multilayer

is deposited on top of the entire structure. Deposition is performed generally by regular

thin-film deposition techniques, i.e. thermal evaporation, sputtering, etc. [111].

Finally, in the liff-off process the resist is removed by dissolving it in a solvent. For

example, acetone and ultrasonic bath is an efficient method to remove the PMMA.

3.2.2 EBL with negative resist and etching

The first step in EBL with negative resist consists of depositing a single material layer or

multilayer on a cleaned substrate. Deposition is performed generally by regular thin-film

deposition techniques, i.e. thermal evaporation, sputtering, etc. [111]. The most used

substrate is polished single crystal silicon, with natural SiO2 layer, or extra thick layer.

However other materials can be used as substrate, such as GaAs, MgO, Al2O3 and MgF2.

Before depositing the material, the substrate must be sonicated in acetone, washed in

isopropanol and finally dried with pure N2 stream.

The second step is the spin-coating of the negative resist on top of the material layer.

The resist is generally a polymer or co-polymer sensitive to the used radiation. In contrast

to positive resist, in negative resist the electron beam irradiation will cause a cross-linking

of the polymer chains, the solubility of the irradiated areas in the developer decreases.

Examples of negative resists are poly-chloromethylstyrene and SU8 . The spinning speed

and the resist viscosity will determine the final resist thickness as in the case of positive

resist. The following steps, exposure and development of the resist are similar to the case

of a positive resist, as described above.

Next, in order to remove the material that is not protected by the resist, dry or

wet etching is used. Dry etching techniques use gases which are usually dissociated and

ionized in a plasma. The most common dry etching techniques are high-pressure plasma

etching, reactive ion etching (RIE) and ion milling. The advantages are high definition

and high anisotropy. Figure 3.11 shows a schematic of possible dry etching.

High-pressure plasma etching is performed at pressures of 10−1 - 5 Torr. Highly

reactive species are created that react with the material to be etched. Products are

volatile and diffuse away, leaving the new material exposed to the reactive species.


Fig. 3.11: Schematic of possible dry etching techniques. (a) ion milling, (b) high-pressure plasmaetching and (c) RIE [107].

RIE is used for materials that chemically react with reactive ions and the reaction

products are pumped away. RIE combines physical and chemical processes and consists

of four steps. First, ion sputtering which promotes absorption of gas molecules onto the

material surface. Second, reactive etching in which reactive ions react with the material

atoms to form volatile species which evaporate from the substrate surface. Third, radical

formation where the ions can dissociate the absorbed gas molecules to produce radicals

on the substrate surface. Fourth, radical etching in which the radicals can move around

the surface and react with the material surface atoms to form volatile compounds leaving

the surface.

Ion milling is a pure physical ion sputtering process. The main characteristic is its

very low etching rates (few nanometers per minute) and poor selectivity. It differs from

RIE because ion milling separates the generation of ions from sample etching. Figure 3.12

shows a schematic of an ion beam milling system [112]. Electrons are emitted from the

cathode and accelerated by the field between the cathode and the anode. The noble gas

in the chamber, typically Ar, is ionized to Ar+ by the electrons and then extracted from

the ion chamber to the sputtering chamber in form of a broad jet and accelerated to the

sample. Argon gas is commonly used for ion milling due to the fact that Ar+ ions do not

react chemically with the materials. Ion milling with Ar+ occurs for energies between 10

eV and 5000 eV. The etch rate depends on the sputtering yield of the specific material.


Fig. 3.12: Schematic of an ion beam milling system [112].

Wet etching uses acids or solvents. Reaction products are washed away in the liquid.

The advantage is the high chemical selectivity. Examples of silicon etchants are potassium

hydroxide (KOH), ethylene diamine pyrochatechol (EDP) and tetramethyl ammonium

hydroxide (TMAOH).

Finally, the resist is removed by disolving it in a solvent, i. e. acetone, using an

ultrasonic bath.

Chapter 4

Characterization techniques of

magnetic nanostructures

The study of nanostructures requires highly sophisticated instrumentation techniques.

New breakthroughs to understand nanostructures have resulted from the development of

new imaging techniques, for example transmission electron microscopy (TEM) [113,114],

scanning electron microscopy (SEM) [114], scanning tunneling microscopy (STM) [115]

and magnetic force microscopy (MFM) [116,117]. Time-resolved X-ray magnetic circular

dichroism (tr-XMCD) [118] and ferromgnetic resonance (FMR) are powerful tools for ex-

amining the dynamics of heterogeneous magnetic materials. Low angle X-ray diffraction,

together with gas adsorption, give information about the structure of mesoporous ma-

terials [119–121]. Superconducting quantum interference device (SQUID) magnetometry

allows to determine the overall magnetic moment of a sample.

This chapter describes the experimental techniques which were used to characterize

the magnetic nanostructures discussed in Chapters 5 and 6.

4.1 Gas adsorption-desorption techniques

Gas adsorption-desorption measurements are widely used in the characterization of solid

materials. Adsorption refers to the process where the adsorptive gas is transferred and

accumulated in the interfacial layer, whereas the desorption refers to the inverse pro-

51

52 Characterization techniques of magnetic nanostructures

cess. Gas adsorption-desorption measurements give valuable information on the surface

area, pore size distribution and pore volume. The pores can be classified according to

their diameter size in macropores (>50 nm), mesopores (between 2 nm and 50 nm) and

micropores (smaller than 2 nm) [122,123].

4.1.1 Classification of the gas adsorption isotherms

”Adsorption isotherm” refers to the relation between the amount adsorbed and the equilib-

rium pressure of the gas at constant temperatures. The shape of gas adsorption isotherms

gives important qualitative information on the adsorption process(es), i. e. monolayer-

multilayer adsorption, capillary condensation or micropore filling. According to the ad-

sorption process(es) the isotherms are classified in six types (Figure 4.1). In this section,

the isotherms type I to V according to the International Union of Pure and Applied

Chemistry (IUPAC) classification will be discussed [122].

Fig. 4.1: Types of gas adsorption - desoportion isotherms [103]. Red arrows show the adsorptionbranch of the isotherm, whereas blue arrows show the desorption branch.

Type I isotherms are reversible and have a concave shape to relative pressures (the

4.1 Gas adsorption-desorption techniques 53

equilibrium vapor pressure divided by the saturation vapor pressure). The shape of the

isotherms is caused by the interactions between adsorptive and absorbent, indicating

monolayer formation or micropore filling for purely microporous materials.

Type II isotherms are reversible and present two main features. The first one at

low relative pressures is concave indicating monolayer formation. The second one in the

middle of the hysteresis is almost linear indicating the complete monolayer coverage and

the beginning of multilayer adsorption. These isotherms are characteristic for non-porous

or macroporous solids.

Type III isotherms are reversible and are characterized by the convex shape in the

whole range of relative pressures. This behavior is attributed to the strong lateral inter-

actions between adsorbed molecules in comparison to interactions between the adsorbent

surface and adsorbate.

Type IV isotherms are not reversible and have two characteristic regions. The first one

at low relative pressure is qualitatively similar to the one observed for type II isotherms

and therefore attributed to the monolayer-multilayer adsorption. The second region, at

higher pressures, shows an irreversible behavior given by the hysteresis loop, indicat-

ing the capillary condensation in the mesopores. A hysteresis loop is observed when

the capillary condensation (adsorption) and the capillary evaporation (desorption) occur

at different relative pressures. The type IV isotherms are characteristic of mesoporous

materials. However, it is possible to find isotherms for mesoporous materials without

hysteretic behavior as shown in Fig. IVc [103].

Type V isotherms are not reversible and have two characteristic regions. The first one

at low relative pressure is qualitatively similar to the one observed for type III isotherms

and therefore attributed to the weak interactions between the adsorbent surface and

adsorbate. The second region, at higher pressures, is cause by the capillary condensation

in the mesopores as described for type IV isotherms.

4.1.2 Types of adsorption-desorption hysteresis loops

Hysteresis loops in the isotherms are in most cases due to the capillary condensation in the

mesopores as discussed above. Furthermore, pore connectivity effects can also produce


irreversible behavior of the adsorption-desorption isotherms. Therefore, hysteresis loops

give important information about the pore structure. Most of the experimentally observed

hysteresis loops are due to the combination of capillary condensation and network effects.

Following the IUPAC recommendation, the hysteresis loops are classified in four types as

shown in Figure 4.2 [103,122].

Fig. 4.2: Types of adsorption-desorption hysteresis loops taken from Ref. [103].

Type H1 loops show two parallel and almost vertical branches. This kind of hysteresis

is associated to porous materials consisting of agglomerates or homogeneous spherical

particles. H1 hysteresis loops are representative for materials with uniform pore size

and facile pore connectivity. In contrast, type H4 loops show two parallel and almost

horizontal branches and are attributed to large mesopores embedded in a matrix with

pores of much smaller size. Type H2 and H3 loops are seen as intermediate loops between

type H1 and H4 loops. The H2 has a triangular shape and observed for materials with

uniform channel-like pores whereas type H3 loops are observed for materials composed

of aggregates of platelike particles [103,122].

4.1.3 Determination of surface area

The surface area in this research was obtained using the Brunauer-Emmett-Teller (BET)

method [124]. It calculates the specific surface area from the monolayer capacity. The

4.1 Gas adsorption-desorption techniques 55

latter is defined as the number of adsorbed molecules in the monolayer on the surface of a

material. The main BET calculation considers a flat surface, the same adsorption energy

for all adsorption sites, no lateral interactions between adsorbed molecules, the adsorption

energy for all molecules is equal to the liquefaction energy with exception of the first layer

and an infinite number of layers, which can form. Despite the considerations of the BET

equation differ for porous materials, it is currently the best method to determine the

specific surface area of porous materials. Thus,

As(BET ) = namLam (4.1)

where As(BET) is the total and specific surface area of the adsorbent, am is the

molecular cross-sectional area, nam is the monolayer capacity area and L is the Avogadro

constant. The BET surface area is typically extracted from the linear part of the so called

BET plot.

4.1.4 Determination of pore volume

The total pore volume can be calculated from the amount of vapor adsorbed at a relative

pressure close to the saturation vapor pressure by assuming that the density of condensed

adsorbate in the pores is equal to the density of bulk liquid adsorbate. The absorbed

amount is converted to the corresponding volume of liquid adsorbate at the temperature

of the adsorption measurement. For N2 at 77 K, the conversion factors from the amount

adsorbed to the volume of liquid adsorbate is 0.0015468 cm3 STP g−1 [103], where STP

stands for standard temperature and pressure.

4.1.5 Determination of pore size distribution

The pore size can be calculated using the Barrett-Joyner-Halenda (BJH) algorithm [125].

This method considers cylindrical pores and that the equilibrium between the gas phase

and the adsorbed phase during desorption is determined by two mechanisms, the physical

adsorption on the pore walls and the capillary condensation. The BJH algorithm takes

into account the Kelvin equation [122], which describes the relationship between the pore


radius and the relative pressure. The pore size distribution is usually expressed in the

graphical form ΔV/ΔD vs. D, where V, is the total pore volume and D is the pore

radius [122].

Nitrogen adsorption-desorption isotherms were measured with an ASAP 2010 adsorp-

tion analyzer (Micromeritics) at liquid nitrogen temperature (77 K) with prior degassing

of the calcined silica samples under vacuum at 200 ◦C and nanocasted Co3O4 at 150 ◦C

overnight. Total pore volumes were determined using the adsorbed volume at a relative

pressure of 0.97. BET surface area was estimated from the relative pressure range from

0.06 to 0.2. The pore size distribution of the mesoporous materials was analyzed using

the BJH algorithm using the desorption branch.

4.2 X-ray diffraction

By employing X-ray diffraction technique it is possible to obtain information about the

crystal structure, chemical composition, and physical properties of the studied system.

Furthermore, it is also a powerful tool to characterize mesostructured materials. The in-

formation is obtained by the use of X-ray beams of radiation. The latter can be described

by its wavelength λ, its direction of traveling and its amplitude A [126]. The direction

of the beam as well as its wavelength can be expressed using the wave vector k, which

points along the direction of the beam with a magnitude |k| = 2π/λ. In three directions,

the incident plane wave can be described as [126]

ψ = A exp(ik.x) (4.2)

where x is a position in space. The quantity k.x is the phase angle.

The scattering of radiation from two particles separated by the vector r is shown in

Figure 4.3. The initial wave vector is ki and the scattered wave vector is ks. The two

rays come in with the same phase, however in the scattering process they have different

path lengths which leads to different phases of the two scattered rays. The total phase

difference is the sum of the two separate phase differences,

4.2 X-ray diffraction 57

Fig. 4.3: Scattering of radiation from two particles separated by the vector r [126].

2πl1λ

+2πl2λ

= (ki − ks).r (4.3)

where l1 and l2 are the path length differences. The change in wave vector Q is called

scattering vector, i. e.

Q = ki − ks (4.4)

The total scattering is given by the sum of the two rays,

ψ1(x) + ψ2(x) = exp(iks.x) × (1 + exp(iQ.r)) (4.5)

and the amplitude of the scattered beam is

F (Q) = 1 + exp(iQ.r) (4.6)

For a collection of particles the amplitude of the scattered beam can be obtained using

the explanation given above. In this case the position of each particle must be defined

with respect to an origin as rj, thus

F (Q) =∑

j

exp(iQ.rj) (4.7)

If one takes into account different particles, each particle will scatter the radiation

beam differently. Therefore the factor fj known as scattering factor or form factor must


be considered, thus

F (Q) =∑

j

fj exp(iQ.rj) (4.8)

The scattering of X-rays by atoms can be seen as the scattering from the continuous

distribution of electrons around the atom [126]. The X-ray atomic scattering factor is

f(Q) =

∫ρel(r) exp(iQ.r)dr (4.9)

Note that the amplitude of the scattered signal is given by the Fourier transform of the

electron density. On mesoporous materials, XRD studies are not trivial. The standard

crystallographic procedures cannot be used for their characterization due to the lack of

ordering at the atomic level. In the case of mesoporous materials the obtained Bragg

peaks are caused by the ordering of pores of uniform size [120], i. e., the scattering power

only depends on the electron density contrast between the solid matter with a constant

electron density (on the mesoscale) and the empty pores with zero electron density [127].

The XRD patterns for mesoporous materials generally contain 3 to 5 reflections. They

are located in the low angle 2 θ range from 0.4◦ to 3◦ degrees because of the presence of

relatively large ordered pores.

Several approaches have been reported for X-ray diffraction (XRD) structural investi-

gations of the ordered mesoporous materials [127–134]. By modeling the XRD intensities

of a mesoporous material it has been shown that it is possible to obtain values of lattice

parameters, pore diameters and wall thicknesses of the studied materials. For example,

X-ray diffraction studies on SBA-15 have shown that this structure consists of hexagonally

close packed cylindrical pore channels belonging to the p6mm space group. They exhibit

four or more charactersitic reflections. The most intensive peak is the (100) reflection,

the other three less intensive peaks are the (110), (200) and (210) [94, 96]. Furthermore,

quantitative XRD analysis of the SBA-15 diffraction pattern indicates that this silica

material displays not only the mesoporosity (pore diameter >2 nm) due to the hexago-

nal arrangement of cylindrical aggregates but also microporosity (pore diameter <2 nm)

liberated by the poly(ethylene oxide) (PEO) moieties [128]. Studies by Morishige and

4.2 X-ray diffraction 59

Tateishi show that the relative reflection intensities of these ordered mesoporous materi-

als depend on the ratio between wall thickness and pore diameter, on the hexagonality

of the pore shape and on the roughness of the pore wall [120].

Using X-ray powder diffraction it is also possible to model the structure and structural

transformation of mesoporous materials [133,135] (Figure 4.4). Solovyov et al. have used

the continuous density function technique [133] and the Rietveld full-profile formalism

[136] to determine the geometric textural characteristics of mesoporous carbon, CMK-

1. The mesoporous CMK-1 was obtained using MCM-48 as template. Figure 4.4(a)

shows the XRD pattern of MCM-48, which consists of two separate enantiomeric sub-

pore systems forming a cubic bicontinuous structure (Ia3d) [137]. Figure 4.4 (b) shows

a fragment of one sub-pore system and (c) shows the mesoporous carbon, CMK-1.

Fig. 4.4: Experimental and calculated powder XRD diffraction pattern of (a) mesoporous MCM-48material, (b) a single enantiomeric carbon sub-framework and (c) the CMK-1 material [127].

The XRD patterns were recorded on a Stoe theta/theta diffractometer in Bragg-

Bretano geometry (Cu Kα radiation) at room temperature.


4.3 Microscopy techniques

In 1986 half of the Nobel Prize in physics was awarded to Ernst Ruska for ”his fundamental

work in electron optics and for the design of the first electron microscope” and it was

pointed out in the press release on the 15th of October of that year as ”one of the most

important inventions of this century” [138]. The outstanding developments in electron

microscopy techniques have significantly enhanced the understanding of nanostructures.

4.3.1 Transmission electron microscopy

In the early 20th century, Louis de Broglie proposed that the wavelength λ of a particle

of a certain momentum p is given by

λ = h/p = h/(mv) (4.10)

where h = 6.626 x 10−34 Js is the Planck constant, m and v represent the mass and

speed of the particle, respectively [139]. Using this relation one finds that the wavelength

of an electron depends on the accelerating voltage, i. e. increasing the electron energy

(and therefore the momentum) decreases the de Broglie wavelength of electrons. For

an accelerating voltage of 50 keV the wavelength is λ ≈ 0.005 nm. Such high-energy

electrons can penetrate distances of several microns into a solid. If the solid is crystalline,

the electrons are diffracted by atomic planes inside the material [140–142]. Therefore, it

is possible to form a transmission electron diffraction pattern from electrons that have

passed through a thin specimen.

Transmission electron microscopy (TEM) is a powerful imaging tool to study systems

of smaller length scales. Employing TEM one gets information about the crystal dislo-

cations, crystal quality, grain size and crystal orientation. The electron energy is in the

range of 60-150 keV or up to 400 keV in the case of high resolution transmission electron

microscope (HRTEM) [142]. Using the latter one, it is possible to observe the atomistic

structure of crystalline solids in real space. The TEM is not only a highly magnifying

camera but it is an instrument of precise physical measurements. A transmission elec-

tron microscope consists of an illumination system, specimen stage and imaging system

4.3 Microscopy techniques 61

(Figure 4.5).

Fig. 4.5: The principle set-up of a TEM.

The illumination system is composed of the electron gun and two or more condenser

lenses that focus the electrons onto the specimen. The electron gun produces an electron

beam whose kinetic energy is high enough to enable them to pass through thin areas of

the TEM specimen. The gun consists of an electron source and an electron-accelerating

chamber. The conventional way to generate electrons is to use thermionic emission or

a field emission gun [141, 142]. In the former the material is heated to a high enough

temperature. Thus, when the electrons in the cathode have enough energy to overcome

the work function φ, they will escape from the source. The current density Jc coming

from the source is expressed by the Richardson law,

Jc = AT 2exp(φ/kT ) (4.11)


where A is a constant that depends on the cathode material, T is the emission tem-

perature and k = 1.38 x 10−23 J K−1 is the Boltzmann constant [141,143]. Therefore, the

cathode material should have a high melting point as in the case of tungsten or low work

function as LaB6. Field emission guns consist of a pointed cathode tip and at least two

anodes. A voltage between the field emission tip and the first anode controls the field-

emission current. The latter depends on the work function and on the field strength.

A second voltage between tip and the second anode determines the final energy of the

electrons.

The most important parameter of the electron gun is its brightness defined as the

beam current per unit area per solid angle Ω [141], and is conserved when the beam

passes an (ideal) electron lens.

B =Ie

AsΩ(4.12)

where Ie is the available emission current, As is the emitting area.

The TEM incorporates a two lens-system in order to focus the electron beam on the

specimen, change the illumination aperture and produce a small electron probe (2-100

nm diameter) [141].

The specimen stage allows specimens to either be held stationary or else intentionally

moved. Its mechanical stability is an important factor for spatial resolution of the TEM

image. TEM specimens are always fabricated circular with a diameter of 3 mm [142].

The specimen must be thin enough and the energy of the incident electrons must be high

enough to allow that most of the incident electrons are transmitted to form the magnified

image.

Once the electrons are focused at the specimen with the condenser lenses, the electron

intensity distribution behind the specimen is imaged with a three or four stage lens

system, onto a fluorescent screen, on a photographic film, or on the monitor screen of an

electronic camera system [140–142]. The spatial resolution of the image depends on the

quality and design of these lenses, especially on the objective. TEM images shown here

were obtained with a HF 2000 microscope (Hitachi) equipped with a cold field emission

gun.

4.3 Microscopy techniques 63

4.3.2 Scanning electron microscopy

The image formation in the scanning electron microscope (SEM) works completely dif-

ferent compared to the one in the TEM. As mentioned before, in the TEM the rays

transmitted through the sample pass through the lens and form the image. In the case of

the SEM, a focused electron beam is scanned over the sample. The image is an abstract

construction, i. e. it is a map generated serially (point by point) [143]. However, this

map of the sample produced by the SEM gives information that can be interpreted like

an image. Figure 4.6 shows the basic components of the scanning electron microscopy.

Fig. 4.6: The principle set-up of a SEM [144].

The SEM incorporates an electron-optical column that operates similar to the princi-

ples already discussed in TEM, however the SEM mostly operates in the range of 10-20

keV accelerating voltage which is lower than for a TEM [142, 143]. Primary electrons

are focused into a small-diameter electron probe that is scanned across the specimen.

By applying electrostatic or magnetic fields at right angles to the beam, it is possible to

change its direction of travel. This is done by using the condenser lenses and the objective


lenses. The former determine the beam current that impinges on the sample, whereas the

objective lenses determine the final spot size of the electron beam [142, 143]. Therefore,

in an electric field E and magnetic field B, the electron experiences the Lorentz force,

F = −e(E+ v ×B) (4.13)

where e is the charge of the electron and v is the velocity of the electron.

The smallest diameter of the electron probe is determined by the minimum acceptable

electron probe current. The resolution of an SEM depends on its incident-probe diameter.

Fig. 4.7: Schematic of specimen-electron beam interaction [145].

When electrons with energies of 1-50 keV impinge on a material, a number of inter-

actions with the atoms of the target sample are produced. For example, elastic scat-

tering (change in direction with negligible energy loss) which leads to the formation of

backscattered electrons (BSE) and inelastic scattering (energy loss with negligible change

in direction) which lead to the formation of secondary electrons (SE) and Auger electrons

(AE). SE electrons are low energy electrons (E < 50 eV) caused by the inelastic scatter-

ing of weakly bound electrons. The SE coefficient strongly depends on the inclination of

the surface and increases slightly with the atomic number Z. BSE are primary electrons

that have been ejected from a solid by elastic scattering inside the sample. The energy

of the BSE is in the range of the primary electrons down to about 50 eV. Thus, the

secondary and backscattered electrons can be distinguished due to their kinetic energy.

