Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase...

51
Physik-Department Walther-Meißner-Institut Bayerische Akademie Lehrstuhl E23 für Tieftemperaturforschung der Wissenschaften Fluctuations and frustrated magnetism in sulphur substituted iron selenide Bachelor’s Thesis Ramona Melinda Stumberger Supervisor: PD Dr. Rudi Hackl Advisor: Dr. Andreas Baum Garching, 14. August 2019 Technische Universität München

Transcript of Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase...

Page 1: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

Seite 1 von 1

Physik-Department Walther-Meißner-Institut Bayerische Akademie

Lehrstuhl E23 für Tieftemperaturforschung der Wissenschaften

Fluctuations and frustratedmagnetism in sulphur substituted

iron selenide

Bachelor’s ThesisRamona Melinda Stumberger

Supervisor: PD Dr. Rudi HacklAdvisor: Dr. Andreas BaumGarching, 14. August 2019

Technische Universität München

Page 2: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8
Page 3: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

Contents

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

1 The iron chalcogenides . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Unit cell and structural distortion . . . . . . . . . . . . . . . . . . . . . 11.2 Phase diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 Raman spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.1 Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Intensity calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.3 Experimental set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3 Sample preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.1 SQUID magnetometry . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.2 Sample orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154.1 Spectra at 310 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154.2 Resonance at 40 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164.3 Temperature dependence in B1g symmetry . . . . . . . . . . . . . . . . 174.4 Phonons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174.5 Spectra in B2g symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . 18

5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215.1 Symmetry analysis at 310 K . . . . . . . . . . . . . . . . . . . . . . . . 215.2 Resonance at 40 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225.3 Magnon and luminescence . . . . . . . . . . . . . . . . . . . . . . . . . 235.4 Fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255.5 Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

A Sensitivity of the optical set-up of lab Raman II . . . . . . . . . . . . 31

B Superconductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

i

Page 4: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

Contents

C Correction factors of the B1g channel . . . . . . . . . . . . . . . . . . 35

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

ii

Page 5: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

Introduction

The study of various ordering phenomena and their interrelation is a main focusof contemporary solid-state physics. Here a class of materials called iron-basedsuperconductors (IBS) has gained considerable interest over the last decade [1–3] asvarious ordered phases such as magnetism, superconductivity, and nematicity canbe found in close proximity [4–7]. Each of these phenomena by itself already raisesseveral questions, and their interplay even more: What is the ’glue’ behind theformation of Cooper pairs up to high critical temperatures [8, 9]? Is the magnetismbased on localized or itinerant spins [10, 11], and how might superconductivity andmagnetic order cooperate, compete or interact [4, 12]? What is the origin of thenematic phase where puzzlingly large anisotropies of electronic phenomena arise atand even precede the small orthorhombic distortion of the lattice [13–15]? Herethe IBS provide access to these intertwined phases by control parameters such aspressure [16] or atomic substitution [5–7, 17, 18].

Among the IBS the iron chalcogenides such as FeSe and FeS stand out sincethe seemingly intimate link between magnetism and nematicity appears to belifted [19, 20] and thus the chicken and egg problem of finding the instability behindthese phenomena [21] might be solved here. However, recent studies on FeSe haverevealed magnetic interactions of considerable strength [22], which show ties to thenemato-structural phase transition [23]. One step towards better insight into thesematerials was achieved using Raman spectroscopy, a versatile method for invest-igating such correlated systems. The temperature and polarization dependence ofthe spectra show that magnetism in FeSe is comparable to what is found in thecuprates, but the emergence of long-range order is suppressed by frustration [24].In the related compound FeS the role of magnetism is even more obscure as severalcontradicting reports on the existence or absence of an ordered state exist [25–28].To fill the gap this study uses Raman spectroscopy to investigate FeSe0.7S0.3, acompound between the two end members found right at the border where thenematic phase is suppressed to zero temperature. Here a quantum critical point(QCP) [18] or a Lifshitz transition [29] were suggested to exist, therefore makingthis a crucial area of the phase diagram.

To this end this thesis is structured as follows: Chapter 1 introduces the iron-selenium-sulphur material class and gives an overview of the ordering phenomenafound therein. Raman spectroscopy and the corresponding setup used in the course

iii

Page 6: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

Introduction

of this thesis are presented in chapter 2. Chapter 3 then illustrates the steps takento prepare the sample for the Raman experiment, the results of which are presentedin chapter 4 and are discussed in chapter 5. The focus will be placed on similaritiesor disparities of the response from fluctuations and magnetism with respect to whatis found in the parent compound FeSe.

iv

Page 7: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

Chapter 1

The iron chalcogenides

1.1 Unit cell and structural distortion

Iron chalcogenides consist of quasi two-dimensional layers of Fe and chalcogen atoms(Se, Te or S) [Fig. 1.1(a)]. The Fe 3d orbitals dominate the electronic properties ofthe material [30–32].At room temperature iron chalcogenides have a tetragonal crystal structure [35].Fig. 1.1(b) shows the unit cell as seen along the c axis. The crystallographic unitcell is shown as green lines. As it contains two iron atoms per plane it is also called2-Fe cell. Another unit cell which can be defined contains 1 Fe atom and is shownas red dashed lines. This cell with the axes a and b is used when focussing on theelectronic and magnetic properties.Below a temperature Ts the crystal transforms from tetragonal to orthorhombic[Fig. 1.1(c)] [35]. This distortion takes place along the direction of the Fe-Fe bonds,which are drawn as dashed red lines. The relative change between the orthorhombicaxes a and b is less than 1% [36].