Furthermore, analytical information is obtained from the X-ray spectrum and Auger elec-

4.4 The superconducting quantum interference device: SQUID 65

trons [142, 143]. The most important signals are produced by secondary electrons and

backscattered electrons.

In contrast to TEM which uses a stationary incident beam, the focused electron beam

of diameter dp of a SEM is scanned in two perpendicular (x and y) directions across

the specimen. Thus a square or rectangular area of specimen can be covered and an

image of this area can be formed by collecting secondary electrons from each point on

the specimen.

HRSEM images of the samples shown here were taken using a Hitachi S-5500 ultra-

high resolution cold field emission scanning electron microscope. All samples were pre-

pared on lacey carbon films supported by a copper grid. The obtained images were

analyzed using the Scandium 5.0 software package from Soft Imaging System GmbH.

The electron beam lithography was performed using a QUANTA 200 FEG SEM with

a Raith Elphy Quantum lithography unit. The patterns were designed using a GDSII

database included in the lithography software.

4.4 The superconducting quantum interference device:

SQUID

The superconductive state can be described by a macroscopic quantum wave function ψ

for the Cooper pairs, of the form,

ψ(r, t) = ψ0(r, t)eiθ(r,t) (4.14)

where θ is the phase common to all the Cooper pairs in the condensate.

The properties of a supercurrent through a tunnel barrier were studied theoretical by

Brian David Josephson. The Josephson junction consists of two weakly coupled super-

conducting electrodes [146]. Let us consider that the two superconductors are identical

and ψ1 is the probability amplitud of electron pairs on one side of the junction and ψ2

is the probability amplitud on the other side. The supercurrent density (Js) depends

on the phase of the wave functions. If the coupling between the two superconductors

is weak enough, the relation between the supercurrent density to the phase difference


(ϕ = θ2 − θ1) in the absence of any scalar and vector potential is

Js = Jcsinϕ (4.15)

where Jc is the critical or maximum Josephson current density. This relation is the

first Josephson equation.

If ϕ changes with time, then one obtains the second Josephson equation, i.e.

∂ϕ

∂t=

2π

Φ0

∫ 2

1

E(r, t).dl (4.16)

where Φ0 represents the flux quantum (Φ0 = h/2e) and∫ 2

1E(r, t).dl is the voltage

drop across the junction.

This discovery is the base of the superconducting quantum interference device (SQUID).

SQUID devices combine two physical phenomena, i.e. the Josephson effect and the flux

quantization in superconducting loops [147]. SQUIDs are very sensitive instruments

which measure magnetic flux variations. They work as a highly sensitive flux to voltage

converter giving a flux dependent output voltage with a period of one quantum flux.

The minimum flux variation which can be measured using the SQUID is of the order

of fractions (≈ 10−5) of the flux quantum Φ0 [146]. There are two main operational

modes in superconducting quantum interference device, i. e., direct current (dc) and

radio frequency (rf). The former consists of a closed superconducting loop including two

Josephson junctions in the loop’s current path, whereas the latter consists of a supercon-

ducting loop with one Josephson junction [7,147,148]. In this section the dc-SQUID will

be explained in more detail .

The dc SQUID

The direct current superconducting quantum interference device consists of a supercon-

ducting ring with two Josephson junctions as depicted in Figure 4.8 [7, 147, 148]. The

second junction allows a finite, time-averaged, direct voltage difference to be established

across the junctions by a direct bias current. The junctions, 1 and 2, are characterized

by the first Josephson equation, i. e. Is1 = Icsinϕ1 and Is2 = Icsinϕ2. The total current

Is through the circuit is composed of the current in each junction, i. e. Is = Is1 + Is2.


Fig. 4.8: Schematic of a dc SQUID adapted from Ref. [147].

Considering the line integral along the contour (Fig. 4.8), the phase differences are

related to the flux according to

ϕ2 − ϕ1 = 2πn +2πΦ

Φ0

(4.17)

Using the second equation of Josephson and assuming that the loop inductance is

negligible, the flux inside the SQUID is then just the applied flux. The maximun su-

percurrent, given by equation 4.18, is a periodic function of the applied field (Figure

4.9 [7,146–148]). Maxima are obtained for integral multiples of the flux quantum, whereas

the minima correspond to half-integral multiples.

Ims = 2Iccos

∣∣∣∣(

πΦ

Φ0

)∣∣∣∣ (4.18)

However, in many cases one should consider the finite inductance L of the supercon-

ducting loop. Then the flux inside the SQUID is

Φ = Φext + ΦL (4.19)


Fig. 4.9: Critical current of a dc SQUID as a function of the applied flux when the inductance isnegligible [149].

4.4.1 SQUID magnetometer

The SQUID magnetometers are a straightforward application of SQUID. The SQUID

magnetometers are vector devices which measure the changes in the magnetic field com-

ponent perpendicular to the plane of the flux pick-up coil. The pick-up coil is connected

to the input coil of the SQUID forming a superconducting flux transformer [148,149].

Magnetometry measurements of the samples were performed using a Quantum De-

sign MPMS5 superconducting quantum interference device magnetometer. The MPMS5

system includes several different superconducting components, i. e. the superconducting

quantum interference device, the superconducting shield, the superconducting detection

coil and the superconducting magnet (Figure 4.10) [150].

The SQUID is located inside of a superconducting shield. The latter shields the

SQUID detector from the large magnetic field produced by the superconducting magnet.

The SQUID is connected to the detection coils with superconducting wires. The detection

coil is a single piece of superconducting wire configured as a second-order gradiometer

and is located at the center of the superconducting magnet outside of the sample cham-

ber. The upper and lower coils are wound clockwise, whereas the intermediate coils are

wound counter-clockwise (Figure 4.10). The gradiometer configuration is sensitive to the

magnetic stray fields of the sample and cancels out the homogeneous contributions from

any external fields.


Fig. 4.10: Schematic representation of commercial SQUID-magnetometer (MPMS-5S, Quantum De-sign) adapted from Ref. [150].

The sample is mounted in a tube with a nominal inside diameter of 9 mm which is

attached to the end of a rigid sample rod. The sample space is maintained at low-pressure

with static helium gas. Next, the sample is located within the superconducting detection

coil which is surrounded by the superconducting magnet. The latter produces a uniform

constant magnetic field over the entire coil region. The sample moves vertically through

the superconducting detection coil. Any change in the sample position modifies the flux

within the detection coil which is inductively coupled to the SQUID sensor. A linear scan

of the sample with constant velocity through the pick-up coil produces a characteristic

voltage vs. position curve. This curve is fitted to the one of an ideal point-like magnetic

dipole with moment μ. From this fit the value of the magnetic moment of the sample is


extracted.

4.4.2 Applications of SQUID magnetometers

Often used magnetic measurements employing dc SQUID device magnetometer are mag-

netization vs. temperature M(T ) and magnetization vs. field M(H). Examples of M(T )

are the well known zero field cooled (ZFC) or field cooled (FC) curves. The ZFC magne-

tization curve is obtained by first cooling the system in zero field from high temperatures

to a low temperature. Next, the field is applied and subsequently the magnetization

is recorded while increasing the temperature gradually. The FC magnetization curve is

measured by decreasing the temperature in the same applied field used in the ZFC pro-

cedure (Figure 4.11). Other measurements modes, such thermo-remanent mangetization

(TRM) and isothermo-remanent magnetization (IRM) are explained in Section 7.2.3.

H=0

FC

H=0ZFC

M (e

mu)

T (K)

(1)(2)

(3)

Fig. 4.11: Schematic representation of ZFC and FC magnetization curves. The arrows indicate thedirection of the measurement.

Hysteresis loops M(H) are measured at a fixed temperature. The magnetization is

recorded while the field is varied (Figure 4.12).


(3)

(2)

(1)

M (e

mu)

H (Oe)

Fig. 4.12: Schematic representation of hysteresis loops. The arrows indicate the direction of themeasurement.

Chapter 5

Synthesis and structural

characterization of antiferromagnetic

nanostructures

Magnetic nanoparticles and nanowires have attracted much interest among magnetism

researchers for decades. This is not only due to their huge potential in technological ap-

plications either in purely magnetic areas as recording technology [31], but also in other

disciplines such as in biology and medicine [32, 151, 152]. In fundamental research they

usually serve as ideal model systems, mentioning e.g. the Stoner-Wohlfarth and the Néel-

Brown model [30] or to study the finite size effect [33]. The latter one is in particular

relevant for nanoparticles and nanowires consisting of an antiferromagnetic (AF) material.

As the size of a magnetic system decreases, the significance of the surface spins increases.

Since an antiferromagnet usually has two mutually compensating sublattices, the surface

always leads to a breaking of the sublattice pairing and thus leading to ’uncompensated’

surface spins. This effect was already discussed by Louis Néel for the explanation of

a net magnetic moment in AF nanoparticles [43]. Various explanations have been pro-

posed, e.g. spin-glass or cluster-glass-like behavior of the surface spins [45–48], thermal

excitation of spin-precession modes [49], finite-size induced multi-sublattice ordering [50],

core-shell interactions [46, 47, 51], or weak ferromagnetism [52, 53]. However, the precise

identification of the nature of the surface contribution has remained unclear. Terms like

73

74 Synthesis and structural characterization of antiferromagnetic nanostructures

’disordered surface state’, ’loose surface spins’, ’uncoupled spins’, ’spin-glass-like behav-

ior’, etc. express the uncertainty in the description of the shell contribution.

With the motivation to explicitly investigate the surface spin contribution in AF

nanosystems, high-quality AF Co3O4 nanostructures have been synthesized using the

nanocasting method described in Chapter 3. As discussed therein, the structure and

the properties of the template play an important role for the synthesis of the metal

oxides [63,73]. This approach has been successfully employed giving well ordered magnetic

nanostructures, such as, NiO [73,153], MnxOy [73], Co3O4 [73–75], Cr2O3 [76,77], Fe2O3

[78], Fe3O4 [79], and Co3O4-CoFe2O4 [71]. It has been demonstrated that direct control

of the pore size of the silica template, typically between 5 and 30 nm, [94, 154] is easily

achieved by selecting an appropriate temperature for the hydrothermal treatment step of

the synthesis protocol. The cobalt nitrate, which is the precursor for the final Co3O4, is

incorporated in the channels of the silica template and later thermally decomposed inside

the silica matrix. In the final step, the silica template is removed yielding nanowire arrays

which are in the same size range as the pores of the silica template [68].

In this section, the synthesis of nanostructured Co3O4 using two silica templates,

two-dimensional hexagonal silica SBA-15 and three-dimensional cubic silica KIT-6, will

be discussed. The samples were characterized by powder X-ray diffraction (XRD), N2-

sorption, high resolution scanning electron microscopy (HRSEM) and high resolution

transmission electron microscopy (HRTEM). Magnetometry studies of Co3O4 as well as

other AF nanostructures will be discussed in Chapter 7.

5.1 Synthesis of mesoporous SBA-15 with variable con-

nectivity and pore size

At the end of the 1990’s Stucky and coworkers from the University of California, Santa

Barbara showed the preparation of well-ordered hexagonal mesoporous silica structures

with uniform pore size varying from 5 to 30 nanometers [94, 96]. These materials, called

SBA-15 (Santa Barbara), are usually synthesized under strongly acidic condition using

a block copolymer as a structure-directing agent. The mesoporous SBA-15 have walls

5.1 Synthesis of mesoporous SBA-15 75

with a thickness from 3.1 to 6.4 nanometers. The pore size and the thickness of the silica

walls of the two dimensional array of channels in SBA-15 can be tuned by the thermal

treatments. Further studies on SBA-15 show that the large uniform adjacent ordered

pores in SBA-15 are connected by smaller pores [103], the size and fraction of which

can be controlled by adjusting the ratio between the silica precursor and the amphiphilic

triblock copolymers, and especially the synthesis temperature. A schematic illustration

of the synthesis of SBA-15 is depicted in Figure 5.1.

Fig. 5.1: Schematic illustration of the synthesis of mesoporous SBA-15. a) Formation of surfactantmicelles. b) Aggregation of surfactant micelles to micellar rods. c) Formation to a hexagonal array. d)Condensation of silicic acid on the surface. e) Removal of the template. Final structutre of SBA-15 isshown in the HRSEM image adapted from Ref. [71]

Silica samples are designated as SBA-15-T -r, where T stands for the hydrothermal

aging temperature applied during synthesis and r stands for the molar silica precursor to

surfactant ratio. Control of the network connectivity of SBA-15 is possible by adjusting

the ratio between the silica precursor and the amphiphilic triblock copolymers, and the

temperature in the preparation of the hexagonal mesoporous silica [74,96,154].

All SBA-15 ordered mesoporous silicas were synthesized in a 0.3 M aqueous solution

of HCl using poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) (Pluronic

P123, EO20PO70EO20, Sigma-Aldrich) as a structure-directing agent and tetraethoxysi-

lane (TEOS, ACROS 99%) as the silica precursor. High quality samples were obtained


in the range of SiO2:P123 molar ratios (r) of 45-65 [74,154].

1.0 1.5 2.0 2.5 3.0

SBA-15-100-50

(a)N

orm

aliz

ed in

tens

ity

2 0

0

1 1

0

1 0

0

1.0 1.5 2.0 2.5 3.0

��

��

��

��

��

Nor

mal

ized

inte

nsity

�θθ � ��

Fig. 5.2: Small-angle XRD patterns of two-dimensional hexagonal silica SBA-15-100-50 (a) and SBA-15-100-r with SiO2:P123 molar ratios (r) varying from 45-65 (b). The curves are shifted along theintensity axis for better clarity.

In a typical synthesis SBA-15-100-50, 13.9 g of Pluronic P123 were mixed with 252

g of distilled water and 7.7 g HCl (37%). The mixture was stirred at room temperature

until a homogeneous solution was obtained. Next, 25.0 g of TEOS were added at once.

The temperature was increased to 35 ◦C and the solution was stirred for 24 h, followed

by aging at 100 ◦C for 24 h. The resulting product was filtered without washing and

dried for 48 hours at 95 ◦C. Finally the sample was calcined in an air flow at 550 ◦C for

6 hours.

5.1 Synthesis of mesoporous SBA-15 77

The pore connectivity of SBA-15-100 was modified by adjusting the silica to surfactant

ratio [154, 155]. A set of samples was prepared according to the conditions used for the

standard procedure described above (SBA-15-100-50), but in this case the molar ratio of

silica to surfactant (r = 45-65) was varied. Accordingly, TEOS amounts ranging from

22.5 g to 32.46 g were used.

Fig. 5.2 shows small angle X-ray diffraction patterns for the sample SBA-15-100-50

(a) and SBA-15-100 synthesized with different connectivity (b). Three diffraction peaks

are clearly seen in the 2θ range from 0.8◦ to 3◦ degrees, which evidence the 2-D hexagonal

phase of the hexagonal p6mm symmetry [94].

0.0 0.2 0.4 0.6 0.8 1.00

200

400

600

800

0 5 10 15 200.00

0.03

0.06

0.09

dV/d

D (c

m3 g-1

nm-1

)

Relative Pressures (p/po)

Vad

s(cm

3 /g a

t STP

)

pore size (nm)

Fig. 5.3: Nitrogen adsorption-desorption isotherm of mesoporous SBA-15-100-50. Inset shows the poresize distribution.

In order to determine the pore size and the Brunauer-Emmett-Teller (BET) surface

area, nitrogen sorption isotherms were measured. An isotherm is depicted in Fig. 5.3 for

the SBA-15-100-50. The N2 isotherm is of type IV, according to the International Union

of Pure and Applied Chemistry (IUPAC) classification [122]. It is clearly possible to dis-

tinguish three regions. The first one corresponds to the monolayer/multilayer adsorption.

The second one represents the capillary condensation. The last region corresponds to the

multilayer adsorption on the outer particle surface. The synthesized material has a BET

surface area of 804 m2 g−1, a pore volume reaching 1.01 cm3g−1 and an average pore size

of 6 nm.


0.0 0.2 0.4 0.6 0.8 1.00

500

1000

1500

2000V

ads(c

m3 /g

at S

TP)


SBA-15-100-55

SBA-15-100-45

SBA-15-100-60

SBA-15-100-65

Fig. 5.4: Nitrogen adsorption-desorption isotherm of mesoporous SBA-15-100 with SiO2:P123 molarratios r varying form 45-65; the data is shown with an offset of 500 cm3g−1 (SBA-15-100-55), 1000cm3g−1 (SBA-15-100-60) and 1400 cm3g−1 (SBA-15-100-65).

Nitrogen adsorption isotherms of SBA-15-100 synthesized with r = 45, 55, 60 and

65 are shown in Fig. 5.4. The isotherm are of type IV and show the three distinct

regions as discussed above for the SBA-15-100-50. The pore volume was determined

from the desorption branch of the N2 isotherm where a narrow distribution of pore size

was obtained in all cases.

Furthermore, pore size and connectivity of SBA-15-T -50 was modified by adjusting

hydrothermal treatment temperature. A set of samples was prepared according to the

conditions used for the standard procedure described above (SBA-15-100-50), but in this

case the hydrothermal treatment temperature, 40◦ C , 70◦ C and 120 ◦ C, was used in

order to tune the pore size of the silica template. High quality samples, judged by powder

X-ray diffraction patterns and pore size distribution, were obtained in all cases.

5.2 Synthesis of mesoporous KIT-6 79

5.2 Synthesis of mesoporous KIT-6 with variable pore

size

Years after the first synthesis of SBA-15, another high quality mesoporous material was

synthesized by Kleitz et al. in Korea Advanced Institute of Science and Technology

[156]. This mesoporous material called KIT-6 exhibits cubic Ia3d symmetry and can be

represented by a pair of interpenetrating bicontinuous networks of channels. In this case,

Pluronic P123-butanol mixture is used as a structure-directing agent. As reported for

SBA-15, the pore size and connectivity can be easily tuned by hydrothermal treatment.

In the case of the former, from 4 to 12 nm. A schematic illustration of the synthesis of

KIT-6 is depicted in Figure 5.5.

Fig. 5.5: Schematic illustration of the synthesis of mesoporous KIT-6. a) Formation to a cubic array.b) Condensation of TEOS on the surface. c) Removal of the template. Final structutre of KIT-6 isshown in the HRSEM image adapted from Ref. [71]

All KIT-6 ordered mesoporous silicas were synthesized in a 0.5 M aqueous solution

of HCl using Pluronic P123-butanol mixture as a structure-directing agent and TEOS as

the silica precursor. Silica samples are designated as KIT-6-T , where T stands for the

hydrothermal aging temperature applied in the synthesis.


1.0 1.5 2.0 2.5 3.0

KIT-6-100

N

orm

aliz

ed in

tens

ity

3 3

2 4

2 0

2 2

0

2 1

1

1.0 1.5 2.0 2.5 3.0

��

��

��

Nor

mal

ized

inte

nsity

�θθ � ��

Fig. 5.6: Small-angle XRD pattern of three-dimensional cubic silica KIT-6-100 (a) and KIT-6 synthe-sized at different hydrothermal treatment temperatures (b). The curves are shifted for better clarity.

The cubic silica product was obtained according to the procedure reported by Rum-

plecker et al. [74]. In a typical synthesis KIT-6-100, 13.5 g of Pluronic P123 were dissolved

in 487.5 g of distilled water and 26.1 g of HCl (37%). The mixture was stirred at room

temperature until a homogeneous solution was obtained. Next, the temperature was in-

creased to 35 ◦C and 13.5 g of butanol (Aldrich, 99%) were added at once. After the

mixture was stirred for 2 hours, 29.2 g of TEOS were added to the solution. The mixture

was at 35 ◦C under continuous stirring for 24 h, subsequently heated at 100◦ C for 24

h under static conditions. The resulting product was filtered without washing and dried

for 48 h at 95 ◦C. Finally the sample was calcined in an air flow at 550 ◦C for 6 h. Other

sets of samples have been prepared changing the hydrothermal treatment temperature to

5.2 Synthesis of mesoporous KIT-6 81

40 ◦C, 70 ◦C and 135 ◦C.

0.0 0.2 0.4 0.6 0.8 1.00

200

400

600

0 5 10 150.00

0.04

0.08

0.12

pore size (nm)

dV/d

D (c

m3 g-1

nm-1

)

Vad

s(cm

3 /g a

t STP

)


Fig. 5.7: Nitrogen adsorption-desorption isotherm of mesoporous KIT-6-100. Inset shows the pore sizedistribution.

KIT-6-T samples were characterized by powder X-ray diffraction (XRD) and N2 sorp-

tion isotherms. Fig.5.6 shows small-angle XRD patterns of three-dimensional cubic silica

KIT-6-100 (a) and KIT-6 synthesized at different hydrothermal treatment temperatures

(b). The diffraction peaks seen in the 2θ range from 0.8◦ to 3◦ degrees clearly evidence a

well ordered 3-D structure with cubic Ia3d symmetry for all samples [156].

The information of high quality cubic Ia3d silica product obtained by small-angle

XRD is confirmed using Nitrogen adsorption isotherms. Fig. 5.7 shows the synthesized

material KIT-6-100. The N2 isotherm is of type IV, according to the IUPAC classification

with a capillary condensation step and H1 hysteresis loop, that indicates the large channel-

like pores as reported by Kleitz et al. [156]. The BET surface area for KIT-6-100 is 793

m2 g−1 with a high pore volume of 1.043 cm3 g−1 and an average pore size of 7 nm.

Nitrogen adsorption isotherms of KIT-6 synthesized at different hydrothermal treatment

temperatures are shown in Fig. 5.8 (a) while pore size distribution is depicted in (b).

The latter shows that it is possible to tune the mesoporous diameter of KIT-6, by variyng

the hydrothermal treatment, i.e. 4 nm for KIT-6-40, 5 nm for KIT-6-70 and 9 nm for

KIT-6-135. The pore size was determined from the desorption branch of the N2 isotherm.


0.0 0.2 0.4 0.6 0.8 1.00

400

800

1200

Vad

s(cm

3 /g a

t STP

)

(a)

KIT-6-135 KIT-6-70 KIT-6-40


0 4 8 12 16 200.00

0.05

0.10

(b)

dV/d

D (c

m3 g-1

nm-1

)

pore size (nm)

KIT-6-135 KIT-6-70 KIT-6-40

Fig. 5.8: (a) Nitrogen adsorption-desorption isotherm of mesoporous KIT-6 synthesized at differenthydrothermal treatment temperatures. The data is shown with an offset of 200 cm3g−1 (KIT-6-70)and 400 cm3g−1 (KIT-6-135). (b) Pore size distribution for mesoporous KIT-6 synthesized at differenthydrothermal treatment temperatures.

The connectivity is also modified by varying the hydrothermal treatment temperatures.

5.3 Synthesis and structural characterization of Co3O4

nanowires

Nanowires of Co3O4 were obtained using the method reported in Ref. [74]. In a typical

synthesis, 5 g of SBA-15 aged at 100 ◦C were mixed with 57 ml of 0.8 M solution of

5.3 Synthesis and structural characterization of Co3O4 nanowires 83

Co(NO3)2*6H2O in ethanol and stirred for 2 h at room temperature. Subsequently the

ethanol was evaporated at 80 ◦C overnight. The sample was then calcined at 200 ◦C for

6 h. The composite was re-impregnated again followed by calcination at 450 ◦C for 6

h (with an intermediate plateau at 200 ◦C for 4 hours). The silica template was then

removed using 125 ml of 2 M NaOH aqueous solution, followed by several washing steps

with water and a final drying step at 50 ◦C. The impregnation procedure was also followed

for SBA-15-100 with different connectivities and SBA-15 aged at 40 ◦C, 70 ◦C and 120◦C. A schematic illustration of the of the synthesis of Co3O4 nanowires is depicted in

Figure 5.9.

Fig. 5.9: Schematic illustration of the synthesis of Co3O4 nanowires. a)Impregnation of SBA-15 withCo(NO3)2*6H2O. b) Calcination at 450 ◦C. c) Removal of the silica template with NaOH. Final structureis shown in the HRSEM image.

The samples are denoted as Co3O4-nw-T -r, where T indicates the aging temperature

and r stands for the molar silica precursor to surfactant ratio of the parent template. To

confirm that the nanocasted wires are clean of template, energy dispersive X-ray analysis

(EDX) studies were performed, showing less than 1 % of Si in the Co3O4.

Initial characterization of the sample was performed by X-ray powder diffraction.


1.0 1.5 2.0 2.5 3.0

��

��

��

N

orm

aliz

ed in

tens

ity

θθ � ��

Fig. 5.10: Small-angle XRD pattern of Co3O4 nanowires with different connectivities. The curves areshifted for better clarity.

Fig. 5.10 shows small X-ray diffraction patterns for Co3O4 replicated from SBA-15-100-r.

Co3O4-nw-100-45 and Co3O4-nw-100-50 exhibit three diffraction peaks in the 2θ range

from 0.8◦ to 3◦, which are characteristic of the 2-D hexagonal phase with hexagonal

p6mm symmetry, as discussed above. It indicates that Co3O4 nanowires are a perfect

negative replica of the hexagonally ordered SBA-15. Co3O4-nw-100-55, synthesized with

increased molar silica precursor to surfactant ratio of the parent silica template, shows

less resolved diffraction peaks, indicating a decrease of the size of ordered domains or an

overall decrease of long range order.

The wide-angle XRD pattern of Co3O4-nw-100-50 shows broad reflections due to the

reduced size of the crystalline phase. Bulk Co3O4 has a normal spinel structure of the

form AB2O4, where Co2+ ions occupy the tetrahedral (A) site, while the two Co3+ ions

occupy the octahedral (B) sites.

Figure 5.11 shows the X-ray diffraction pattern at room temperature performed on the

powdered polycrystalline sample. Rietveld refinement using the FullProf software [157]

was performed on the nanowires. The refinement shows a single phase of Co3O4 with


Fig. 5.11: High-angle XRD pattern of Co3O4 nanowires.

space group Fd3̄m in good agreement with Ref. [17]. The lattice constant corresponds to a

= 8.0823 Å, which is slightly larger than the value a = 8.065 Å for the bulk compound [17],

attesting an expansion of 0.3 % of the unit cell in the nanowires.

The XRD diffraction pattern indicates the highly crystalline structure of the walls,

in good agreement with the HR-TEM analysis results (Fig. 5.12). The nanowires have a

diameter of 8 nm and an average length of 50 nm estimated from high resolution trans-

mission electron microscopy (HRTEM) and high resolution scanning electron microscopy.

Figure 5.13 shows high resolution scanning electron microscopy (HRSEM) images of

Co3O4 nanowires with different diameter size.

Furthermore, Co3O4 nanowires have been characterized using nitrogen adsorption

isotherms. Fig. 5.14 shows the N2 isotherm for Co3O4-nw-100-50. The synthesized

material has a BET surface area of 114 m2 g−1 and pore volume reaching 0.17 cm3

g−1. These values are in agreement with previous studies on nanocasted Co3O4 [155].

Co3O4 obtained from higher molar silica precursor to surfactant ratio of the parent silica


Fig. 5.12: TEM (a,b) and HRSEM (b,c and d) and HRTEM (e) image of the Co3O4 nanowires afterremoval of the template. The average diameter of the wires is 8 nm and the average length 50 nm.

template shows a small feature for the ordered mesopore system and a broad capillary

filling range in the sorption isotherms.

Effects of the calcination temperature on the structure of Co3O4 nanowires were also

investigated. First, 1 g of SBA-15 aged at 100 ◦C was mixed with 11.5 ml of 0.8 M solution


Fig. 5.13: HRSEM images of Co3O4 nanowires with (a) 5 nm, (b) 6 nm, (c) 7nm and (d) 9 nmcrystallite size.

of Co(NO3)2*6H2O in ethanol and stirred for 1 h at room temperature. Subsequently the

ethanol was evaporated at 80 ◦C overnight. The sample was then calcined at 200 ◦C for

6 h. The composite was re-impregnated again. Next, 0.4 g of the sample were calcined

at 650 ◦C for 6 h (with an intermediate plateau at 200 ◦C for 4 hours). Another 0.4 g

of the sample were calcined at 850 ◦C for 6 h (with an intermediate plateau at 200 ◦C

for 4 hours). The remaining sample was calcined at 200 ◦C for 6 h. The silica template

was then removed in each case, using 10 ml of 2 M NaOH aqueous solution, followed by

several washing steps with water and a final drying step at 50 ◦C.

The samples calcined at 200 ◦C and 650 ◦C are black as expected for Co3O4, whereas


0.0 0.2 0.4 0.6 0.8 1.00

50

100

150

0 5 10 15 200.000

0.005

pore size (nm)dV/d

D (c

m3 g-1

nm-1)

Vad

s(cm

3 /g a

t STP

)

0.0 0.2 0.4 0.6 0.8 1.00

50

100

150

200

250

300

Co3O4-nw-100-45

Co3O4-nw-100-55

Co3O4-nw-100-60

Co3O4-nw-100-65

Vad

s(cm

3 /g a

t STP

)

Relative Preassure (p/po)

Fig. 5.14: Nitrogen adsorption-desorption isotherm of Co3O4-nw-100 (a). Inset shows the pore sizedistribution. Nitrogen adsorption-desorption isotherms for Co3O4-nanowires with different connectivies(b).

the sample calcined at 850 ◦C is pink. Figure 5.15 shows the X-ray diffraction pattern

at room temperature measured on the powdered polycrystalline samples. Below 850 ◦C,

the sample shows a single phase of Co3O4. This is in agreement with the structural and

textural studies of Co3O4 nanocasted from KIT-6 as a template [158]. However, the XRD

pattern for the sample calcined at 850 ◦C corresponds to the Co2SiO4 phase. This implies

that for higher temperatures the metal oxide reacts with the silica template, forming

cobalt silicates. TEM images on this sample have shown that the ordered structure is

5.4 Synthesis and structural characterization of cubic Co3O4 nanostructures 89

20 30 40 50 60 70

��

��

��

N

orm

aliz

ed in

tens

ity

�θθ � ��

Fig. 5.15: High-angle XRD pattern of Co3O4 and Co2SiO4. The curves are shifted for better clarity.

lost after this high temperature calcination. The sample consists of domains with an

average size of 500 nm.

5.4 Synthesis and structural characterization of cubic

Co3O4 nanostructures

Cubic ordered mesoporous Co3O4 was synthesized according to a chemical route reported

by Rumplecker [155]. In a typical synthesis, 1 g of KIT-6 was dispersed in 10 ml of 0.8

M Co(NO3)2*H2O in ethanol and stirred for 1 h at room temperature. Subsequently

the ethanol was evaporated at 80 ◦C overnight. The sample was then calcined at 200◦C for 6 h. The composite was re-impregnated again followed by calcination at 450 ◦C

for 6 h (with an intermediate plateau at 200 ◦C for 4 hours). The silica template was


then removed using 25 ml of 2M NaOH aqueous solution, followed by several washing

steps with water and a final drying step at 50 ◦C. This impregnation procedure was also

followed for KIT-6 aged at 40 ◦C, 70 ◦C and 135 ◦C. A schematic illustration of the

synthesis of cubic Co3O4 nanostructures is depicted in Figure 5.16.

Fig. 5.16: Schematic illustration of the synthesis of cubic Co3O4 nanostructures. a) Impregnation ofKIT-6 with Co(NO3)2*6H2O. b) Calcination at 450 ◦C. c) Removal of the silica template with NaOH.Final structure is shown in the HRSEM image.

Initial characterization of the sample was performed by X-ray powder diffraction.

Fig. 5.17 shows small X-ray diffraction patterns for Co3O4 replicated from KIT-6 aged

at different temperatures, i.e. 40, 70 and 100 ◦C. Characteristic reflections of the Ia3d

cubic structure are clearly seen in the 2θ range from 0.8◦ to 3◦, which evidence that the

cubic phase is retained after the removal of the template.

Figure 5.18 shows the X-ray diffraction pattern at room temperature recorded on the

powdered polycrystalline sample. Rietveld refinement using the FullProf software [157]

showed a phase pure of Co3O4 with space group Fd3̄m and a slightly larger lattice constant

in agreement with the results discussed for Co3O4 nanowires.

The N2 adsorption-desorption isotherm shown in Fig. 5.19 for Co3O4-Cubic-100 is a


0.5 1.0 1.5 2.0 2.5 3.0

��

��

��

Nor

mal

ized

inte

nsity

�θθ � ��

Fig. 5.17: Small-angle XRD pattern of cubic Co3O4 synthesized at different temperatures of hydrother-mal treatment. The curves are shifted for better clarity.

Fig. 5.18: High-angle XRD pattern of cubic Co3O4 nanostructures.


0.0 0.2 0.4 0.6 0.8 1.00

50

100

150

200

0 10 20 300.000

0.004

dV/d

D (c

m3 g-1

nm-1)

pore size (nm)

Vad

s(cm

3 /g a

t STP

)


Fig. 5.19: Nitrogen adsorption-desorption isotherm for cubic mesoporous Co3O4-Cubic-100. Insetshows the pore size distribution.

type IV, confirming the mesoporosity of the samples. The specific surface area estimated

from the BET is 121 m2 g−1. The inset of Fig. 5.19 shows the pore size distribution.

Note that in contrast to Co3O4 nanowires, the sample Co3O4-Cubic-100 shows two peaks.

The first one at 3.3 nm is in agreement with the wall thickness expected for KIT-6,

whereas the second peak at 11 nm implies that some parts the two sub-frameworks,

corresponding to the previous pores of the parent silica, are not connected. Previous

studies on NiO synthesized using KIT-6 as a hard template show that it is possible to

obtain a bimodal pore distribution by controlling the microporous bridging between the

two interpenetrating bicontinuous networks of channels in the KIT-6 [153] (Figure 5.21).

By reducing the aging temperature of the silica template, KIT-6, the micropores are less

well developed, reducing the connectivity between the two sets of mesopores.

The N2 adsorption-desorption isotherms for both Co3O4-Cubic 40(a) and Co3O4-

Cubic-70(b) are displayed in fig. 5.20. The type IV isotherms confirm the mesoporosity.

The specific surface areas of cubic Co3O4-Cubic-40 and Co3O4-Cubic-70 estimated from

the BET method are 152 m2 g−1, 129 m2 g−1 , respectively. The pore size distributions

are shown in the insets of the Figure 5.20. A bimodal pore size distribution composed of

small and large diameter pores is observed. Note that for Co3O4 obtained form KIT-6


0

100

200

300

0 10 20 300.000

0.005

Vad

s(cm

3 /g a

t STP

)

dV/d

D (c

m3 g-1

nm-1)

(a)

pore size (nm)

0.0 0.2 0.4 0.6 0.8 1.00

100

200

0 10 20 300.000

0.005

(b)


pore size (nm)dV/d

D (c

m3 g-1

nm-1)

Vad

s(cm

3 /g a

t STP

)

Fig. 5.20: Nitrogen adsorption-desorption isotherms for cubic mesoporous Co3O4-Cubic-40(a) andCo3O4-Cubic-70(b). Insets show the pore size distributions.

aged at 40 ◦C the second pore size is higher in intensity compared with Co3O4 obtained

from KIT-6 aged at higher temperatures. These results confirmed that lower aging tem-

perature of the silica template lead to sets of mesopores less connected, allowing growth

of Co3O4 in only one set of the KIT-6 mesopores. The value of the larger diameter pore

is then the dimensions of two walls plus a pore of the KIT-6. Further details about the

bimodal pore size distribution encountered in metal oxides nanocasted from KIT-6 can

be found in Ref. [153,155].

HRSEM images of the system shown in Fig. 5.22 confirm the results obtained in N2

adsorption-desorption isotherms. Co3O4 which had been obtained from KIT-6 aged at

lower temperature indicates a mostly open structure in which the two sub-frameworks,


Fig. 5.21: Schematic of how one or two pore sizes in mesoporous materials can occur. [153]

corresponding to the previous pores of the parent silica, are not connected (Figure 5.22

(a) and (b)). The other Co3O4 shows a much denser structure in which the two sub-

frameworks are closely intertwined, due to the high interconnectivity of the previous pore

systems (Figure 5.22 (d)).

Fig. 5.22: HRSEM images (a, c and d) and TEM image (b) of cubic Co3O4 nanostructures with (aand b) 5 nm, (c) 7 nm and (d) 8nm crystallite size.

5.5 Synthesis of cubic CoO and Cr2O3 nanostructures 95

5.5 Synthesis of cubic CoO and Cr2O3 nanostructures

Ordered cubic CoO and Cr2O3 were provided by H. Tüysüz (Max-Planck-Institut für

Kohlenforschung, see Ref. [158]). Briefly, ordered cubic CoO nanostructures were pre-

pared from Co3O4 by using glycerol as reducing agent [72]. The reduction of Co3O4

was carried out at 320 ◦C in a fixed bed reactor with a stainless steel inlet (7 mm inner

diameter). Glycerol aqueous solution (50 wt %) was pumped into the reactor at a flow

rate of 1 ml/h with a syringe pump (Pharmacia Fine Chemicals P-500). The reduction

time was 15 h and during the process no carrier gas was used. Afterwards, the reactor

was cooled to room temperature under a nitrogen flow of 20 ml/h. Figure 5.23 shows the

HRSEM image of cubic ordered AF CoO nanostructures, adapted from Ref. [158].

Fig. 5.23: HRSEM image of cubic ordered mesoporous CoO, adapted from Ref. [158].

Mesoporous Cr2O3 was prepared by the decomposition of CrO3 using cubic ordered

mesoporous silica KIT-6 as hard template. First, 1 g of CrO3 was dissolved in 10 ml

water (1 M solution) and added to 1 g KIT-6. The mixture was stirred for 3 h at room

temperature and subsequently the water was evaporated at 70 ◦C. The composite was

calcined at 775 ◦C for 6 h. Finally, silica template was removed by using 2M NaOH


aqueous solution, followed by several times washing with water and drying at 50 ◦C.

Figure 5.24 shows the HRSEM image of Cr2O3 cubic ordered AF nanostructures with 8

nm crystallite size, adapted form Ref. [158].

Fig. 5.24: HRSEM image of cubic ordered mesoporous Cr2O3 with 8 nm crystallite size, adapted fromRef. [158].

5.6 Summary and conclusions

Ordered antiferromagnetic nanostructures have been prepared by the nanocasting method

from two-dimensional hexagonal and three-dimensional cubic silica templates, SBA-15

and KIT-6 respectively. It has been demonstrated that direct control of the size of

the Co3O4 nanostructures is easily achieved using hydrothermal treatments during the

synthesis.

Co3O4 which had been obtained from KIT-6, aged at lower temperature, indicates

a mostly open structure, in which the two sub-frameworks, corresponding to the previ-

ous pores of the parent silica, are not connected, while the other Co3O4 shows a much

denser structure in which the two sub-frameworks are closely intertwined, due to the high

interconnectivity of the previous pore systems.

Chapter 6

Synthesis and structural

characterization of iron oxide

nanoparticles

Research on magnetic nanoparticles (NPs) and fabrication of magnetic nanostructures by

lithographic methods have attracted intense attention in the last decade. In particular,

magnetic nanoparticles and wires with sizes smaller than 20 nm are in the focus of huge

interest, because they could serve as building blocks for future high-density data storage

media [159–161]. Other potential technological applications of magnetic nanoparticles are

found in electronics [162,163], photonics [164], sensors [165], and in contrast enhancement

agents for magnetic resonance imaging [166].

Rapid developments in the chemical synthesis of magnetic nanoparticles in the last

years offer the possibility to exploit new magnetic, optical and electrical properties that

emerge when reducing the size of the particles. Nanoparticles can be synthesized with

controlled size, shape and surface coating. In most cases they consist of a ferromagnetic

(FM) or ferrimagnetic material. However, core-shell nanoparticles are equally interesting.

From a technological perspective magnetic core-shell nanoparticles with functionalyzed

shells and coatings are suitable in biomedicine for applications in targeted delivery and

diagnostics [167,168]. From a fundamental perspective core-shell nanoparticles might be

even more interesting than those with a single ferro- and ferrimagnetic phase, because of

97

98 Synthesis and structural characterization of iron oxide nanoparticles

the variety of novel interfacial coupling phenomena [51,169].

In this chapter the self-assembly of exchange coupled iron oxide nanoparticles on

a solid substrate will be discussed. Subsequent annealing under air converts the self-

assembled two-phase nanoparticles into one-phase ferrimagnetic nanoparticles. Further-

more, using electron beam lithography patterned trenches of 40-1000 nm width and pat-

terned circles of 60-830 nm width were fabricated for the assisted self-assembly of iron

oxide nanoparticles. Magnetic characterization of the resulting structures is discussed in

Chapter 8.

6.1 Crystal structures of bulk iron oxides

Wüstite, FexO is a nonstoichiometric phase with a known stability range from x = 0.83 to

0.96. At room temperature wüstite crystallizes in a rock salt structure, which is a close-

packed fcc O2− lattice with Fe2+ ions occupying the B interstitial sites. Roth proposed

that FeO crystallize in the space group F3dm, where the oxygen atoms are in in 32(e) sites

and the cations are distributed in the octahedral sites, 16(c) and 16(d), that corresponds

to the metal positions in the rock salt structure and in the tetrahedral sites, 8(a) and

8(b), which are in the interstitial sites [170]. Below 198 K, there is a slight elongation

along the [111] direction and the crystal becomes rhombohedral. Figure 6.1 shows the

defect structure of wüstite [170].

Fig. 6.1: Defect structure of wüstite adapted from Ref. [170]. Red and blue dots represent iron atomsin octahedral and tetrahedral sites, respectively. Defects shown in (A) and (B) are equivalent. (C)desribes a cluster of two defects. (D) and (E) show layers in the atomic array of Fe3O4.

6.1 Crystal structures of bulk iron oxides 99

In a nonstoichiometric phase, the repulsion between the interstitial cation and the

nearest neighbors in the octahedral site could cause movement of the interstitial ion to

an intermediate position between the two tetrahedral sites (see Fig. 6.1 (B)). Because of

the repulsion between cations in tetrahedral and octahedral sites, it is possible that an

octahedral vacancy is shared by two interstitial cations, as shown in Fig. 6.1 (C). The

latter leads to the formation of Fe3O4 as shown in Fig. 6.1(D) and (E).

Magnetite, Fe3O4 has an ”inverse-spinel” structure of the form AB2O4 at room temper-

ature. Similar as in the case of ”direct spinel” of Co3O4 discussed in Chapter 5, magnetite

has two sites, tetrahedrally and octahedrally coordinated. However, in contrast to Co3O4,

the tetrahedrally coordinated A sites are occupied by Fe3+, and the octahedrally coordi-

nated B sites are equally occupied by iron atoms with formal +3 and +2 charges. Figure

6.2 shows the crystal structure of magnetite.

Fig. 6.2: Crystal structure of magnetite. Blue atoms are tetrahedrally coordinated Fe2+; red atomsare octahedrally coordinated, 50/50 Fe2+/Fe3+; white atoms represent oxygen [171].

Below 120 K, magnetite exhibits a metal-insulator transition known as Verwey tran-

sition, which is accompanied by a structural phase transition at the same temperature.

Magnetite can be oxidized to maghemite, γ-Fe2O3. Maghemite has an ”inverse-spinel”

structure of the form AB2O4 similar to magnetite. However, it differs from magnetite by

the presence of cationic vacancies within the octahedral sites.


6.2 Synthesis of iron oxide nanoparticles

Several approaches for synthesizing magnetic nanoparticles have been investigated during

the past decade including chemical precipitation [47,172–175], sol-gel processes [53,176],

thermal and sonochemical decomposition of organometallic precursors [57, 161, 177, 178],

high temperature reduction of metal salts [161, 179–182] and reduction inside reverse

micelles [183].

In 2004, Park et al. reported a general method for fabricating large amounts of

well-defined nanocrystals with controllable size between 6 and 30 nm [57]. The large

scale synthesis of nanoparticles by thermal decomposition of metal - oleate precursors in

high boiling solvent, as reported therein, has the advantage to procedure homogeneous

nanoparticles suitable for magnetic studies. Furthermore, depending on the reaction

conditions, different shapes, sizes, and crystal structures of iron oxide nanoparticles can

be obtained. Schematic representation of the synthetic procedure as described by Park

et al. is depicted in Figure 6.3.

Fig. 6.3: Synthesis of monodispersed nanocrystals adapted from Ref. [57].

In detail, uniform iron oxide nanoparticles were synthesized by thermal decomposition

of iron oleate in trioctylamine in presence of oleic acid1. In a typical synthesis, the metal-

oleate complex was prepared by reacting 3 g of iron chloride (FeCl3*6H2O) and 10.13

g of sodium oleate with 22.21 ml ethanol, 16.62 ml water and 38.88 ml n-hexane. The

mixture was heated to 70 ◦C for 4 h.