1.2 Phase diagram

Each family of iron-based superconductors has its own phase diagrams dependingon the type of control parameter [5–7, 17, 18, 37–39]. Substitution of atoms on bothlattice site is possible. This allows one to use the substitution of Se by S in FeSe asa control parameter, which yields the phase diagram shown in Fig. 1.2.Pure FeSe undergoes a structural transition from a tetragonal to an orthorhombiccrystal structure at Ts = 90K [19, 35]. This transition isn’t followed by the onsetof magnetic order [19, 20], unlike in other materials such as BaFe2As2 [41]. Su-perconductivity is found below Tc ≈ 9K [42]. Substitution of selenium by sulphursupresses the nematic phase and slightly enhances Tc to about 11K before suppress-ing superconductivity again. The other end member, FeS, does not exhibit anystructural changes down to lowest temperatures [35] and is superconducting belowTc ≈ 5K [43].

1

Page 8: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

Chapter 1 The iron chalcogenides

FeS/Se

T > Ts

(b)

Fe

Se/S

ab

c

T < Ts

(c)

a~

b~

(a)

cba

Figure 1.1: Unit cell of FeSe/FeS. Red and grey spheres represent Fe and Se/S atoms,respectively. (a) The FeSe/FeS layers are stacked along the c-axis. (b) View alongthe c axis in the tetragonal state. Red dashed lines denote the bonds between theFe atoms. Green lines depict the crystallographic 2-Fe cell. (c) Below Ts the crystaldeforms orthorhombically along the Fe-Fe bonds. The orthorhombic distortion isstrongly exaggerated here. Adapted from Refs. [33, 34].

The isovalent substitution of Se by S is supposed to provide only chemical pressure.Then one can assume that the application of external pressure has similar effects.However, as can be seen from Fig. 1.3, the phase diagram of FeSe under hydro-static pressure is strikingly different from that of FeSe1−xSx. While both sulphursubstitution and pressure suppress the nematic phase, the external pressure leads toa quadruplication of Tc and gives rise to a magnetically ordered spin density wavephase (SDW). These differences highlight that both phase diagrams are worth beingstudied in more detail.

1.2.1 Nematicity

The orthorhombic phase below Ts found in FeSe and FeSe1-xSx (x < 0.30) is callednematic phase which breaks the C4 rotational symmetry while preserving the trans-lational invariance. This goes along with strong anisotropies in several propertiessuch as magnetic susceptibility [45], thermal expansion [36] or orbital order [46],which cannot be explained in terms of the small anisotropy of the a and b axes.Unlike in the related iron pnictides, nematicity in FeSe1−xSx is not connected withlong-range magnetic order. This separation lead to the early conjecture that thenematic order in FeSe should not be driven by magnetism [19, 20]. However, as

2

Page 9: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

1.2 Phase diagram

Ts Tc

Sulphur content x

Tem

pera

ture

T (K

)

1

10

100

0.0 0.2 0.4 0.6 0.8 1.0

Nematic

Superconducting

FeSe1-xSx

Figure 1.2: Phase diagram of sulphur substituted FeSe. All compounds are tet-ragonal and paramagnetic at high temperatures. Pristine and slightly substitutedFeSe exhibit an orthorhombic paramagnetic phase, called nematic phase (shadedblue), below Ts (blue triangles). Superconductivity (yellow shaded area) is foundfor all substitution levels below Tc (blue line). Image courtesy of C. Petrovic [40]

was found during the last years, magnetic interactions play a more prominent rolein FeSe than previously thought [22, 24] and may still account for the observednematicity [47].

1.2.2 Magnetic order

No long range magnetic order was found in FeSe down to lowest temperat-ures [19, 20, 48] and no sign thereof was reported upon intermediate sulphur substi-tution (see Fig. 1.2). However, strong spin fluctuations were found and the fluctu-ating magnetic moment exceeds that of BaFe2As2 [22]. From theory the exchangeinteraction between neighbouring spins was predicted to be of similar size as in thecuprates [49]. It was observed by Raman scattering that the response in FeSe bears

3

Page 10: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

Chapter 1 The iron chalcogenides

Figure 1.3: Phase diagram of FeSe under hydrostatic pressure. Increasing the pres-sure P suppresses the nematic phase (blue) but promotes superconductivity (red),increasing the critical temperature Tc from 9K to almost 40K. Simultaneously longrange magnetic order arises (green) [44].