In the next step, 6 g of iron oleate and 0.96 ml of oleic acid were added to 43.53

ml of trioctylamine and stirred in a three-neck round-bottom flask. The mixture was1The NPs were synthesized together with M. Feyen (Max-Planck-Institut für Kohlenforschung)

6.2 Synthesis of iron oxide nanoparticles 101

heated to 320 ◦ C with a heating rate of 3.3 ◦C/min under vigorous stirring. Once

the temperature was reached, the reaction mixture was kept at that temperature for

30 min. The initial reddish-brown color of the reaction solution turned brownish-black.

The resultant solution was then cooled to room temperature. The nanoparticles were

separated by centrifugation and washed with ethanol. This procedure was repeated five

times. After washing, the resultant NPs were separated by centrifugation and dissolved

in toluene for long-term storage.

Figure 6.4 shows TEM images of the as-prepared nanoparticles. The images reveal

the formation of highly homogeneous particles with an average size of 20 nm. Although

the nanoparticles are characterized by narrow size distribution they have an irregular

egg-like shape as previously observed for nanoparticles with size around 20 nm [57].

Fig. 6.4: TEM images of 20 nm monodisperse iron oxide nanoparticles.


6.3 Self-assembly of three and two dimensional arrays

of iron oxide nanoparticles

Iron oxide nanoparticles were deposited by spin-coating on a Si substrate with a native

oxide surface. The coating of the sample was performed using SPIN 150 spincoater from

Semiconductor Product Systems. The spin-coating technique for self-assembly of col-

loidal particles on solid substrates has the advantages to be inexpensive, fast, uses only

a small volume of fluid and is compatible with standard microfabrication processes. In

order to self-assemble nanoparticles onto a solid substrate one should consider three im-

portant factors: First, the interactions between the solvent and the substrate; second, the

interactions between the particles and the substrate; and third, the interactions between

two particles [184]. Figure 6.5 depicts a schematic of the self assembly of nanoparticles

in solid substrates.

Fig. 6.5: Schematic illustration of nanoparticles self-assembly in solid substrate via solvent evaporation.

Oriented silicon wafers (100) were provided by CrysTec GmbH. The substrates were

cut into 1 x 1 cm2 pieces, ultrasonically cleaned in acetone for 15 min, rinsed with

isopropanol and dried with a pure N2 stream. In a typical procedure, 0.2 ml of iron

oxide nanoparticles solution was spun at 3000 rpm for 30 s and dried on a hot plate

at 80 ◦C for 20 min. Due to the stabilization of the particles by the organic surfactant

they can self-assemble into ordered two- or three-dimensional arrays when the solvent is

evaporated on a solid substrate. The number of layers of nanoparticles can be controlled

6.3 Self-assembly of three and two dimensional arrays of iron oxide nanoparticles 103

by adjusting the concentration of the solution, the number of cycles of the spin-coating

and the spinning speed. Figure 6.6 shows SEM images of the self-assembled nanoparticles

on a Si substrate with approximately ten monolayers (a) and one monolayer (b), showing

a densely packed hexagonal array of iron oxide nanoparticles. In this experiment as well

as the experiments described below, the number of layers was adjusted by changing the

concentration of the solution, whereas the number of cycles of the spin-coating and the

spinning speed were kept constant. The number of layers of nanoparticles was estimated

using scanning electron microscopy (SEM).

Fig. 6.6: SEM image of iron oxide nanoparticles on Si(100), ten monolayers (a) and one monolayer(b).

In order to check the influence of the solvent and the substrate on the magnetic

behavior of the iron oxide nanoparticles, another set of samples was prepared. In this

case, 0.2 ml of a benzene solution of iron oxide nanoparticles was spun at 3000 rpm for

30 s and dried on a hot plate at 80 ◦C for 20 min. The adsorption of benzene on Si

(100) closely resembles that of toluene, therefore it is expected that the nanoparticles

self-assemble in a densely packed hexagonal array as in the case of toluene. Furthermore,

to check the interactions between the particles and the substrate, iron oxide nanoparticles

in toluene were spun on top of PMMA to avoid the interaction toluene-Si(100). Figure 6.7

shows a SEM images of one monolayer of iron oxide nanoparticles, dissolved in benzene,

on Si substrate (a) and one monolayer of iron oxide nanoparticles on top of PMMA(b).

The images show densely packed hexagonal arrays of iron oxide nanoparticles.

By annealing in oxidizing atmospheres, it is known that the wüstite nanocrystals

can be transformed into high quality magnetite or maghemite nanocrystals [185, 186].


Fig. 6.7: SEM image of one monolayer of iron oxide nanoparticles, dissolved in benzene, on Si(100)(a) and one monolayer of iron oxide nanoparticles on top of PMMA (b).

Fig. 6.8: SEM image of iron oxide nanoparticles on Si(100) dried at 170 ◦C, ten monolayers (a) andone monolayer (b).

Therefore, in a next experiment, 0.2 ml of iron oxide nanoparticles solution was spun at

3000 rpm for 30 s and annealed on a hot plate at 170 ◦ C for 20 min (with an intermediate

plateau at 80 ◦ C for 20 min). SEM images from the resulting films indicate that the

particles did not coalesce during annealing at 170 ◦C, which results in particles with the

same size and distribution.

Additional structural characterization of the iron oxide monolayer films was carried

out by X-ray diffraction. The Bragg scans were carried out at BL09 beamline of the

DELTA synchrotron facility in Dortmund. The energy was chosen at 11KeV (λ= 1.127

Å) with a Si (311) double crystal monochromator. The angle of incidence was kept fixed

at 0.2◦. The beam size at the sample position was 0.2mm x 2mm. The 2θ angle of the

detector was scanned from 10◦ to 60◦ with a step size of 0.05◦. The nanoparticles being

randomly oriented show a powder diffraction pattern as depicted in Fig. 6.9, for samples

dried at 80 ◦C (a) and 170 ◦C (b).

6.3 Self-assembly of three and two dimensional arrays of iron oxide nanoparticles 105

10 20 30 40 50 60

(a)

N

orm

aliz

ed in

tens

ity

FeO

Fe3O4 or γγFe2O3

(220

)(3

11)

(111

)

(200

)

(511

)

(220

)

10 20 30 40 50 60

��

(311

)

(422

)

�θθ � ��

�� γγ��

Nor

mal

ized

inte

nsity

(220

)

(511

)

(400

)

(440

)

Fig. 6.9: XRD patterns of iron oxide nanoparticles on Si(100), dried in air at 80 ◦C (a) and 170 ◦C(b).

Analysis of the diffraction pattern gives an indication of the presence of a mixture

of iron oxide phases in the case of the sample dried at 80 ◦C. The broad peak at 25.7◦

hints toward the presence of two crystalline phases, wüstite and spinel. The main diffrac-

tion peaks (111), (200) and (220) of FeO are clearly identified. However, one observes

diffraction peaks at (220) and (511) which correspond to the spinel F3O4 or γ-Fe2O3. As

reported elsewhere, the mixture of iron phases in one nanoparticle could be attributed

to the surface oxidation of the FeO nanoparticles, resulting in the formation of a F3O4

layer around the nanoparticles [186], or due to the incomplete removal of the surfactans

inside the nanoparticles during the synthesis, leading to a lower intensity in the mid-


dle of the particle that inhibits the formation of one single iron oxide phase [178]. By

annealing the sample at 170 ◦C for 20 min in air, the FeO phase undergoes a chemical

and structural conversion into F3O4 or γ-Fe2O3 evidenced by the shift of the diffraction

peaks to high angles, increase of intensities of (200), (311) and (511) and appearance of

(422). These results suggest the presence of spinel structure as single or major phase in

the nanoparticles.

6.4 Templated self-assembly of iron oxide nanoparti-

cles in lithographical patterns

This section shows an easy approach to direct the self-assembly of iron oxide nanoparticles

into periodic arrays on patterned lines and circles using electron-beam lithography and

the spin-coating technique.

Periodic patterned lines and circles were prepared by e-beam lithography, described

in Chapter 3. Iron oxide nanoparticle dispersions were spin-coated onto these patterned

surfaces and the resist was removed, leaving periodic nanoparticle patterns on flat sur-

faces. Figure 6.10 shows a schematic of directed assembly of nanoparticles into patterned

lines, using e-beam lithography and spin-coating.

Oriented silicon wafers (100) substrates were cut into 1 x 1 cm2 pieces, ultrasonically

cleaned in acetone for 15 min, rinsed with isopropanol and dried with a pure N2 stream.

The resist, poly-methylmethacrylate (PMMA 200 K, 4wt.%), 220 nm-thick layer, was

spun at 2000 rpm for 30 s on the precleaned sample and baked on a hot plate at 170 ◦

C for 10 min. Second, the PMMA layer was exposed to a focussed 20-keV electron beam

which is position controlled by a pattern generator. Upon exposure, cross-links in the

PMMA polymer matrix are broken, which allows the dissolution of the polymer in the

developer solution. The programmed patterns consisted of arrays of trenches or circles,

where iron oxide nanoparticles will be deposited. In order to fabricate a parallel array of

trenches of 130-1000 nm width of lines, the electron dose was fixed at 400 μC/cm2 and the

beam current at 71 pA. In the case of the smaller trenches, i.e. 40 nm width, the electron

dose was fixed at 1000 pC/cm2 and the beam current at 51 pA. The bigger circles, i.e.

6.4 Templated self-assembly of iron oxide nanoparticles in lithographical patterns 107

Fig. 6.10: Schematic illustration of deposition of iron oxide NPs into patterned lines (1) depositionof PMMA into Si Substrate (2) expose PMMA using e-beam lithography; (3) development; (4) etching:(5) deposit iron oxide particle using spin coating; (6) lines of iron oxide NPs.

150 - 830 nm, were fabricated using a dose of 320 μC/cm2 and the beam current was

fixed at 45 pA, whereas the 60 nm circle was obatined by changing the dose to 0.04 pC.

The exposed PMMA was developed in a 1:3 mixture of methyl isobutyl ketone (MIBK)

and isopropanol for 40 seconds, rinsed with isopropanol for 30 s and dried with a pure

N2 stream.

The ion-milling technique was used in order to remove the remaining resist from the

developed area. The etch rate experiments were conducted at a power of 70 W for 4 min.

The etch runs were done at a pressure of 1.6 x 10−3 mbar.

Next, 0.2 ml of a solution of iron oxide nanoparticles dispersed in toluene were de-

posited on the patterned lines and circles by the spin coating method. The spin coating

was for 30 s at 3000 rpm with acceleration 1000 rpm/s2. The suspension was agitated

for 5 min in an ultrasonic bath before spin-coating.

The substrate was then baked at 80 ◦ C for 20 min at ambient environment to evapo-

rate the toluene and fix the nanoparticles in the substrate. Finally, the PMMA resist was

removed in the lift-off process by ultrasonically washing in acetone for 4 min, in order

to remove all nanoparticles that were not on the substrate, leaving only the designed

pattern of iron oxide nanoparticles.


Parallel arrays of lines were fabricated successfully with width between 40 and 10000

nm. Furthermore, circles between 60 and 830 nm diameter were also obtained. The

morphology (period, layer width and thickness, etc.) of the particle patterns can be

controlled by varying the process conditions.

Scanning electron microscopy (SEM) images of the samples after lift-off were taken

using a 20 keV electron beam. Figure 6.11 shows parallel arrays of self-assembled nanopar-

ticles in patterned lines with different width of 1000 nm (a), 700 (b), 130 (c) and 40 (d).

Fig. 6.11: SEM image of parallel arrays of self-assembled nanoparticles in patterned lines with differentwidth of 1000 nm (a), 700 nm (b), 130 nm (c) and 40 nm (d).

Figure 6.12 shows self-assembled nanoparticles forming a ring of 110 nm width (a),

and self-assembled nanoparticles in patterned circles with different width of 830 nm (b),

150 nm (c) and 60 nm (d).

In order to study the magnetism in the confinement of the nanoparticles and compare

it with the two dimensional array of iron oxide nanoparticles, bigger arrays of templated

nanoparticles were fabricated. Figure 6.13 shows SEM images of parallel arrays of self-

assembled nanoparticles in patterned lines with 130 nm width baked at 80 ◦C for 20

6.4 Templated self-assembly of iron oxide nanoparticles in lithographical patterns 109

Fig. 6.12: SEM image of self-assembled nanoparticles forming a ring of 110 nm width (a), and self-assembled nanoparticles in patterned circles with different width 830 nm (b), 150 nm (c) and 60 nm(d).

min.

Fig. 6.13: SEM image of parallel arrays of self-assembled NPs in patterned lines with 130 nm widthdried at 80 ◦C.

Furthermore, to study the magnetic properties of the confinement of the nanoparticles

and compare it with the two dimensional array of iron oxide nanoparticles annealed at

170 ◦ C for 20 min, another set of samples was prepared following the same procedure

described for parallel arrays of self-assembled nanoparticles into patterned lines with 130

nm width baked at 80 ◦ C, followed by annealing the sample at 170 ◦ C. Figure 6.14


shows SEM images of parallel arrays of self-assembled nanoparticles in patterned lines

with 130 nm width annealed at 170 ◦C for 20 min.

Fig. 6.14: SEM image of parallel arrays of self-assembled NPs in patterned lines with 130 nm width,annealed at 170 ◦C.


Monodispersed iron oxide nanoparticles with an average size of 20 nm were synthesized

by thermal decomposition of metal- oleate precursors in high boiling solvent and later

self-assembled on Si substrates.

Structural characterization of the self-assembled iron oxide nanoparticles dried at 80◦C showed that the nanoparticles consist of a mixture of iron oxide phases, wüstite and

spinel. By annealing the nanoparticles at 170 ◦C in air it is possible to favor the spinel

phase in the nanoparticles without the unwanted particle coalescence. Furthermore, a

simple approach for fabricating by e-beam lithography defined trenches with a width as

low as 40 nm and circles up to 60 nm diameter of iron oxide nanoparticles was reported.

Chapter 7

Magnetic characterization of

antiferromagnetic nanostructures

Upon decreasing the size, nanosized ferromagnetic structures enter so-called superpara-

magnetism, i.e. a thermally activated single-domain state. However, antiferromagnetic

nanosystems are governed by core-shell behavior. In this case the surface plays a partic-

ularly important role for the magnetic behavior.

After the pioneering work of Néel [187] in the 1940s, many efforts have concentrated

on characterizing and understanding the magnetic properties of antiferromagnetic (AF)

nanosystems. Néel proposed that ’uncompensated’ spins will be found at the surface

due to mutually not compensated AF sublattices [188]. These ’uncompensated’ sur-

face spins lead to a non-zero total magnetic moment being responsible for various in-

teresting magnetic properties exhibited by small systems in comparison to bulk materi-

als [45–50,173,189,190]. Usually it is not possible to separate surface and core magnetic

contributions. Various explanations have been proposed, e.g., surface spin-glass behav-

ior [45–48], excitation of spin precession modes [49], multi-sublattice ordering [50] or

exchange-coupling between core and shell [46,48,173]. However, the precise nature of the

surface contribution has remained unclear and diffuse up to now.

Employing magnetometry measurements, antiferromagnetic (AF) nanostructures were

studied focusing on the core-shell behavior. Antiferromagnetic nanostructures from Co3O4,

CoO and Cr2O3, have been prepared by the nanocasting method as described in Chap-

111

112 Magnetic characterization of antiferromagnetic nanostructures

ter 5. In this chapter, a magnetic decoupling of the surface from its AF core in Co3O4

nanostructures with different morphologies and different structure sizes will be discussed.

Strikingly, this decoupling enables the independent identification of both contributions.

It was evidenced that the shell behaves as a two-dimensional (2d) diluted antiferromagnet

in a field (DAFF), whereas the core shows regular antiferromagnetic behavior. Further-

more, the potential of remanence magnetization measurements as fingerprints of magnetic

systems is emphasized.

The magnetic properties of the samples were measured using a commercial supercon-

ducting quantum interference device (SQUID) magnetometer (MPMS, Quantum Design),

in applied magnetic fields up to 50 kOe.

7.1 Magnetic properties of bulk Co3O4

Bulk Co3O4 has a normal spinel structure of the form AB2O4. Employing magnetic

susceptibility measurements P. Cossee [191] proposed that Co2+ ions occupy the tetrahe-

dral (A) site, while the two Co3+ ions occupy the octahedral (B) sites (Fig. 7.1). Cossee

based his explanation on the Co3+ ion having zero moment in a crystal field of octahedral

symmetry. The charge distribution is represented by [Co2+]8a[Co23+]16d[O4

2−]32e.

Fig. 7.1: Crystal structure of Co3O4 [192].

7.1 Magnetic properties of bulk Co3O4 113

Some years later, W. L. Roth confirmed Cossee’s interpretation from an extensive

neutron diffraction study [17]. Roth showed that the transition temperature for a bulk

Co3O4 corresponds to 40 K and the magnetic ordering occurred with an unusually high

A-A interaction. The exchange mechanism involves indirect exchange through the Co3+.

Thus, the magnetic interaction between Co2+ ions proceeds via multiple exchange paths

involving several Co2+-O-Co3+-O-Co2+ bonds [17, 193]. The magnetic moment on an A-

site is 3.26 μB at 4.2 K. This value is slightly higher than the spin-only value for a Co2+

ion (3 μB) due to small contribution from spin-orbit coupling. Below TN the Co2+ ions

are in the high-spin (HS) state with S=3/2, whereas the Co3+ ions are in the low-spin

(LS), S=0. The latter is explained by the splitting of the 3d levels by the octahedral

cubic field into upper doublet eg and lower triplet t2g levels. Figure 7.2 shows the level

configuration for Co2+ and Co3+ ions in the tetrahedral and octahedral field adapted

from Ref. [17].

Fig. 7.2: Level configuration for Co2+ and Co3+ ions in the tetrahedral and octahedral field adaptedfrom ref. [17].


7.2 Magnetic properties of Co3O4 nanowires

7.2.1 Magnetization vs. temperature curves

Very useful experiments to analyze the type of magnetism and related important param-

eters in a defined system are the so called zero-field-cooled (ZFC) and field-cooled (FC)

magnetization curves [194,195]. The ZFC magnetization curve is obtained by first cooling

the system in zero field from high temperature to a low temperature. Next, the field is

applied and subsequently the magnetization is recorded while increasing the temperature

gradually. The FC magnetization curve is measured by decreasing the temperature in

the same applied field used in the ZFC procedure.

0 50 100 150 2000

1

2

3

0 50 100 150 2000

1

2

3

(a)

T (K)

M (1

0-3em

u/g)

ZFC FC

M (e

mu/

g)

H = 40 kOe

(b)

H = 50 Oe ZFC FC

Fig. 7.3: M vs. T curves after zero field cooling (ZFC) and after field cooling (FC) measured at twoapplied fields, i.e. 40 kOe (a) and 50 Oe (b).

Fig. 7.3 shows M vs. T curves after ZFC and after FC measured at two applied

7.2 Magnetic properties of Co3O4 nanowires 115

fields, 40 kOe (a) and 50 Oe (b) for Co3O4 nanowires (NWs) of 8 nm diameter. In each

case the sample was cooled down from above the Néel temperature to 5 K.

One finds two characteristic features. First, a bifurcation of the FC and ZFC magne-

tization below a temperature Tbf , which is a typical feature of either spin glass, super-

paramagnetic or random field behavior. In general, it signifies irreversible (’non-ergodic’)

contributions. Second, a peak in the ZFC curve is found, which usually signifies either

spin glass, superparamagnetic or simply AF behavior.

0 20 40 600.0

0.1

0 20 40 600.0

0.3

(a)

27 K

ΔM (1

0-3em

u/g)

ΔM (e

mu/

g)

T (K)

(b)

30 K

Fig. 7.4: ΔM vs. T . The bifurcation temperature Tbf is marked by an arrow.

A regular non-diluted bulk AF shows a peak, when the field is applied along the

anisotropy direction. The inflection point left to the peak position then marks the critical

temperature Tc(H), with Tc(0) = TN . The peak position in the ZFC curve marks the

onset of AF long range order and is also often considered to mark the critical temperature

TN . In this study, the inflection point is taken for the TN definition.

In most AF systems the field dependence of the critical phase boundary is very small in

the range of the usually accessible experimental field values, i.e. H < 50 kOe. Therefore,

the ZFC peak position is not expected to show any significant shift with increasing field.


This matches well with the observation seen in Fig. 7.3. Comparing the ZFC curves for

40 kOe and 50 Oe, one finds virtually no change of the peak position (TN ≈ 27 K). Note

that the Néel temperature of the nanowires is reduced compared to the bulk value of

TN = 40 K due to the finite size effect [33, 196].

From this finding it is possible to conclude that the Co3O4 wires consist of AF ordered

cores, which behave purely AF. Hence, superparamagnetic (SPM) behavior of the entire

nanowires can be ruled out. In a SPM system the peak positions, marking the blocking

temperature, would show a much stronger shift with increasing field [30].

0 10 20 30 40 50 60

2.8

3.0

3.2

3.4

3.6

10 20 30T (K)

ΔM

tw= 12h

T (K)

M (1

0-3em

u/g)

Fig. 7.5: Temperature dependence of the reference magnetization, Mref (H) (solid circles), and ofthe magnetization with stop-and-wait protocol, M(T ). The inset shows the difference curve, ΔM =Mref − MZFC .

By plotting the difference between the magnetization curves, ΔM = MFC-MZFC (Fig.

7.4) only the irreversible contributions are displayed. One finds monotonically decreasing

curves reflecting the expected thermally induced decay of magnetization. The ΔM curves

reach zero at the bifurcation temperature, Tbf = 27 K (FC in 40 kOe) and Tbf = 30 K

(FC in 50 Oe), which matches roughly with the ZFC peak positions.

In order to identify the shell contribution, further magnetometry studies were per-

formed. The presence of the memory effect [39,41,197] has been checked, which would be

an indicator for spin glass behavior of the wire shells. The ZFC curve has been recorded


0 50 100 150 200

1

2

3

4

0 50 100 150 200

1

2

3

4

M

(em

u/g)

(a)

T (K)

M (1

0-3em

u/g)

ZFC FC

H = 40 kOe

ZFC FC

(b)

H = 50 Oe

Fig. 7.6: M vs. T curves after zero field cooling (ZFC) and after field cooling (FC) measured at twoapplied fields, i.e. 40 kOe (a) and 50 Oe (b). Black curves correspond to Co3O4-nw-100-45 (dw = 8nm). Blue curves corresponds to Co3O4-nw-100-60 (dw = 8 nm). The curves are shown with an offsetof 1 emu/g (ZFC and FC of Co3O4-nw-100-60 measured at 40 kOe) and 0.001 emu/g (ZFC and FC ofCo3O4-nw-100-60 measured at 50 Oe) for better clarity.

after cooling the sample from room temperature in zero field to 5 K with an intermediate

halt of 12 h duration at T = 20 K. When this curve is subtracted from a regular ZFC

curve without intermediate halt, then a spin glass system would exhibit a peak at the halt

temperature in the difference curve [39, 41]. However, such a peak is absent in the data.

This implies either that the shells do not show any spin glass behavior or that the signal

was too weak. However, estimating the surface-to-core ratio of the material, i.e. approx-

imately 0.3 [198], and considering the overall large signal in the SQUID data, one can

exclude the possibility that the signal from the wire surfaces is too small. Consequently

spin-glass behavior of the shells can be excluded.


It has been shown that using the nanocasting strategy it is possible to synthesize

Co3O4 nanowires with different connectivities and different diameters (dw). To verify that

the Néel temperature found for 8 nm wires replicated from SBA-15-100-50 is independent

of the connectivity between the wires and scales with the diameter due to the finite size

effect [33], magnetization vs. temperature curves at an applied field of 50 Oe and 40

kOe on Co3O4 nanowires with different connectivities and with different diameters were

studied.

Fig.7.6 shows magnetization vs. temperature curves measured at 50 Oe (b) and

40 kOe(a) on Co3O4-nw-100-45 and Co3O4-nw-100-60. For all connectivities, the M

vs. T curves exhibit a splitting of the zero-field-cooled (ZFC) and field-cooled (FC)

magnetization below a splitting temperature Ts. All the samples show one peak at a

temperature T1 = 27 K in the ZFC curve, which marks the critical temperature. These

results are quantitatively equal to the ones obtained for dw = 8 nm.

Magnetization vs. temperature curves at an applied field of 50 Oe and 40 kOe on

Co3O4 nanowires with different diameters, dw = 5, 6, 7 and 9 nm, are shown in Fig.7.7

(b) and (a) respectively. For all sizes, the M vs. T curves exhibit a splitting of the zero-

field-cooled (ZFC) and field-cooled (FC) magnetization below a splitting temperature Ts.

The sample with dw = 9 nm shows one peak at a temperature T1 = 31 K in the ZFC

curve, which marks the critical temperature. These results are qualitatively similar to

the ones obtained for dw = 8 nm.

Surprisingly, for diameters smaller than 8 nm the ZFC magnetization curves exhibit

a second peak at a lower temperature, T2 (Fig. 7.7). This could evidence a second

magnetic sub-system. HRSEM and TEM images of the samples (Fig. 5.13) exclude the

trivial possibility of two distinct types of wires, which would give two separate magnetic

contributions. Rather one assumes that the two peaks signify a decoupled core-shell

behavior, where the first peak at T1 marks the critical temperature of the wire cores

and the second one at the lower temperature T2 the (non-critical) contribution from the

shells. Due to the reduced dimensionality of the shell the transition temperature will

be reduced. Moreover, the field-dependence of the two peaks should show a different

behavior. While for most AF materials T1 = Tc(H) is independent of the magnetic field,

the second temperature T2 of the 2d-shell is expected to show a stronger field-dependence


0 50 100 1500

2

4

6

0 50 100 150

2

3

T1T2

(b)

H=50Oe

H=40kOe

T (K)

(a)

M (1

0-3em

u/g)

M (e

mu/

g)

7nm 6nm

5nm

7nm 6nm 5nm

Fig. 7.7: M vs. T curves after ZFC (solid symbols) and after FC (open symbols) for different diameters,dw = 5, 6, and 7 nm of Co3O4 nanowires measured at 50 Oe (b) and 40kOe (a). Curves are shown withan offset of 0.0015 emu/g (dw = 6 nm measured at 50 Oe) and 0.2 emu/g (dw = 6 nm measured at 40kOe), 0.003 emu/g (dw = 5 nm measured at 40 kOe) and 0.7 emu/g (dw = 5 nm measured at 40 kOe)for better clarity.

due to missing bonds in a DAFF system and thus reduced ’stability’ against application

of a field [24].

In order to probe the magnetic field dependence of both peaks in the ZFC curve,

magnetometry measurements at various fields were performed. Figure 7.8 shows the

magnetization vs. temperature after ZFC in fields H = 1, 5, 10 and 30 kOe for wires

with dw = 6 nm. One observes two different field dependencies of the two peaks. I.e.,

there is virtually no change in the high temperature (T1) peak position. This matches

well with the assumption that the peak at T1 is due to the AF ordered wire core.

The low-temperature peak at T2, however, shows a strong field dependence. With

increasing field it becomes rounder and shifts to lower temperatures. This behavior can

be understood in the framework of a 2d DAFF model applied to the shell.


0 20 40 0 20 40

T1

T1

T2

1 kOe

5 kOe

10kOe

M (a

rb. u

nit.)

T (K)T (K)

40kOe30kOe

20kOe

T2

Fig. 7.8: M vs. T curves after ZFC measured at different applied fields, H = 1, 5, 10 and 30 kOe, fordw = 6 nm. The arrows mark the two peaks at T1 and T2.

A 2d DAFF does not show a phase transition and hence no critical behavior in a field

[24]. This is in contrast to the 3d case, where a sharp phase transition at Tc(H) is present

[25]. However, in 2d DAFF systems it is possible to observe a peak that becomes rounder

and decreases in amplitude with increasing field [25]. Rounded maxima at Tround(H) have

been observed, e.g., in the specific heat [28] or susceptibility [27] in Rb2Co0.85Mg0.15F4. It

marks the (non-critical) transition from the paramagnetic state to a metastable domain-

state with short-range AF order [26]. The domain-state is characterized by an irreversible

(non-ergodic) behavior. This fact is responsible for the splitting of the ZFC and FC

curves as seen in Fig. 7.7 (a) and (b). The curves strongly resemble those observed on

archetypical DAFF systems [22], such as for Fe1−xZnxF2. Furthermore, from the fact

that the splitting of the ZFC and FC curves at Ts correlates with the peak at T2 rather

than with the one at T1, one infers that the T2-peak is due to a 2d DAFF shell. This is


consistent with the notion that the onset of irreversibility should match with the onset

of 2d DAFF behavior in the shell. In contrast, the core shows regular AF order. Here no

irreversibility is expected since undiluted AF systems show reversible (ergodic) behavior

in M vs T .

Moreover, the AF core/DAFF shell model implies a systematic size dependence of the

peak temperatures, T1 and T2. The core contribution is expected to show, aside from the

finite-size effect, a small dependence on the diameter. In contrast, the shell contribution

should exhibit a stronger size dependence because of an increasing surface-to-core ratio.

In addition, with decreasing size surface disorder is likely to increase. Fig. 7.9 shows the

dependence of T1 and T2 as a function of dw at an applied field of 50 Oe after ZFC. The

observed behavior matches well with the expectations, i.e., T2 shows a relatively strong

and T1 a relatively weak dependence upon dw. This finding again supports the notion

that the Co3O4 wires consist of AF ordered cores, which behave purely AF like, and that

their surfaces behave like a 2d DAFF system by virtue of their natural surface roughness.

12 15 18 21 24 27 30 33

5

6

7

8

9 T2

T1

d w(n

m)

T (K)

Fig. 7.9: Dependence of T1 and T2 as a function of dw at an applied field of 50 Oe.

The presence of two separate peaks in ZFC may be explained by a decoupling of the

magnetic contributions of the shell from the core below a critical size of the nanowires.

While for dw≥ 8 nm both contributions overlap (viz. only one peak is observed in the

MZFC vs. T curves) and might be magnetically coupled, for smaller sizes the shell and


the core act magnetically independent. One may infer that the origin of the decoupling is

simply a crossover of the ratio of coupling energies. For large structure sizes, i.e. dw > 8

nm, the ratio of core spins to shell spins is relatively large so that the core is magnetically

dominant. The shell with a thickness of ≈ 1 nm [198] is completely coupled and thus

magnetically dependent upon the core. The shell thickness was measured using neutron

powder diffraction. Diffraction patterns after ZFC were measured in a temperature range

from 5 to 60 K. The quantitative information of the shell thickness was obtained from the

(111) Bragg peak which contains the nuclear and the magnetic contribution of the Co3O4

nanowires. Upon decreasing the diameter d the shell thickness does not change [198].

Since the wire length remains approximately constant the shell volume thus depends

linearly on d. However, the core volume has a stronger d 2 dependence. Consequently,

below a critical diameter, in our case 8 nm, a crossover occurs, where the intra-shell

coupling energy becomes larger compared to the (inter) core-shell coupling and thus

leading to a magnetic decoupling of shell from core.

Fig. 7.10: (a) HRSEM image of the Co3O4 nanowires after removal of the template. The averagediameter of the wires is 8 nm and the average length 50 nm. (b) Cartoon illustrating the nanowires,and (c) showing a zoom-in together with a schematic representation of the spin-structure. The arrowsup and down indicate the two mutually compensating sublattices in AF, the rough surface leads to adisruption of the sublattice pairing and thus relates directly to a ’dilution’ (i.e. with missing magneticsites).

Figure 7.10 shows a HRSEM image of Co3O4 nanowires with a diameter of dw = 8 nm.

One observes bundles with wires having an average length of 50 nm. A cartoon of the


wires is depicted in Fig. 7.10 (b). Panel (c) depicts a zoom-in together with a schematic of

the core-shell spin-structure. The wire cores show regular AF order, whereas the surface

exhibits natural surface roughness, which in turn is directly related to a ’dilution’ (i.e.

missing magnetic sites) within a 2d AF shell. The shell is therefore expected to show 2d

DAFF-behavior [26,27].

7.2.2 Hysteresis loops

One of the most familiar ’fingerprints’ of magnetic systems is the hysteresis loop M(H).

Hysteresis loops in ferromagnetic (FM) and ferrimagnetic systems are usually character-

ized by a non-linear M(H) curve and irreversible behavior upon field cycling (viz. ’open

loop’). AF systems -in contrast- usually show a linear M vs. H dependence with no

coercivity and very large saturation fields (> 10 T). Numerous studies on the hysteretic

behavior of the exchange bias effect discovered by Meiklejohn and Bean in 1956 [199] are

reported in literature [see Reviews e.g. [51, 200–202]]. The exchange bias, which results

from the interaction between an AF and a FM manifests itself by a displacement of the

hysteresis loop along the field axis after the system is cooled in a magnetic field. Fur-

thermore, it has also been shown that by studying hysteresis loops on submicron circular

nanomagnets it is possible to identify a vortex vs. a single-domain state [203].

-40 -20 0 20 40-3

-2

-1

0

1

2

3

30 35 40

2.0

2.5

-2 -1 0 1 2-0.1

0.0

0.1

0.2

ZFC FC

M (e

mu/

g)

H (kOe)

(a)

(b)

Fig. 7.11: M vs. H hysteresis curves at 5 K after zero field cooling (ZFC) and after field cooling (FC).The insets show (a) an enlarged view at 40 kOe and (b) of the central part.


Fig. 7.11 shows M(H) curves measured at 5 K after ZFC or FC in 40 kOe. The

ZFC curve is point symmetric with a very small coercivity of 110 Oe and a virtually

linear shape in the field range used. Such a curve is expected from a regular AF system,

again confirming that the dominant contribution is due to the AF ordered wire cores. The

hysteresis curve measured after FC in 40 kOe displays an enhancement of the coercive field

to 185 Oe. Moreover, one finds a vertical shift to larger M(H) values. The consequence

of the vertical shift is to observe also a horizontal one (see inset (b)). This might lead

to the interpretation that an exchange bias effect is present [172]. However, comparing

the ZFC and FC curves to those from a diluted bulk-AF, e.g. Fe1−xZnxF2 [22], one finds

a compelling similarity and thus leading to a much more straightforward scenario in the

AF nanowires. One can assume that the shell behaves like a DAFF system by virtue

of its natural surface roughness. I.e. any roughness directly relates to a ’dilution’ (i.e.

missing magnetic sites) at the surface.

-40 -20 0 20 40

-2

0

2

-2 0 2-0.2

0.0

0.2

-40 -20 0 20 40

-2

0

2

-40 -20 0 20 40

-2

0

2

-40 -20 0 20 40

-2

0

2

-2 0 2-0.2

0.0

0.2

-2 0 2-0.2

0.0

0.2

-2 0 2-0.2

0.0

0.2

M (e

mu/

g)

(a)

M (e

mu/

g)

ZFC FC

(c)

ZFC FC

H (kOe)

(b)

H (kOe)

ZFC FC

(d)

ZFC FC

Fig. 7.12: M vs. H hysteresis curves at 5 K after ZFC and after FC for dw = 5 nm (a), 6 nm (b), 7nm (c) and 9 nm (d). The insets show an enlarged view of the central part.


Magnetization hysteresis loops after ZFC and FC were measured at 5 K for all wire

sizes. Figure 7.12 depicts M vs. H curves for dw = 5, 6, 7, and 9 nm. For dw = 6

nm, representatively, one observes a small coercivity of 230 Oe in the ZFC curve and a

virtually linear shape in the field range used, H < 40 kOe. The hysteresis curve measured

after FC in 40 kOe displays an enhancement of the coercive field to 570 Oe and a vertical

shift to larger M(H) values. Qualitatively similar behavior is observed for all samples

with different sizes [Fig. 7.12(a-d)].

7.2.3 Remanent magnetization curves

The necessity for a characteristic magnetic ’fingerprint’ arises so that different systems

can be classified and distinguished. Above, one of the most familiar ’fingerprints’ of

magnetic systems has been discussed, i.e.the hysteresis loop M(H).

So-called first-order reversal curve (FORC) diagrams are a useful tool to characterize

magnetic systems with respect to their magnetization reversal behavior [204, 205]. An

example is the clear difference found between diagrams of a random-field Ising model

(RFIM) and the Edwards-Anderson Ising spin glass (EASG). In the EASG case the

FORC diagrams are characterized by a marked horizontal ridge, indicative of a broad

range of effective coercivities in the system, but narrow range of biases. However, in a

RFIM the FORC diagrams display a well-developed vertical feature reflecting a rather

narrow range of effective coercivities and a broad range of biases [204].

A method probing specifically the dynamic behavior is the so-called Cole-Cole plot,

where the imaginary part of the ac susceptibility χ” is plotted against the real part, χ’. It

has been demonstrated that e.g. superparamagnetic systems can be distinguished from

superspin glass or superferromagnetic ones by the shape of the χ” vs. χ’ curve [206].

Another fingerprinting method employs the measurement of the remanence (the re-

maining magnetization after the applied magnetic field is reduced to zero). This is par-

ticularly important in systems suitable for magnetic recording purposes, where magnetic

interactions can have a strong influence on the signal-to-noise ratio [30, 31]. Applying a

dc magnetic field, it is possible to measure three relevant remanent magnetization curves,

namely the thermo-remanent mangetization (TRM), the isothermo-remanent magnetiza-


tion (IRM) and the dc demagnetization (DCD) curve.

TRM: Thermo-remanentmagnetization

IRM: Isothermo-remanentmagnetization

H (kOe)

(3)(1)(2)

measureH=0

H=0FC

M (e

mu)

TRMIRM

T (K)M

(em

u)

(1)

(2) H=0

H=0

M (e

mu)

T (K)

H=0(3)(4) measure

TRM

IRM

Fig. 7.13: The experimetal procedure to measure TRM and IRM vs. H

To measure the TRM, the system is cooled in the specified field from a high temper-

ature down to the measuring temperature, the field is then removed and subsequently

the magnetization is recorded. To measure the IRM, the sample is cooled in zero field

from high temperature down to the measuring temperature, the field is then momentarily

applied, removed again and then the remanent magnetization is recorded. Figure 7.13

shows the experimental procedure to measure TRM/IRM vs. H. The DCD is measured

after the sample is cooled in zero field from high temperature down to the measuring

temperature, where the sample is first saturated in one field direction. The field is then

momentarily applied in the opposite direction, removed again and then the remanent

magnetization is recorded. One example of the use of remanence curves is the well know

ΔM method where ΔM(H) curves are obtained from DCD and IRM procedures. The

ΔM is defined by ΔM(H) = MDCD(H)-[1- 2 MIRM(H)] and is often used to characterize

magnetic interactions between nanostructures [207]. If the interparticle coupling is dom-


inated by exchange interaction, M is positive, whereas for interactions of dipolar type,

M becomes negative [207].

Next, the TRM/IRM magnetization curves as a function of field and temperature will

be discussed. TRM and IRM vs. H were measured at 5 K in the field range, 50 Oe

≤ H ≤ 50 kOe. Figure 7.14 shows the TRM and IRM curves as function of magnetic

field for Co3O4 nanowires of 8 nm.

0 10 20 30 40 500.0

0.2

0.4

0.6

0.8

1.0

TRM IRM

T = 5K

M (1

0-1em

u/g)

H(kOe)

Fig. 7.14: TRM and IRM vs. H of 8 nm Co3O4 nanowires at 5 K. The solid line represents a fit to apower law, TRM ∝ HνH with νH = 0.42. The broken line is a guide to the eye.

To measure the TRM, the system was cooled in the specified field from room tem-

perature down to 5 K, the field was removed and then the magnetization recorded. To

measure the IRM the sample was cooled in zero field from room temperature down to 5

K, the field was then momentarily applied (duration 10 s, amplitude 1-50 kOe), removed

again and the remanent magnetization recorded.

It is important to note that the TRM and the IRM probe two different states. The

TRM probes the remanent magnetization in zero field after freezing in a certain magne-

tization in an applied field during FC. However, the IRM probes the remanent magneti-

zation in zero field after ZFC (in a demagnetized state) and magnetizing the system at

low temperatures. Therefore, systems with a non-trivial H − T -phase diagram will show

a characteristic difference between TRM and IRM. E.g. the spin glass state strongly

depends on whether it is cooled in a field or not [208]. In contrast, a diluted antiferro-

magnet falls in two different universality classes, i.e., in zero field it behaves like a random


exchange system, whereas in not too large applied fields it behaves like a random field

system [19,22]. In the latter case a metastable domain state is frozen in during FC [209].

Therefore, by comparing the TRM/IRM plots for Co3O4 nanowires with those of e.g.

spin glass and DAFF systems one can draw conclusions about the behavior in the Co3O4

nanowires.

Fig. 7.15 shows the TRM and IRM curves as function of magnetic field (a) of the

canonical spin glass system AuFe adapted from Ref. [210], (b) of Fe particles, with a

mean diameter of 3nm embedded in alumina matrix adapted from Ref. [211] and (c) of

the bulk-DAFF system, Fe1−xZnxF2 adapted from Ref. [22].

0 5 10 15 200.0

0.1

0.2

0.3

0 20 40 600.0

0.3

0.6

0.0 0.2 0.40.00.30.60.91.2

(a)

Nor

mal

ized

Rem

anen

ceM

(em

u/g)

M (1

0-2em

u/g) SG

T = 1.2K

TRM IRM

(c)T = 4.5K

DAFF

TRM IRM

(b) TRM

H(kOe)

SPM

IRMT = 10K

Fig. 7.15: TRM and IRM vs. H (a) of the spin glass system AuFe(0.5%) adapted from Ref. [210], (b)of Fe particles, with a mean diameter of 3 nm embedded in alumina matrix adapted from Ref. [211] and(c) of the DAFF system Fe0.48Zn0.52F, adapted from Ref. [22].

In case of a spin glass [Fig. 7.14 (a)] one observes two features. First, the IRM in-

creases relatively strongly with increasing field, then meets the TRM curve at moderate

field values, where both then saturate. Second, the TRM exhibits a characteristic peak

at intermediate fields, which is also reproduced from several other studies found in lit-

erature [212–214]. This feature is absent in other systems. It has been known that a


spin glass system (SG) strongly depends on whether it is cooled in a field or not [208].

Therefore, characteristic differences between TRM and IRM are observed. Theoretical

studies using Monte-Carlo simulations show that the remanent magnetization curves de-

pend on the final temperature and the field which was applied initially. Higher values

of TRM in comparison with IRM are expected due to the fact that TRM starts from a

high magnetization. TRM grows linearly with the field and exhibits a characteristic peak

for field energies of the order of the interaction energy (≈ kBTf ) [212]. The interaction

field is assumed to be negative and increases as the field increases [215]. The TRM as a

function of temperature decays linearly with temperature, whereas the IRM as a function

of temperature has a maximum that is explained due to the variation of the single cluster

relaxation time with temperature [212].

A superparamagnetic system shows a qualitatively similar TRM-IRM behavior, how-

ever, without this characteristic peak in the TRM curve [211]. In a superparamagnetic

(SPM) system, the remanence is related to the distribution of energy barriers in the sys-

tem [30]. At a given measurement temperature and after removing the applied field, only

the particles which are in the blocked regime will contribute to the remanent magneti-

zation [30]. Theoretical [211] and experimental [211, 216] studies on Fe particles in an

alumina matrix show that in a system of non-interacting nanoparticles TRM increases

with field and reaches saturation more rapidly than the IRM. The latter one increases

relatively strongly with increasing field and meets the TRM curve where both then sat-

urate [Fig. 7.14 (b)]. In contrast, 3d DAFF systems are characterized by two interesting

scenarios. Upon ZFC the systems develops long range order, whereas upon FC the system

breaks up into a metastable domain-state. This behavior yields zero IRM for all fields

and TRM which increases proportionally to R−1, where R is the domain size.

There is no similarity of the TRM/IRM curves for the Co3O4 nanowires (Fig. 7.14)

to the one shown in Fig. 7.15 a. In the case of Co3O4 nanowires, the IRM stays at very

small values even for fields up to 50 kOe, whereas the TRM curve shows a monotonic

increase starting to saturate at approximately 50 kOe. Hence, one can exclude again the

possibility of spin glass and also superparamagnetic behavior. However, comparing to the

TRM/IRM plot of a DAFF system [panel (c)] one finds good correspondence. The bulk-

DAFF system is characterized by a virtually zero IRM and a monotonically increasing


TRM. The solid line in panel (c) is a fit to the TRM data according to the power law,

TRM ∝ HνH [217], with νH = 3.05 [22]. The TRM of the Co3O4 nanowires displays also

a monotonically increasing curve, however with νH = 0.42 (Fig. 7.14).

The TRM value is considered as a characteristic quantity of random field systems.

Theoretical studies on the 3d random field Ising model (RFIM) predict an inverse pro-

portionality between TRM and the domain size, i.e. TRM ∝ R−1 with [217, 218]. One

assumes that the dimensionality and the finite size of the DAFF system play a crucial role

in the TRM/IRM behavior and in particular the field dependence of the TRM so that a

2-dimensional finite-size DAFF system is likely to show a TRM vs. H behavior as found

in the Co3O4 nanowires. To the best of our knowledge, no such theoretical study has

yet been published in the literature for comparison. One can argue that the TRM/IRM

behavior of the Co3O4 shells corresponds more to DAFF than to the spin glass. However,

a crossover from DAFF to SG behavior in the shells might be observed [22], when the

feature size is reduced or the disorder is increased.

0 20 400

4

8

12

IRM

TRM

5nm 6nm 7nm

T = 5K

M(1

0-2em

u/g)

H (kOe)

Fig. 7.16: TRM (solid symbols) and IRM (open symbols) vs. H for different diameters of Co3O4

nanowires, dw = 5, 6 and 7 nm, at 5 K. This plot serves as a magnetic fingerprint of the irreversiblemagnetization contribution.

TRM/IRM vs. H were measured for small wire sizes in order to check the possible


crossover from DAFF to SG shell. Figure 7.16 shows the TRM/IRM vs. H at 5 K for

various wire diameters. For all samples one observes that the IRM stays at very small

values even for fields up to 50 kOe, whereas the TRM curve shows a monotonic increase

starting to saturate at approximately 50 kOe. This behavior of the TRM and IRM curves

resembles those of a DAFF system [22]. As dw decreases the TRM increases while the

curve shape shows gradually more a rounded maximum at H 30 kOe. A maximum in

the TRM is considered to be characteristic for a spin glass phase [214]. Monte Carlo

simulations suggest that the maximum in TRM is due to the interaction field, which is

assumed to be negative and increases as the field increases [215]. However, the hysteresis

curves [e.g. Fig. 7.12] do not support a spin-glass scenario, because they would show

a pronounced S-shape with significant loop opening [208]. Moreover, the small IRM

signal and the shape of the curve as seen in Fig. 7.16 contradict both a spin-glass and a

superparamagnetic behavior. It is more likely that the shape of the TRM curve is due to

the reduced dimensionality of the DAFF system.

0 10 20 30 40 500

4

8

12

T1

T2

TRM IRM ΔΔM

M(1

0-2em

u/g)

T (K)

dw = 6nm

Tf

Fig. 7.17: TRM (solid squares), IRM (open squares) vs. T of Co3O4 nanowires with dw = 6 nmmeasured upon warming in zero field after FC in 40 kOe or ZFC with subsequent application of a fieldof 40 kOe, respectively. Furthermore the corresponding difference curve ΔM = MFC − MZFC (opencircles) vs. T is displayed.

Figure 7.17 shows the TRM (measured upon warming in zero field after FC in 40 kOe)


and IRM (measured upon warming in zero field after ZFC with subsequent application

of a field of 40 kOe) vs. T for wires with dw = 6 nm. One finds three important key

features: First, the IRM vanishes at around 19 K, which matches well with T2 measured

in an applied field of 40 kOe (see Fig. 7.8). Second, the TRM shows two characteristic

temperatures, i.e., on the one hand, a change in the inflection point at Tf = 21 K that can

be attributed to the frozen behavior of the 2d DAFF shell. It is known that in 2d DAFF

systems the equilibrium region is reached at T = Tround when the ZFC and FC have no

visible hysteresis [26]. On the other hand, one observes a characteristic temperature, T

= 30.5 K, at which the TRM vanishes. It matches with the peak temperature T2, which

marks the ordering temperature of the AF cores. This interestingly small magnetization

between Tf and T2 may be attributed to a weak coupling between the AF core and

the 2d DAFF shell. Furthermore, by plotting ΔM = MFC − MZFC , one observes that

its behavior is qualitatively similar to the TRM curve and exhibits both characteristic

temperatures even more pronounced.

7.3 Magnetic properties of cubic Co3O4

The scenario explained above is applicable not only to Co3O4 nanowires, but also to

completely different structures. Co3O4 nanostructures in a so-called ’cubic’ structure

have been prepared as described in Chapter 5. The crystallite size is 8 nm. Here, the

magnetic properties of cubic Co3O4 nanostructures will be discussed.


Fig. 7.18 shows M vs. T curves on Co3O4 nanostructures after ZFC and after FC

measured at two applied fields, i.e. 40 kOe (a) and 50 Oe (b). In each case the sample

was cooled down from room temperature to 5 K. Qualitatively a similar behavior is found

as in the case of Co3O4 nanowires, i.e. a peak in ZFC curve with the inflection point

marking the critical temperature and a splitting of ZFC-FC curves below Tbf . There is

no field dependence of the inflection point in the ZFC curve. Therefore, 27 K corresponds

to the Néel temperature of cubic Co3O4 and it is reduced compared to the bulk value of

7.3 Magnetic properties of cubic Co3O4 133

TN = 40 K due to the finite size effect [33].

0 50 100 150 2000

1

2

3

0 50 100 150 2000

1

2

3

0 25 500.0

0.1

0 25 500.0

0.3

25K

27K

ΔΔM

(a)

T (K)

M (1

0-3em

u/g)

ZFC FC

M (e

mu/

g)H = 40 kOe

ΔΔM

(b)

H = 50 Oe ZFC FC

Fig. 7.18: M vs. T curves after zero field cooling (ZFC) and after field cooling (FC) measured at twoapplied fields, i.e. 40 kOe (a) and 50 Oe (b) of Co3O4. The insets show ΔM = MFC − MZFC . Thebifurcation temperature Tbf is marked by an arrow.

Magnetometry experiments on Co3O4 with cubic shape and different sizes were per-

formed following the same characterization methods applied to the nanowires. Magneti-

zation vs. temperature curves at an applied field of 50 Oe and 40 kOe on cubic Co3O4

structures with different diameters, dw = 5, 6, and 10 nm, are shown in Fig.7.19 (b)

and (a) respectively. For all sizes, the M vs. T curves exhibit a splitting of the zero-

field-cooled (ZFC) and field-cooled (FC) magnetization below a splitting temperature


Ts. The sample with dw = 10 nm shows one peak at a temperature T1 = 33 K in the

ZFC curve, which marks the critical temperature. For diameters smaller than 8nm, two

magnetic peaks were found in the ZFC curve. This observation matches perfectly with

the interpretation given for T1 and T2 in the nanowires.

0 50 100 1500

2

4

6

0 50 100 150

1

2

3

4

6 nm 10 nm (b)

T (K)

5 nm

H=50Oe

H=40kOe

5 nm 6 nm 10 nm (a)

M (e

mu/

g)M

(10-3

emu/

g)

Fig. 7.19: M vs. T curves after ZFC (solid symbols) and after FC (open symbols) of different diameters,dw = 5, 6, and 10 nm, of the cubic structure measured at 50 Oe (b) and 40kOe (a). Curves are shownwith an offset of 0.001 emu/g (dw = 7 nm measured at 50 Oe) and 0.5 emu/g (dw = 7 nm measured at40 kOe), 0.002 emu/g (dw = 6 nm measured at 40 kOe) and 1 emu/g (dw = 6 nm measured at 40 kOe)for better clarity.

7.3 Magnetic properties of cubic Co3O4 135


Magnetization hysteresis loops at 5 K after ZFC and FC were measured on cubic Co3O4

nanostructures with different sizes. Figure 7.12 depicts M vs. H curves for dw = 5, 6, 8,

and 10 nm. For dw = 8 nm, representatively, one observes a small coercivity of 78 Oe in

the ZFC curve and a virtually linear shape in the field range used, |H| < 40 kOe. This

matches well with the previous results found on Co3O4 nanowires [219]. The overall linear

behavior is due to the regular AF nanostructure cores, while the irreversible contribution

(viz. the loop opening) has been attributed to the 2d-DAFF shells [219]. The hysteresis

curve measured after FC in 40 kOe displays an enhancement of the coercive field to 146

Oe and a vertical shift to larger M(H) values. This matches as well with previous results

on Co3O4 nanowires [219] and with hysteresis loops on DAFF systems [22]. Qualitatively

similar behavior to Co3O4 nanowires is observed for all samples with different sizes [Fig.

7.20(a-d)].

-40 -20 0 20 40

-2

0

2

-2 -1 0

0.0

0.1

-40 -20 0 20 40

-2

0

2

-40 -20 0 20 40

-2

0

2

-40 -20 0 20 40

-2

0

2

-1 0-0.10.00.1

-1 0

0.0

0.1

-1 0

0.0

0.1

(a)

M (e

mu/

g)

ZFC FC

(b)

ZFC FC

(c)

H (kOe)H (kOe)

ZFC FC

M (e

mu/

g)

(d)

ZFC FC

Fig. 7.20: M vs. H curves after ZFC (solid line) and after FC (dashed line) of dw = 5 (a), 6 (b), 8 (c)and 10 nm (d) of the cubic structure measured at 5 K. The insets show an enlarged view of the centralpart.



Figure 7.21 shows the TRM/IRM vs. H at 5 K for various diameters. For all samples one

observes that the IRM stays at very small values even for fields up to 50 kOe, whereas the

TRM curve shows a monotonic increase starting to saturate at approximately 50 kOe.

This behavior of the TRM and IRM curves is very similar to the TRM/IRM curves for

the Co3O4 nanowires.

0 10 20 30 40 500.00

0.02

0.04

0.06

0.08

0.10

10 nm

5 nm 6 nm 8 nm

IRM

TRMT = 5 K

M (e

mu/

g)

H (k Oe)

Fig. 7.21: TRM (open sysmbols) and IRM (solid symbols) vs. H of different diameters of Co3O4

with cubic structure, dw = 5, 6, and 10 nm, at 5 K. This plot serves as a magnetic fingerprint of theirreversible magnetization contribution.

Figure 7.22 shows the TRM vs. T measured upon warming in zero field after FC in 40

kOe of cubic Co3O4 nanostructures. One observes a characteristic temperature at which

the TRM vanishes. It matches with TN , which marks the ordering temperature of the AF

cores, i. e. 27 K. The decay of TRM with increasing the temperature can be attributed

to the frozen behavior of the 2d DAFF shell, which finally completely vanishes at TN .

7.4 Magnetic properties of cubic CoO 137

0 10 20 30 40 500

2

4

6

27 K

T (K)

M (1

0-2em

u/g)

Fig. 7.22: TRM vs. T measured upon warming in zero field after FC in 40 kOe of cubic Co3O4

nanostructures. The Néel temperature TN is marked by an arrow.

7.4 Magnetic properties of cubic CoO

CoO has sodium chloride structure in the paramagnetic state. Below the Néel temper-

ature, TN = 290 K CoO becomes tetragonal with c/a<1 [220]. The spins are aligned

parallel to (111) planes and antiparallel stacked along the [111] direction. CoO nanos-

tructures in a so-called ’cubic’ structure have been prepared as described in Chapter 5.

The crystallite size is 8 nm.


Fig. 7.23 shows M vs. T curves of CoO nanostructures after ZFC and after FC measured

at two applied fields, i.e. 40 kOe (a) and 50 Oe (b). In each case the sample was cooled

down from 400 K to 5 K. Qualitatively a similar behavior is found as in the case of Co3O4

nanostructures, i.e. a peak in ZFC curve with the inflection point marking the critical

temperature and a splitting of ZFC-FC curves below Tbf . There is no field dependence

of the inflection point in the ZFC curve. Therefore, 260 K corresponds to the Néel

temperature of CoO and it is reduced compared to the bulk value of TN = 290 K due to

the finite size effect [33].


0 100 200 3000

2

4

6

200 300

4.2

0 100 200 3000

1

2

3

4

200 300

2.4

2.6M

(10-3

emu/

g)

T (K)

CoO

(b)

H = 50 Oe

ZFC FC260 K

M

(em

u/g)

CoO

(a)

H = 40 kOe ZFC FC

260 K

Fig. 7.23: M vs. T curves after zero field cooling (ZFC) and after field cooling (FC) measured at twoapplied fields, i.e. 40 kOe (a) and 50 Oe (b) of cubic CoO antiferromagnet. The insets show an enlargedview of TN .


Fig. 7.24 shows hysteresis loops at 5 K after ZFC and FC on cubic CoO nanostructures.

The M vs. H curve after ZFC is completely closed, i. e. does not show any hysteretic

behavior. The corresponding curve after FC in 40 kOe displays an enhancement of the

coercive field to 264 Oe and a vertical shift to larger M(H) values similar to the case on

Co3O4 nanostructures.

7.4 Magnetic properties of cubic CoO 139

-40 -20 0 20 40

-2

0

2

-3 0

0.0

0.3

H (kOe)

ZFC FC

M (e

mu/

g)

Fig. 7.24: M vs. H hysteresis curves at 5 K after ZFC and after FC of ordered cubic CoO nanostruc-tures.


Figure 7.25 shows the TRM/IRM vs. H at 5 K for cubic ordered CoO. One observes that

the TRM has qualitatively similar behavior to that found on Co3O4 nanowires, however

the IRM is zero even for large fields up to 50 kOe. This hints to a more pronounced

DAFF type behavior with less surface disorder.

Figure 7.26 shows the TRM vs. T measured upon warming in zero field after FC in

40 kOe of CoO nanostructures. One observes a characteristic temperature at which the

TRM vanishes. It matches with TN , which marks the ordering temperature of the AF

cores, i. e. 260 K. The decay of TRM with increasing temperature can be attributed to

the frozen behavior of the 2d DAFF shell, which finally completely vanishes at TN .


0 10 20 30 40 500.00

0.05

0.10

0.15

0.20

T = 5 K TRM IRM

MC

oO(e

mu/

g)

H (kOe)

Fig. 7.25: TRM (circle open symbols) and IRM (square solid symbols) vs. H for cubic ordered CoOat 5 K with a crystallite size of 8nm.

0 100 200 3000.0

0.5

1.0

1.5

2.0

T (K)

M (1

0-1em

u/g)

260K

Fig. 7.26: TRM vs. T measured upon warming in zero field after FC in 40 kOe of 8nm cubic CoO.The Néel temperature TN is marked by an arrow.

7.5 Magnetic properties of cubic Cr2O3

Cr2O3 which is a uniaxial antiferromagnet, crystallizes in a corundum structure (R3̄c)

and has a characteristic spin-flop phase [221]. Below the Néel temperature (TN = 307

7.5 Magnetic properties of cubic Cr2O3 141

K) [222], in zero magnetic field, the Cr3+ spins align antiferromagnetically along the (111)

easy axis, whereas at the spin-flop transition the spins are reoriented in the basal plane

maintaining the AF order [223]. The spin-flop field value for bulk Cr2O3 corresponds to 60

kOe at 4.2 K [221]. With decreasing particle size the spin-flop field HSF decreases. Values

of HSF = 36 kOe and 10 kOe at 5 K were measured for nanostructures with a size of 8

nm [158] and nanoparticles with ellipsoidal shape with the major axis of approximately

170 nm and the minor axis 30 nm [223], respectively. Cr2O3 nanostructures in a so-called

’cubic’ structure have been prepared as described in Chapter 5. The crystallite size is 8

nm.

Fig. 7.27: The magnetic structure of Cr2O3 [224]


Fig. 7.28 shows M vs. T curves on cubic Cr2O3 nanostructures after ZFC and after FC

measured at two applied fields, i.e. 40 kOe (a) and 50 Oe (b). In each case the sample

was cooled down from 400 K to 5 K. Qualitatively a similar behavior is found as in the

case of Co3O4 nanostructures, i.e. a peak in ZFC curve with the inflection point marking


the critical temperature and a splitting of ZFC-FC curves below Tbf . There is no field

dependence of the inflection point in the ZFC curve. Therefore, 300 K corresponds to

the Néel temperature of Cr2O3 and it is reduced compared to the bulk value of TN = 310

K due to the finite size effect [33].

0 100 200 3000

1

2

200 300 400

1.8

2.0

0 100 200 300 4000.0

0.4

0.8

1.2

200 300 400

0.9

Cr2O3

M (1

0-3em

u/g)

T (K)

(b)

H = 50 Oe ZFC FC300 K

Cr2O3

M (e

mu/

g)

(a)

H = 40 kOe ZFC FC

300 K

Fig. 7.28: M vs. T curves after zero field cooling (ZFC) and after field cooling (FC) measured at twoapplied fields, i.e. 40 kOe (a) and 50 Oe (b) of cubic Cr2O3 nanostructures. The insets show an enlargedview of TN .



Fig. 7.29 shows M(H) curves measured at 5 K after ZFC or FC in 40 kOe for Cr2O3.

The ZFC curve has a very small coercivity of 110 Oe and shows a deviation from linearity

in the field range used. The deviation from linearity of the ZFC M vs. H is attributed

to a spin-flop transition [223]. The corresponding M vs. H curve measured after FC in

40 kOe shows two characteristic features. First, a similar deviation of the linearity as

observed for the ZFC curve. Second, a shift in the hysteresis loop as reported for Co3O4

and CoO nanostructures.

-40 -20 0 20 40

-1

0

1

-0.8 0.0-0.02

0.00

0.02

ZFC FC

M (e

mu/

g)

H (kOe)

Fig. 7.29: M vs. H hysteresis curves at 5 K after ZFC and after FC of cubic Cr2O3 nanostructures.

Magnetization hysteresis loops for Cr2O3 nanostructures after ZFC at different tem-

peratures 20, 70 and 200 K are shown in Fig. 7.30 (a). One observes that at 20 and 70 K

there is still a deviation from the linearity in M(H), whereas at 200 K the hysteresis show

the linear behavior as expected for AF systems. ZFC and FC magnetization hysteresis

loops at 200 K are shown in Figure 7.30 (b). A small coercivity in the ZFC curve and a

shifted hysteresis after FC in 40 kOe is obtained.


-40 -20 0 20 40

-1

0

1

-40 -20 0 20 40

-1

0

1

-0.05 0.00-0.002

0.000

0.002

ZFC 20K 70K 200K

M (e

mu/

g)

(b)

(a)

200K

ZFC FC

M (e

mu/

g)

H (kOe)

Fig. 7.30: M vs. H hysteresis curves of Cr2O3 at 20 K (circle open symbols), 70 K (triangle opensymbols) and 200 K (solid line) after ZFC(a) and M vs. H hysteresis curves at 200 K after ZFC andafter FC in 40 kOe(b). The inset shows an enlarged view of the central part.


Figure 7.31 shows TRM/IRM vs. H at 5 K and 200 K for Cr2O3 cubic ordered nanostruc-

tures. At 200 K we observe that the IRM stays at very small values even for fields up to

50 kOe, whereas the TRM curve shows a monotonic increase. This result is qualitatively

similar to the TRM/IRM shown by Co3O4 and CoO. Note that the hysteresis loops at

200 K support this scenario. At 5 K one finds that the TRM increases and reaches a


maximum at 20 kOe. The IRM vs. H increases and reaches a maximum at 35 kOe.

These new features could be related with the spin-flop phase being known to occur in

Cr2O3. The reduced maximum of 20 kOe in the TRM compared with the 35 kOe in the

IRM is likely the manifestation of the AF core together with a 2d DAFF shell.

0 10 20 30 40 500

2

4

6

0 10 20 30 40 50

0.0

0.4

0.8

1.2

M(1

0-3em

u/g)

TRM at 5 K IRM at 5 K

M(1

0-3em

u/g)

H (kOe)

TRM at 200K IRM at 200K

Fig. 7.31: TRM (square solid symbols) and IRM (square open symbols) vs. H of cubic ordered Cr2O3

at 5 K with a crystallite size of 8nm. TRM (circle solid symbols) and IRM (circle open symbols) vs. Hfor cubic ordered Cr2O3 at 200 K for the same sample.

Figure 7.32 shows the TRM vs. T measured upon warming in zero field after FC

in 40 kOe from 400 K down to 5 K (solid black squares) and measured upon warming

in zero field after FC in 40 kOe from 400 K down to 200 K (solid red circles) of Cr2O3

nanostructures. One observes a characteristic temperature at which the TRM vanishes.

It matches with TN , which marks the ordering temperature of the AF cores, i. e. 300 K.

The decay of TRM with increasing temperature can be attributed to the frozen behavior

of the 2d DAFF shell, which finally completely vanishes at TN .


0 100 200 300 4000

1

2

3

4

5

60 100 200 300 400

0.0

0.5

1.0M

(10-3

emu/

g) 5 K

T (K)

300 K

M(1

0-3em

u/g)

200K

Fig. 7.32: TRM vs. T measured upon warming in zero field after FC in 40 kOe of cubic Cr2O3. TheNéel temperature TN is marked by an arrow.

7.6 Magnetic properties of Co2SiO4

Bulk cobalt orthosilicate, Co2SiO4, crystallizes in olivine structure and is antiferromag-

net below 49 K. The olivine structure is of the form AB2O4, with tetrahedral A cations

and octahedral B cations coordinated to a close-packed framework of oxygens [225]. The

oxygens form a slightly distorted hexagonal close-packed array in which half of the octa-

hedral sites are filled by cobalt and one eighth of the tetrahedral interstices occupied by

silicon. Synthesis of Co2SiO4 is described in Chapter 5. TEM images showed that the

sample consists of structural domains with an average size of 500 nm.


Magnetization vs. temperature curves at an applied field of 50 Oe and 10 kOe on Co2SiO4

are shown in Figure 7.33. In each case the sample was cooled down from room temperature

to 5 K. One finds a splitting of the ZFC and FC curve and a sharp peak in the ZFC curve.

There is no field dependence of the ZFC peak position which provides evidence that the

inflection point of the ZFC peak measured at 50 Oe and 10 kOe, 49 K, corresponds to

TN . This value is quantitatively equal to the Néel temperature found for bulk Co2SiO4

7.6 Magnetic properties of Co2SiO4 147

as reported by Nomura et al. [225]. The fact that the Néel temperature of the Co2SiO4 is

not reduced is expected due to the big size of the domains. The sharp cusp is likely due to

a structural phase transition ocurring at TN . FC magnetization curve measured in 50 Oe

shows a continuous increase in magnetization as the temperature decreases (Figure 7.33

(b), however for high applied fields, i. e. 10 kOe, the shape of the FC curve resembles

the curve expected for AF.

0 50 100 150 200 250 3000.0

0.5

1.0

1.5

2.0

2.5

(a)

ZFC FC

49 K

M (e

mu/

g)

H= 10 kOe

0 50 100 150 200 250 3000

2

4

6

49 K

(b)

H = 50 Oe ZFC FC

M (1

0-2em

u/g)

T (K)

Fig. 7.33: M vs. T curves after zero field cooling (ZFC) and after field cooling (FC) measured at twoapplied fields, i.e. 10 kOe (a) and 50 Oe (b).



Figure 7.35 depicts magnetization hysteresis loops after ZFC and FC measured at 5 K

for Co2SiO4. One observes a small coercivity of 150 Oe in the ZFC curve and a virtually

linear shape in the field range used, H < 40 kOe. The hysteresis curve measured after

FC in 40 kOe displays an enhancement of the coercive field to 200 Oe and a vertical shift

to larger M(H) values.

-40 -20 0 20 40-6

-4

-2

0

2

4

6

ZFC FC

M (e

mu/

g)

H (kOe)

Fig. 7.34: M vs. H hysteresis curves of Co2SiO4 at 5 K.


Remanent magnetization curves were also measured for Co2SiO4. Figure 7.35 shows

TRM/IRM vs. H at 5 K for Co2SiO4. The TRM has qualitatively similar behavior to

that found for the AF nanostructures discussed so far. The very small IRM even for large

fields up to 50 kOe, hints to a more pronounced DAFF type behavior with less surface

disorder.

Figure 7.36 shows the TRM vs. T measured upon warming in zero field after FC

in 40 kOe (solid black squares) and 50 Oe (solid red circles) of amorphous Co2SiO4.

7.6 Magnetic properties of Co2SiO4 149

0 10 20 30 400.0

0.1

0.2

0.3

0.4

0.5

T = 5 K TRM IRM

M (e

mu/

g)

H(kOe)

Fig. 7.35: TRM (cicle open symbols) and IRM (square solid symbols) vs. H of Co2SiO4 at 5 K.

0 20 40 60 80 1000.0

0.1

0.2

0.3

0.4

0.5

49 K

TRM 50 Oe TRM 40 kOe

M(e

mu/

g)

T(K)

Fig. 7.36: TRM vs. T measured upon warming in zero field after FC in 40 kOe of Co2SiO4. The Néeltemperature TN is marked by an arrow.

One observes a characteristic temperature at which the TRM vanishes, independently

of the applied field during the cooling procedure. The decay of TRM as increasing the

temperature can be attributed to the frozen behavior of the 2d DAFF shell, which finally


completely vanishes at TN as in the case of the AF nanostructures.


Antiferromagnetic (AF) nanostructures from Co3O4, CoO and Cr2O3, have been prepared

by the nanocasting method from cubic silica templates and investigated using magnetom-

etry with emphasis on the core-shell behavior.

It is shown that the properties of these three AF systems are governed by core-

shell behavior, where the core behaves regularly AF, while the shell behaves as a two-

dimensional diluted antiferromagnet in a field (DAFF).

Magnetometry results on Co3O4 nanostructures of different sizes confirm a core-shell

model, involving a regularly ordered AF core and a 2d DAFF shell. Below a critical

structure size of 8 nm, core and shell decouple magnetically and yield independent mag-

netization signatures, evidenced by two temperatures, T1 and T2, in the magnetization

vs. temperature curves. The origin of the decoupling could be due to a crossover of the

ratio of coupling energies, i.e. intra-shell and core and inter-shell and core.

Furthermore, this study reports about a "magnetic fingerprint" method to charac-

terize the magnetic behavior, i.e. it is demonstrated how thermo-remanent (TRM) and

isothermo-remanent (IRM) magnetization curves can serve to identify the irreversible

magnetization contributions usually encountered in nanosized magnetic structures. The

TRM/IRM fingerprint is compared to those of superparamagnetic systems, superspin

glasses or 3d DAFFs.

The results discussed here may have important consequences for the understanding of

the surface behavior of magnetic nanosystems in general. Moreover since many exchange-

bias models consider the understanding of the AF surface to be crucial for the interpreta-

tion of the exchange-bias effect, the present results might lead to a refined consideration

of the AF interfacial magnetization contribution.

Chapter 8

Magnetic characterization of iron oxide

nanoparticles

Magnetic nanoparticles are in the focus of high interest, because they could serve as build-

ing blocks for future high-density data storage, spintronic devices, photonic, bio-medical

or refrigeration applications [226–230]. In particular, magnetite (Fe3O4) nanoparticles

are currently intensively discussed for medical applications due to their bio-compatibility

and for spintronic devices due to their half-metallic properties.

The rapid progress in the synthesis of nanoparticles makes it possible to fabricate

them with tuned size, shape and crystallinity. Furthermore, it is also possible to prepare

core-shell nanoparticles with interesting exchange coupling phenomena.

In chapter 6 the synthesis and the assembly of iron oxide nanoparticles with a di-

ameter of 20 nm on silicon substrate was discussed. Furthermore, using electron beam

lithography patterned trenches of 40-1000 nm width for templated self-assembly were

fabricated to study the influence of the confinement of the nanoparticles. By changing

the annealing conditions (i. e. temperature and atmosphere), AF phase (FeO), FiM

phase (γ -Fe2O3, Fe3O4) or mixed phases of iron oxide can be obtained.

This chapter is devoted to the magnetic characterization of iron oxide nanoparticles

using a Quantum Design MPMS5 superconducting quantum interference device (SQUID)

magnetometer.

151

152 Magnetic characterization of iron oxide nanoparticles

8.1 Magnetic structure of bulk iron oxides

Wüstite (FeO) is an AF insulator [231] with a band gap of 2.4 eV [232]. At room

temperature wüstite is paramagnetic and crystallizes in a rock salt structure as described

in chapter 6. Below 198 K wüstite orders antiferromagnetically. The magnetic moments

are arranged in ferromagnetic sheets parallel to (111) planes. The moment directions

are perpendicular to the ferromagnetic sheets, and point alternately up and down in

adjacent sheets as shown in Figure 8.1 [170]. The PM to AF transition is accompanied

by a slight elongation along the [111] direction where the crystal becomes rhombohedral.

The magnetic ordering can be understood in terms of a predominantly antiferromagnetic

coupling between next-nearest neighbor ions in the [100] lattice directions. Note that the

metal ions in the NaCl structure are separated by oxide ions.

Fig. 8.1: Antiferromagnetic structure of wüstite taken from Ref. [170].

By considering the exchange interactions in a perfect crystal, the dominant magnetic

interaction is antiparallel superexchange between moments on the next-nearest neighbor

cations connected by oxygen anions. i. e.,

The magnetic moment per ion should be 2gμB. However, wüstite is non stoichiometric.

The substitution of a cation vacancy will perturb the superexchange coupling between

8.1 Magnetic structure of bulk iron oxides 153

the vacancy site and the six next-nearest neighbor cation sites. The presence of a cation

vacancy in FeO implies the creation of two Fe+3 ions, and consequently a double exchange

interaction [233] between Fe+2 and Fe+3 ions in the vicinity of the vacancy (Fe+2-O-Fe+3).

Magnetite (Fe3O4) is a ferrimagnetic compound below 858 K [6]. It crystallizes in

cubic spinel structure in the space group Fd3m [234,235]. In the inverse spinel the Fe2+

(3d6) cations are located in the half of the B sites. The other half of the B sites as well

as all A sites are occupied by the Fe3+ (3d5) cations. The Fe2+ and Fe3+ ions in the

octahedral sites are aligned ferromagnetically by the double exchange interaction. The

Fe3+ ions on the tetrahedral site are coupled to the Fe3+ in the octahedral sites by an

AF superexchange interaction. At 0 K the net magnetic moment per formula weight of

Fe3O4 is 4.1 μB which is close to the magnetic moment of Fe2+ (4 μB) [6,232,236]. Thus,

the magnetic moment in Fe3O4 is given by the Fe2+ ions, whereas the magnetic moments

of the Fe3+ are canceled out.

Fig. 8.2: Electron transfer between Fe2+ and Fe3+ states in magnetite [232].

At room temperature, bulk magnetite has a net anisotropy of K1 = −1.35 × 104

J/m3 [236]. The directions of the easy and hard magnetization axes are [111] and [100]

respectively. In contrast to other ferrites, magnetite is a relatively good conductor at room

temperature. The conductivity is associated with the mixed valency which gives rise to

ferromagnetic exchange interactions. Oxides containing a single valency, Fe2+ or Fe3+,

are invariably magnetic insulators. The conductivity of magnetite at room temperature

corresponds approximately to a value of 200 (Ω cm)−1 [232]. It can be understood in

terms of free electron transfer between Fe2+ and Fe3+ states (Figure 8.2). When cooling


below 120 K its conductivity drops by two orders of magnitude accompanied by a slight

crystallographic distortion. This transition is called Verwey transition [237]. The driving

force for this phenomenon is the strong electron-electron and electron-lattice interactions

in the system [238].

Maghemite (γ-Fe2O3) is a ferrimagnetic material below 918 K [236]. It crystallizes

in inverse spinel structure with space group Fd3m similar to magnetite. In contrast

to magnetite, eight Fe3+ ions are located in tetrahedral sites (A-sites) and sixteen Fe3+

occupy the octahedral sites (B-sites) [239]. The interactions between the spins of the Fe

ions are negative in the spinel structure. Therefore the spins tend to be ordered in an

antiparallel direction with neighboring spins. The ferrimagnetism in maghemite is the

result of Fe3+ in the B sites of the spinel structure. The saturation magnetization of

maghemite is 380 kA/m which is smaller compared to 480 kA/m of magnetite.

8.2 Magnetic characterization of two dimensional ar-

rays of iron oxide nanoparticles

Figure 8.3 shows M vs. T curves after zero field cooling (ZFC) and after field cooling

(FC) measured at 50 Oe for one monolayer film of iron oxide nanoparticles dried at 80 ◦C.

The ZFC magnetization curve is obtained by first cooling the system in zero field from

330 K to 15 K. Next, the field is applied and subsequently the magnetization is recorded

while increasing the temperature gradually. The FC magnetization curve is measured by

decreasing the temperature in the same applied field used in the ZFC procedure. Both,

ZFC and FC curves show a sharp peak and are reversible for temperatures above 250 K. A

peak in the ZFC curve and irreversible behavior are characteristic features of non-ergodic

systems such as spin glasses or superparamagnets. A peak in the ZFC curve for a SPM

system is expected when the measuring time (τm) of the specific experimental technique

is equal to the relaxation time of the system. Below the bifurcation temperature an

additional important feature is noticed in the ZFC curve, i. e., a sudden increase in

magnetization close to 190 K which could be associated either with the freezing point

of the solvent [240], with a structural or magnetic transformation or with two magnetic

8.2 Magnetic characterization of two dimensional arrays of iron oxide nanoparticles 155

phases present in the nanoparticles.

0 50 100 150 200 250 3000.0

0.5

1.0

1.5

2.0

ZFC FC

H = 50Oe

M(1

0-5em

u)

T (K)

Fig. 8.3: M vs. T curves after ZFC and FC measured at 50 Oe for one monolayer of iron oxide NPdried at 80 ◦C.

In order to verify if the sudden increase in magnetization close to 190 K is caused

by the freezing point of the solvent, further experiments were performed. Note that the

iron oxide nanoparticles solution was spun on Si substrate and dried on a hot plate at

80 ◦C which is below the boiling point of toluene (110 ◦C). Therefore, it is possible that

the nanoparticles are surrounded by a toluene layer. A potential scenario is that at low

temperatures the liquid matrix around the particles is frozen, thus the nanoparticles are

mechanical fixed. By warming up the system at temperatures higher than the melting

point of the toluene, the matrix unfreezes. In the liquid matrix the particles are free to

rotate. In the presence of the magnetic field, the anisotropy axes will align by a mechanical

rotation of the single particles parallel to the applied magnetic field. Therefore the sudden

increase in the magnetization could be attributed to a mechanical rotation of the particles

when the toluene matrix unfreezes. This scenario is depicted in Figure 8.4. This idea is

supported by the kink in magnetization occurring at a temperature close to the melting

point of the solvent, Tm=180 K.


This scenario has been investigated in our group via scanning electron microscopy

(SEM) and low temperature atomic force microscopy (AFM) measurements [40]. However

no mechanical rotation has been found.

Fig. 8.4: Schematic representaion of mechanical rotation of the nanoparticles in the toluene matrixtaken from Ref. [40]. Tm corresponds to the melting temperature of the solvent.

Furthermore, nanoparticles were prepared in a different solvent, i. e. benzene. The

adsorption of benzene on Si (100) closely resembles that of toluene, however, its freezing

point is 279 K compared with 180 K of toluene. Another sample was prepared on top of

PMMA in order to avoid the interaction toluene-Si (100).

Figure 8.5 shows M vs. T curves after zero field cooling (ZFC) and after field cooling

(FC) measured at 50 Oe for both samples, i.e. nanoparticles dissolved in benzene and

nanoparticles on top of PMMA. Both samples show similar features compared to the

sample dissolved in toluene (Fig. 8.3). All these results lead to the conclusion that

the model of a rotation of the particles most probably does not fit. Consequently the

hypothesis that the increase in magnetization close to 190 K is caused by the freezing

point of the solvent can be excluded. Note that the samples do not oxidize fast under

ambient conditions. Magnetometry studies on the same sample were performed after 3,

6 and 12 months, showing the identical magnetic properties.

The nature of the peak position as well as the sudden increase in magnetization in the


0

4

8

12

(a)

M(1

0-6em

u)

ZFC FC

0 50 100 150 200 250 3000

5

10

(b)

ZFC FC

T (K)

M(1

0-6em

u)

Fig. 8.5: M vs. T curves after ZFC and FC measured at 50 Oe of one monolayer of iron oxide NP (a)dissolved in benzene and (b) on top of PMMA. Both samples were dried at 80 ◦C.

ZFC curve can be proved via field dependence experiments. FC and ZFC magnetization

experiments at low fields are very useful to identify SPM or superspin glass (SSG) state.

In the case of SPM or SSG state it is expected that the peak in ZFC curve shift to lower

temperatures as the field increases. Figure 8.6 shows the magnetization vs. temperature

after ZFC and FC measured at low fields H = 0.2, 0.5, 1 and 2 kOe for one monolayer

film of iron oxide nanoparticles dried at 80 ◦C. One finds that the peak in the ZFC curve

shifts to lower temperatures as the field increases. However the FC peak is constant for

applied fields up to 2 kOe.


0 100 200 3000.0

0.5

1.0

1.5

2.0

2.5 0.2 kOe 0.5 kOe 1 kOe 2 kOe

M(1

0-4 e

mu)

T(K)

Fig. 8.6: M vs. T curves after ZFC and FC measured at different applied fields of one monolayerof iron oxide NP dried at 80 ◦C. The curves are shown with an offset of 3 × 10−5 emu (ZFC and FCmeasured at 0.5 kOe), 7 × 10−5 emu (ZFC and FC measured at 1 kOe) and 8 × 10−5 emu (ZFC and FCmeasured at 2 kOe), for better clarity.

Figure 8.7 shows ZFC and FC magnetization vs. temperature data for the same film

measured at higher fields H = 5, 7, 10 and 20 kOe. There is a splitting between the ZFC

and FC magnetization curves as observed for low fields. However the ZFC and the FC

peaks coincide in temperature and do not shift to lower temperatures with increasing the

magnetic field. This is contrary to the behavior expected for the blocking temperature

(TB) in SPM nanoparticles or the glass temperature (Tg) in SSG systems, were TB or Tg

shifts to lower temperatures values as the field increases [241]. As discussed in chapter

2, in most AF systems the field dependence of the critical phase boundary is very small

in the range of the usually accessible experimental field values. Therefore, the ZFC peak

position is not expected to show any significant shift with increasing field. This matches

well with the observation seen in Fig. 8.7. Comparing the ZFC curves measured at

H > 2 kOe, one finds virtually no change of the peak position at ≈ 206 K. Therefore,

206 K is related with the presence of AF phase. Note that in chapter 5, the structural

characterization using X-rays in the sample dried at 80 ◦C indicates the presence of a

mixture of iron oxide phases, wüstite (FeO) and spinel (Fe3O4 or γ-Fe2O3). Therefore,


206 K corresponds to the Néel temperature of the FeO (wüstite). The Néel temperature

of the FeO nanoparticles is increased compared to the bulk value of TN = 198 K due to

the coupling between the AF, FeO, core and the FiM, Fe3O4 or γ-Fe2O3, shell. From

this finding one can conclude that the iron oxide nanoparticles consist of wüstite and

spinel (Fe3O4 or γ-Fe2O3) phases. Hence, one can rule out one single spinel phase. The

maximum in the ZFC magnetization curve does not correspond to TB or Tg of the system.

0 100 200 300

1.5

2.0

2.5

3.0

3.5

M

(10-4

emu)

T(K)

5 kOe 7 kOe 10 kOe

Fig. 8.7: M vs. T curves after ZFC and after FC measured at different applied fields of one monolayerof iron oxide NP dried at 80 ◦C.

Figure 8.8 shows M vs. T curves after ZFC and after FC measured at 50 Oe for one

monolayer film of iron oxide nanoparticles dried at 170 ◦C. The ZFC magnetization curve

is obtained by first cooling the system in zero field from 330 K to 15 K. Next, the field is

applied and subsequently the magnetization is recorded while increasing the temperature

gradually. The FC magnetization curve is measured by decreasing the temperature in the

same applied field used in the ZFC procedure. One finds that there is a bifurcation of the

FC and ZFC magnetization below a temperature Tbf and a maximum in the ZFC curve.

Furthermore, FC decreases for temperatures below the splitting temperature. Note that

for a superparamagnetic system, the FC magnetization curve always increases as the

temperature decreases. This is due to the fact that the superspins are blocked (or frozen)


in the direction of the field [242]. The decrease of FC, observed in ferromagnetic or fer-

rimagnetic nanoparticles, is attributed to the magnetic interactions between particles in

the system [41, 242]. The free-energy difference between the two states of a superspin

granule is given not only by the Zeeman energy but also by the residual interactions

between the granule and its surroundings [242]. If particles are not sufficiently sepa-

rated from each other the interactions between them can not be neglected, the dipolar

interparticle interactions lead to the appearance of collective behaviors, e. g. superspin

glass (SSG) systems [41]. Thus the particle moments no longer switch independently,

the reversal of one particle moment may modify the energy barriers of the assembly.

Note that the anisotropic character of the dipolar interactions, may favor ferromagnetic

or antiferromagnetic alignment of the moments. Therefore, in the case of interacting

nanoparticles, random distribution of easy axes and frustration of magnetic interaction

is expected, showing most of the features of typical glassy behavior [33]. A peak in the

ZFC curve is found in both SPM and SSG samples, however the observation of a decrease

in magnetization vs. temperature in the FC upon cooling can only be observed in SSG

systems [41]. Thus the sample annealed at 170 ◦C shows a collective behavior evidenced

by the decrease in magnetization in the FC curve.

0 50 100 150 200 250 3000.0

0.5

1.0

1.5

2.0

2.5

T (K)

M(1

0-4em

u)

ZFC FC

H = 50Oe

Fig. 8.8: M vs. T curves after ZFC and after FC measured at 50 Oe of one monolayer of iron oxideNP annealed at 170 ◦C.


The SSG nature of the sample annealed at 170 ◦C is corroborated by the field de-

pendence of the peak position in the ZFC magnetization curve. Figure 8.9 shows the

magnetization vs. temperature after ZFC and FC measured at low fields H = 0.2, 0.5

and 0.7 kOe for one monolayer film of iron oxide nanoparticles annealed at 170 ◦C. The

peak in the ZFC curve shifts towards low temperatures as the field increases, as observed

for other SSG systems. These results favor the presence of spinel structure magnetite

(Fe3O4) or maghemite (γ-Fe2O3) as single or majority phase in the nanoparticles which

is in agreement with the structural characterization1.

0 50 100 150 200 250 3000

1

2

3

4

5

0.2 kOe 0.5 kOe 0.7 kOe

M (1

0-4 e

mu)

T (K)

Fig. 8.9: M vs. T curves after ZFC (close symbols) and after FC (open symbols) measured at differentapplied fields for one monolayer of iron oxide NP annealed at 170 ◦C. ZFC and FC measured at 0.5 and0.7 kOe are shown with an offset of 2 × 10−4 emu for better clarity.

Furthermore, one finds that the Verwey transition expected for magnetite is not

present in any sample. The Verwey transition temperature for a bulk magnetite is 120

K. Evidence of the Verwey transition in nanocrystalline magnetite thin films [243] and

in highly nonstoichiometric nanometric powders [244] were found using magnetic sus-

ceptibility measurements. Studies on magnetite nanoparticles suggest that the Verwey

transition shifts to lower temperatures due to size effects, i. e. decreases as the particle

size decreases and for a critical size the Verwey transition does not take place [235]. The1see chapter 6.


absence of the Verwey transition in these samples may be attributed to the small size

of particles or to the absence of magnetite in the sample. Conductivity measurements

would give a better understanding of the spinel phase present in the samples.

-40 -20 0 20 40

-9

-6

-3

0

3

6

9

-4 -2 0 2

0.0

1.0x10-4

ZFC FC

M (e

mu)

H (kOe)

Fig. 8.10: M vs. H hysteresis curves at 15 K after ZFC and after FC of one monolayer film of ironoxide nanoparticles dried at 80 ◦C. The inset shows an enlarged view of the central part.

Magnetization hysteresis loops after ZFC and FC at 15 K were measured for the

sample dried at 80 ◦C (Figure 8.10). The FC curves were measured after cooling the

system from 330 K to 15 K in 20 kOe. Interestingly, when cooling the sample in a field

one observes that the hysteresis loop differs from the one measured after ZFC by an

enhancement of the coercive field and a horizontal shift to larger M(H) values. Very

probably this effect is related with unidirectional anisotropy (exchange bias) induced at

antiferromagnetic (AF)-ferromagnetic (FM) interfaces after the FC procedures [199]. The

main indication of the existence of exchange bias is the observation of shifted hysteresis

loops along the field axis after field cooling across the Néel temperature of the AF.

Hysteresis loops were measured in the field range up to 40 kOe. The ZFC curve displays

a coercive field of 500 Oe, whereas the hysteresis curve measured after FC displays an

enhancement of the coercive field to 1135 Oe. The increase in the coercive field Hc after

field cooling is related to the unidirectional anisotropy induced in the FM by the field


cooling process. Furthermore, a vertical shift along the magnetization axes is observed.

A vertical shift of the hysteresis loops in core-shell nanoparticles was observed for Ni-

NiO [245], Co-CoO [246],and Fe-Fe2O3 [247] which is generally attributed to the frozen

spins in the shell. Simulation studies on core-shell nanoparticles show that the microscopic

origin of the vertical shift is attributed to the uncompensated pinned moments at the core-

shell interface that facilitate the nucleation of non-uniform magnetic structures during

the increasing field branch of the loops [248].

-10 -5 0 5 10

-4

-2

0

2

4

M(1

0-4em

u)

15 K 330 K

H (kOe)

Fig. 8.11: M vs. H hysteresis curves at 15 K (dashed line) and 330 K (straight line) after ZFC forone monolayer film of iron oxide NP annealed at 170 ◦C.

Figure 8.11 shows the hysteresis loops measured after ZFC at two different tempera-

tures, 15 K and 330 K. One observes that M(H) measured at 330 K shows no hysteresis.

Therefore one expects that the magnetic anisotropy energy per particle responsible for

holding the magnetic moment along certain directions is comparable to the thermal en-

ergy. For temperatures above Tg the thermal fluctuations induce random flipping of the

magnetic moment, thus the particle can spontaneously switch its magnetization from one

easy axis to another. Below the glass temperature, the M(H) curves measured at 15 K

displays a coercive field of 290 Oe.


8.3 Magnetic characterization of iron oxide nanoparti-

cles in lithographical patterns

0 100 200 300

5

6

0 100 200 300

5

6

7

8(a)

T(K)

200 Oe 50 Oe

T(K)

M (1

0-6em

u)

(b)

200 Oe 50 Oe

Fig. 8.12: M vs. T curves after ZFC (solid symbols) and FC (open symbols) measured at two appliedfields, i. e. 50 Oe (circles) and 200 Oe (squares) for patterned trenches of 130 nm width, dried at 80 ◦C.The magnetic field was applied along (a), and perpendicular (b) to the long axis of the trenches. Thecurves, ZFC and FC measured at 50 Oe, are shown with an offset of 2.5 × 10−6 emu (a) and with anoffset of 4 × 10−6 emu (b) for better clarity. The inset shows the direction of the applied magnetic field.

Magnetic characterization was also performed on the patterned trenches of 130 nm

width to study the influence of the confinement in the magnetic properties of the nanopar-

ticles. Figure 8.12(a) shows M vs. T curves after ZFC and after FC measured at 50 Oe

and 200 Oe for iron oxide nanoparticles dried at 80 ◦C. The magnetic field was applied

along the long axis of the trenches. The ZFC and FC procedure is identical to the one

used for the films. One finds similar features to the one observed in the films, i. e. a

peak in the ZFC and FC curves, irreversible for low temperatures and a sudden increase

in magnetization in the ZFC curve.

Figure 8.12(b) shows M vs. T curves after ZFC and after FC measured at 50 Oe

and 200 Oe for iron oxide nanoparticles dried at 80 ◦C. In this case, the magnetic field

was applied perpendicular to the long axis of the trenches. The ZFC curve shows similar

features to the ZFC curve measured when the magnetic field is applied along the long

8.3 Magnetic characterization of iron oxide nanoparticles in lithographical patterns 165

axis. However, the FC curve shows a new feature for low temperatures, i. e. an increase

in magnetization in the FC upon cooling for temperatures below 50 K.

0 100 200 300 4000.0

0.5

1.0

1.5

200 Oe 50 Oe

M (1

0-5em

u)

T (K)

Fig. 8.13: M vs. T curves after ZFC (solid symbols) and FC (open symbols) measured at two appliedfields, i. e. 50 Oe (circles) and 200 Oe (squares) for patterned trenches of 130 nm width annealed at 170◦C.

-10 -5 0 5 10-15

-10

-5

0

5

10

15

15 K 330 K

M (1

0-5em

u/g)

H (koe)

Fig. 8.14: M vs. H hysteresis curves at 15 K (dashed line) and 330 K (straight line) after ZFC forpatterned trenches of 130 nm width annealed at 170 ◦C.


Magnetic characterization was also performed on the patterned trenches of 130 nm

width, annealed at 170◦C. The measurements do not show any influence of the direction

of the applied magnetic field. Figure 8.13 shows M vs. T curves after ZFC and after FC

measured at 50 Oe and 200 Oe. In comparison to the NP films annealed at the same

temperature, similar features were obtained.

Figure 8.14 shows the hysteresis loops measured after ZFC at two different tempera-

tures, i. e. 15 K and 330 K. One observes that the M(H) curve measured at 330 K shows

no hysteresis. The M(H) curve measured at 15 K displays a coercive field of 70 Oe.

8.4 Conclusions

Employing magnetometry measurements and X-ray diffraction 1 it is possible to identify

the magnetic phases in the iron oxide nanoparticles. Magnetometry results on iron oxide

films showed a strong dependence of the magnetic properties on the thermal treatment.

Depending on the annealing temperature nanoparticles exist in either FeO, γ-Fe2O3,

Fe3O4 or mixed phases. Furthermore, magnetometry studies were performed on trenches

with widths of 130 nm. Samples containing mainly nanoparticles in the FeO-phase show

an influence due to the structuring. At low temperatures, the magnetic properties are

influenced by the direction of the applied field during the measurement. However, systems

annealed at higher temperature containing either γ-Fe2O3 or Fe3O4 do not show modified

behavior.

1see chapter 6

Chapter 9

Summary and Final Remarks

Antiferromagnetic (AF) nanostructures from Co3O4 were prepared by the nanocasting

method from two-dimensional hexagonal (SBA-15) and three-dimensional cubic (KIT-6)

silica templates and investigated using magnetometry experiments. The properties of this

AF system are governed by core-shell behavior. The core behaves regularly AF, whereas

the shell behaves as a two-dimensional diluted antiferromagnet in a field (DAFF) (Figure

9.1).

Fig. 9.1: (a) HRSEM image of the Co3O4 nanowires. (b) Cartoon illustrating the nanowires, and (c)showing a zoom-in together with a schematic representation of the spin-structure 1.

Magnetometry results on Co3O4 nanostructures of different sizes showed that below a

critical structure size of 8 nm, core and shell decouple magnetically and yield independent

1for further details see chapter 7

167

168 Summary and Final Remarks

magnetization signatures. The origin of the decoupling could be due to a crossover of the

ratio of coupling energies, i.e. intra-shell and core and inter-shell and core.

Focusing on the core-shell behavior, the studies were extended to CoO and Cr2O3

AF nanostructures. The properties of these two AF systems are in agreement with the

core-shell behavior proposed for Co3O4 nanostructures.

0 20 400.0

0.3

0.6

0.9

0 5 10 15 200.0

0.1

0.2

0.3

0 20 40 600.0

0.3

0.6

0.0 0.2 0.4

0.0

0.3

0.6

0.9

1.2

Co3O4 NWs

Nor

mal

ized

Rem

anen

ce

(d)

M (1

0-2em

u/g)

M (e

mu/

g)

T = 4.5K TRM IRM

(b)

(c)

(a)

H(kOe)

T = 5K

M (1

0-1em

u/g)

H(kOe)

SG

T = 1.2K

TRM IRM

DAFF

TRM IRM

SPM

TRM IRM

T = 10K

Fig. 9.2: TRM and IRM vs. H of the spin glass system AuFe(0.5%) [210] (a), of Fe particles [211] (b),of the DAFF system Fe0.48Zn0.52Fe [22] (c) and of Co3O4 nanowires at 5 K [219](d) 1.

Furthermore, this study reports about a "magnetic fingerprint" method to character-

ize the magnetic behavior, i.e. it was demonstrated how thermo-remanent (TRM) and

isothermo-remanent (IRM) magnetization curves can serve to identify the irreversible

magnetization contributions usually encountered in nanosized magnetic structures. Fig-

ure 9.2 shows the TRM/IRM fingerprint of superparamagnetic systems, superspin glasses,

3d DAFFs and Co3O4 nanowires (NWs). Using TRM/IRM plots vs. field one can confirm

a core-shell behavior, i.e. a regular AF core and a 2d DAFF shell for all three systems.

Monodispersed iron oxide nanoparticles with an average size of 20 nm were synthesized

by thermal decomposition of metal-oleate precursors in high boiling solvent and subse-

quently self-assembled on Si substrate. Structural characterization of the self-assembled1for further details see chapter 7

169

iron oxide nanoparticles dried at 80 ◦C showed that the nanoparticles consist of a mix-

ture of iron oxide phases, wüstite and spinel. By annealing the nanoparticles at 170 ◦C

in air it is possible to favor the spinel phase in the nanoparticles without the unwanted

particle coalescence. Furthermore, using electron beam lithography, patterned trenches

of 40-1000nm width for templated self-assembly were fabricated to study the influence

of the confinement of the nanoparticles. Circles up to 60 nm diameter of iron oxide

nanoparticles were also fabricated (Figure 9.3).

Fig. 9.3: SEM image of self-assembled nanoparticles into patterned structures (a) line of 40 nm widthand (b) circles of 60 nm diameter (b).

Magnetometry results on iron oxide films showed a strong dependence of the magnetic

properties on the thermal treatment. Depending on the annealing temperature nanopar-

ticles exist in either FeO, γ-Fe2O3, Fe3O4 or mixed phases. Furthermore, magnetometry

studies were performed on trenches with widths of 130 nm. Samples containing mainly

nanoparticles in the FeO-phase show some influence on the structuring. At low tempera-

tures, the magnetic properties are influenced by the direction of the applied magnetic field

during the measurement. However, systems annealed at higher temperatures containing

either γ-Fe2O3 or Fe3O4 do not show modified behavior.

The results discussed in this thesis have important consequences for the understand-

ing of the surface behavior of magnetic nanosystems in general. Moreover since many

exchange-bias models consider the understanding of the AF surface to be crucial for the

interpretation of the exchange-bias effect, the present results might lead to a refined

consideration of the AF interfacial magnetization contribution.

Increasing density requirements in the microelectronics and magnetic-storage data

170 Summary and Final Remarks

continue to motivate the production of devices at ever smaller dimensions. The results

presented in this thesis show that combining conventional lithography, chemical synthesis,

and self-assembly it is possible to fabricate sub-100-nm arranges of iron oxide NP. These

results can be extended to other NP, such as CoPt or FePt. It has been reported by Black

et al. that self-assembled devices composed of periodic arrays of 10-nanometer-diameter

cobalt nanocrystals display spin-dependent electron transport [249] with magnetoresis-

tance ratios on the order of 10% below 20 K. Electron transport properties of magnetite

nanocrystal arrays should be very interesting as well. Magnetite is a half-metal, where the

electronic density of states is spin polarized at the Fermi level. The conductivity is dom-

inated by spin-polarized charge carriers. At the time of this writing, magnetoresistance

experiments on these iron oxide NPs are carried out in our group.

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Acknowledgement

At first and foremost, I would like to thank my supervisors Prof. Dr. Dr. h.c. Hartmut

Zabel and Prof. Dr. Ferdi Schüth to provide me with sufficient freedom in this project.

I express my deepest gratitude to them for their vital encouragement and invaluable

suggestions throughout the course of my studies.

I am deeply indebted to PD Dr. Oleg Petracic for his valuable advice and support.

It has been pleasing to discuss with him many aspects of physics and magnetism in a

friendly and relaxed atmosphere. I also thank him for taking the time to read my thesis.

Our discussions on the completion of the thesis have been of great value.

Furthermore I would like to thank Dr. Harun Tüysüz and Mathias Feyen not only

for explaining me the syntheses but also for providing me some of the materials used in

this dissertation. I appreciate their willingness and kindness to help me any time when

I had questions. I sincerely thank Philipp Szary not only for his excellent comments

but also for listening to me whenever I had doubts or ideas for our project. This is also

extended to Durga Mishra who provided me several useful XRD patterns of iron oxide

nanoparticles.

Furthermore I would like to recognize many valuable contributions from Prof. Dr.

Kurt Westerholt, Dr. Lorena Salabas, Dr. Wolfgang Schmidt, Dr. Florin Radu, Dr.

An-Hui Lu and Dr. Claudia Weidenthaler.

I would like to acknowledge the help from the Microscopy Department at Max-Planck-

Insititut für Kohlenforschung, in the persons of Dr. Bernd Tesche, Dr. Christian W.

Lehmann, Bernd Spliethoff, Axel Dreier and Hans Bongard.

I owe my special thanks to Dr. Miriana Vadalá and Dr. Nan Li for their warm

welcome and their help in personal issues especially during the first months of my doctoral

189

190 Acknowledgement

project.

Special thanks to my office mates, Dr. Miriana Vadalá, Dr. Numan Akdogan, Dr.

Harun Tüysüz, Dr. Anja Rumplecker, Dr. Arti Dangwal Pandey, Durga Mishra, Alexan-

der Cepak, Piotr Bazula and Astrid Ebbing for distinct helpfulness and for maintaining

a nice working atmosphere. I am grateful for the nice time spent in conferences and

schools with my colleagues and especially I would like to thank Alexandra Schumann for

organizing our hotels. I would like to thank Jörg Dudek for giving me a hand with the

helium bottle any time that I needed it.

I am grateful to Petra Hahn, Bazar Öztamur, Claudia Wulf, Inis Gottmannshausen,

Helga Wasilewski and Angelika Rathofer, for their kind help on many administrative

issues.

I would also like to thank Peter Stauche, Horst Glowatzki, Deniss Schöpper and

Marjan Tomas, for their help on technical problems.

Many others at Experimentalphysik IV and Max-Planck-Insititut für Kohlenforschung

that have been involved also deserve recognition. It is, however, not possible to list them

all here. Their support in this effort is greatly appreciated.

I gratefully acknowledge a fellowship trough the International Max-Planck Research

School for Surface and Interface Engineering in Advance Materials (IMPRS-Surmat). I

also would like to thank to Dr. Angelika Büttner, Dr. Christoph Somsen and Dr. Rebekka

Loschen for their wonderful help and support with regards to various official matters. I

would like to thank all the Surmat students for very pleasant and friendly atmosphere

during our meetings and seminars.

It is a pleasure to express my gratitude wholeheartedly to Folsche’s and Cadenbach’s

family for their kindness and affection. I would also like to thank all my friends from

different parts of the world for wishing me luck towards this research.

Me gustaría agradecer de todo corazón a mi familia por su inmenso amor y su apoyo

constante. A mis padres Susana y Guillermo, quienes me han alentado a seguir mi corazón

y enseñado que si hay una meta, hay un camino. A mis abuelitos Teresa y Segundo, por

todas sus oraciones. A mi tía Ligia, quien con mucho amor siempre me ha apoyado y

a disfrutado de mis logros. A mis hermanos Felipe y Sebastián, quienes a pesar de la

distancia han estado siempre conmigo, contagiándome su buen humor. A mi tío Claudio,

Acknowledgement 191

a Bachita y a Andrea.

Words fail me to express my appreciation to my best friend and my great love Thomas

for his everlasting love, motivation, support and encouragement. I would like to thank

him for reading the whole thesis thoroughly and correct the English spelling and grammar

and also for our long scientific discussions. You are a powerful source of inspiration and

an example of perseverance. I am really blessed to have you. I love you with all my heart.

Thank you all for your insights, guidance and support!

193

Curriculum Vitae Name: María José Benítez Romero Date of Birth: February, 16 1981 Place of Birth: Quito - Ecuador Nationality: Ecuadorian Office Adress: Ruhr-Universität Bochum, NB4 Institut für Experimentalphysik/Festkörperphysik Universitätsstraße 150 44801 Bochum

Germany Office Phone: ++492343223626 Email Adress: [email protected]

EDUCATION

� Since Sept. 2006 Ph.D. Thesis in Physics“Self-assembled Magnetic Nanostructures: Synthesis and Characterization”

Faculty of Physics and Astronomy, Experimental Physics 4, Ruhr-University Bochum, Germany, Supervisor: Prof. Dr. Dr. h. c. Hartmut Zabel Supervisor: Prof. Dr. Ferdi Schüth

� 1999-2005 Diploma in Physics “Synthesis and characterization of calcium doped zirconia

nanopowder.” Final Grade: With Distinction

194

Faculty of Physics, Escuela Politecnica Nacional Quito, Ecuador, Supervisor: Dr. Luis Lascano

� 1999 Highschool degree in Ecuatoriano Suizo, Quito, Ecuador. Score: 19/20

AWARDS AND FELLOWSHIPS

� 2009 Awarded for one of the best two contributed oral presentations of young scientists at Nanomagnets 2009.

� 2006 Awarded 3 years scholarship for graduate studies from International Max-Planck Research School for Surface and Interface Engineering in Advanced Materials “Surmat”.

� 2005 Awarded partial scholarship to 2nd European Hydrogen Energy Conference. Zaragoza - Spain.

� 2005 Awarded full scholarship to the 7th Giambiagi Winter School. Buenos Aires, Argentina.

� 2004 Awarded full scholarship to the ICTP Spring College on Science at the Nanoscale. Trieste, Italy.

PUBLICATIONS

� Benitez, M. J.; Petracic, O.; Tüysüz, H.; Schüth, F.; Zabel, H. “Decoupling of magnetic core and shell contributions in antiferromagnetic Co3O4 nanostructures”, Europhys. Lett. In press.

195

� Benitez, M. J.; Petracic, O.; Salabas, E. L., Radu, F.; Tüysüz, H.; Schüth, F.; Zabel, H. “Evidence for core-shell magnetic behavior in antiferromagnetic Co3O4 nanowires”, Phys. Rev. Lett. 101, 097206 (2008).

Manuscripts Under Revison or In Preparation:

� Benitez, M. J.; Petracic, O.; Tüysüz, H.; Schüth, F.; Zabel, H. “Fingerprinting the magnetic behavior of antiferromagnetic nanostructures using remanent magnetization curves”, submitted to Phys. Rev. B.

� Benitez, M. J.; Petracic, O.; Szary, P.; Mishra, D.; Feyen, M.; Lu, A-H.; Schüth, F.; Zabel, H. “Magnetic and structural characterization of self-assembly iron oxide nanoparticles”, in preparation.

� Benitez, M. J.; Petracic, O.; Szary, P.; Feyen, M.; Mishra, D.; Lu, A-H.; Schüth, F.; Zabel, H. “Templated self-assembly of iron oxide nanoparticles in lithographically nanopatterned structures”, in preparation.

CONTRIBUTIONS TO CONFERENCES/WORKSHOPS

� Benitez, M. J.; Petracic, O.; Tüysüz, H.; Schüth, F.; Zabel, H. “Evidence for core-shell magnetic behavior in antiferromagnetic nanostructures”, presented at ICMFS 2009, Berlin, Germany. March 29th-April 3rd, 2009 (Oral).

� Benitez, M. J.; Petracic, O.; Tüysüz, H.; Schüth, F.; Zabel, H. “Evidence for core-shell magnetic behavior in antiferromagnetic nanostructures”, presented at the European Workshop Self-organized Nanomagnets 2009, Aussois, France. March 29th-April 3rd, 2009 (Oral).

196

� Benitez, M. J.; Petracic, O.; Feyen, M.; Mishra, D.; Lu, A-H.; Schüth, F.; Zabel, H. “Templated self-assembly of Fe3O4 nanoparticles in lithographically nanopatterned lines”, presented at the European Workshop Self-organized Nanomagnets 2009, Aussois, France. March 29th-April 3rd, 2009 (Poster).

� Benitez, M. J.; Petracic, O.; Tüysüz, H.; Schüth, F.; Zabel, H. “Evidence for core-shell magnetic behavior in antiferromagnetic nanostructures” presented at DPG Spring Meeting 2009, Dresden, Germany. March 22th-27th, 2009 (Oral).

� Benitez, M. J.; Petracic, O.; Feyen, M.; Mishra, D.; Lu, A-H.; Schüth, F.; Zabel, H. “Templated self-assembly of Fe3O4 nanoparticles in lithographically nanopatterned lines”, presented at DPG Spring Meeting 2009, Dresden, Germany. March 22th-27th, 2009 (Poster).

� Benitez, M. J.; Petracic, O.; Salabas, E. L., Radu, F.; Tüysüz, H.; Schüth, F.; H. Zabel “Understanding the behavior of Co3O4 nanowires using thermoremanent magnetization curves as fingerprints of magnetic systems”, presented at the Summer School 2008, Nässlingen, Sweden. Sep 14th-19th, 2008 (Poster).

� Benitez, M. J.; Petracic, O.; Tüysüz, H.; Schüth, F.; H. Zabel “Preparation and Characterization of Self-Assembled Magnetic Nanostructures”, presented at the 2nd IMPRS-SurMat Workshop on Surface and Interface Engineering in Advanced Materials. Bochum, Germany. July 15th-16th, 2008 (Oral).

� Benitez, M. J.; Petracic, O.; Salabas, E. L., Radu, F.; Tüysüz, H.; Schüth, F.; H. Zabel “Understanding the behavior of Co3O4 nanowires using remanent magnetization curves as fingerprints of magnetic systems”, presented at the 2nd IMPRS-SurMat Workshop on Surface and Interface Engineering in Advanced Materials. Bochum, Germany. July 15th-16th, 2008 (Poster).

� Benitez, M. J.; Petracic, O.; Salabas, E. L., Radu, F.; Tüysüz, H.; Schüth, F.; H. Zabel “Understanding the behavior of Co3O4 nanowires using remanent magnetization curves as

197

fingerprints of magnetic systems”, presented at the Materials day. Bochum, Germany. July 17th, 2008 (Poster).

� Benitez, M. J.; Petracic, O.; Salabas, E. L., Radu, F.; Tüysüz, H.; Schüth, F.; H. Zabel “Understanding the behavior of Co3O4 nanowires using TRM-IRM curves as fingerprints of magnetic systems”, presented at the DPG Spring Meeting, Berlin, Germany. Feb 25th-29th, 2008. (Poster).

� Benitez, M. J.; Rodríguez J., Lascano L. “Synthesis and characterization of calcium stabilized zirconia nanopowder”, presented at the 2nd European Hydrogen Energy Conference, Zaragoza, Spain. November 22nd - 25th, 2005 (Poster).

� Benitez, M. J.; Rodríguez J., Lascano L. “Synthesis and characterization of calcium stabilized zirconia nanopowder”, presented at XLC SECV Conference, Sevilla, Spain. November 2nd – 5th, 2005 (Poster).

� Benitez, M. J.; Rodríguez J., Lascano L. “Synthesis and characterization of calcium stabilized zirconia nanopowder”, presented at the 1st Science and Technology International Conference. Escuela Politécnica del Ejército. Quito, Ecuador. October 26th-28th, 2005 (Oral).

� Benitez, M. J.; Rodríguez J., Lascano L. “Synthesis and characterization of calcium stabilized zirconia nanopowder”, presented at the Seventh Giambiagi Winter School. Buenos Aires, Argentina. July 25th – 29th, 2005 (Poster).

TEACHING EXPERIENCE

� 2005-2006 Instituto Tecnológico Edwards Deming. Lecturer for Introduction to Statistics and Mathematics I to

undergraduate students.

� 2004-2005 Department of Physics, Escuela Politécnica Nacional.

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Teaching Assistant in Molecular Physics, Physics III and Modern Physics, to undergraduate physics and mechanical engineering students. Responsible for laboratory class preparation including conducting experiments, and grading of laboratory reports.

LANGUAGE SKILLS

� English: fluent � Italian: fluent � French: fluent � German: moderate � Spanish: fluent native

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