4

Page 11: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

1.2 Phase diagram

more similarities to the cuprates than to BaFe2As2 [24]. Altogether these resultsindicate that FeSe hosts strong interactions of mainly localized spins, whereby long-range order is suppressed by frustration due to the competition of different typesof magnetic order. The temperature dependence of the magnetic response suggestsa relationship to the structural transition [22–24]. The magnetic ground state ofpure FeS is even more unclear with reports ranging from no magnetic order [43, 50]over short-range magnetism [25, 26] to an ordered state below 120K [27]. No in-dication for the response from localized spins was found by Raman spectroscopy inpure FeS [51]. The study of this effect in FeSe0.7S0.3, where Ts is supposed to be justsuppressed to 0K (see Fig. 1.2), is part of this thesis.

1.2.3 Superconductivity

In 1996 superconductivity in iron-based systems was found [52]. Only since thepublication by Kamihara et al. ten years later [53], the interest in the iron-basedsuperconductors increased.

The temperature Tc of the superconducting transition of FeSe is about 9K at ambi-ent pressure [42]. This is among the lowest in the iron-based superconductors, butthere are many possibilities of increasing Tc, e.g. application of hydrostatic pres-sure [4] or intercalation of ions or molecules [38, 54]. Tc of FeSe can even reach morethan 100K [55] in monolayers.

5

Page 12: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8
Page 13: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

Chapter 2

Raman spectroscopy

This chapter introduces Raman spectroscopy as the main experimental method em-ployed in the course of this thesis and presents the setup used. More details onRaman scattering in correlated systems are given in Ref. [56].

2.1 Principle

The inelastic scattering of visible light from matter is called Raman scattering. Itwas predicted by Smekal in 1923 [57]. Experimentally it was discovered by Ramanand Krishnan in liquids in 1928 [58] and, in the same year, by Landsberg andMandelstam in crystals [59].Fig. 2.1 shows the principle of Raman scattering. In the course of a scattering eventa photon of energy ωi and momentum ki is absorbed and excites the system fromthe inital state |I〉 to an intermediate state |ν〉.This intermediate state |ν〉 can now couple to low energy excitations, e.g. phononsor magnons. This coupling creates or destroys an excitation of energy Ω. Thus thesystem assumes another intermediate state |ν ′〉 and then relaxes to its final state|F 〉 by emitting another photon with energy ωs and momentum ks.The so-called Raman shift Ω is the energy difference between the incident and theemitted photon, which is equal to the energy transferred from or to the material.

Ω = ωi − ωs (2.1)

The process whereby an excitation is created [Fig. 2.1(a)] is called Stokes process.Here the energy of the emitted photon is smaller than the energy of the incidentphoton. Its counterpart is called Anti-Stokes process [Fig. 2.1(b)]. Here, the de-struction of an excitation of energy Ω leads to the emission of a photon of higherenergy with respect to the incident light.In both cases the transferred momentum q can be considered small, putting Ramanscattering in the limit |q| = 0.Every scattering process involves two dipole transitions |I〉 → |ν〉 and |ν ′〉 → |F 〉.These transitions and the symmetry of the crystal are the basis of the Raman selec-tion rules.

7

Page 14: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

Chapter 2 Raman spectroscopy

(a) Stokes process (b) Anti-Stokes process

(Ω, q)|ν>

|ν'>

(ωs, ks)(ωi, ki)

|I> |F>

|ν'>

|F>(ωs, ks)

(Ω, q)

|ν>

(ωi, ki)

|I>

Figure 2.1: Simplified scheme of a Raman scattering process. The incident photon(ωi,ki) (green wavy line) excites the system from its initial state |I〉 to an interme-diate state |ν〉. By either (a) creating or (b) destroying an excitation (Ω,q) (curledline) the system makes a transition to a second intermediate state |ν ′〉, and relaxesto its final state |F 〉 by emission of a (a) red- or (b) blue-shifted photon (ωs,ks) [34].

As shown in Fig. 2.2, every set of polarizations (ei, es) of the incident and scatteredlight projects the sum of two symmetries. Thus, each symmetry can be extrac-ted as a linear combination of spectra. The relevant coordinate system for theselection rules is given by the sample unit cell. Therefore, througout this thesis,the polarizations ei,s will be expressed in terms of the crystal axes (a, b, a, b) (seeFig. 1.1). In the iron chalcogenides different unit cells can be defined. The crystal-lographic unit cell (in the tetragonal state) is called the 2-Fe cell as it contains twoiron atoms. It is the relevant cell for phonons. For electronic and magnetic excit-ations the 1-Fe cell, shown as solid lines in Fig. 2.2, is the basis of the selection rules.

In general, both intermediate states |ν〉 and |ν ′〉 are virtual states, which exist withintime and energy uncertainty. But these intermediate states can also be eigenstatesof the system. Then, the scattering intensity diverges as the energy denominator (inperturbation theory) becomes zero [61]. This effect is called resonance and providesa probe to the electronic structure of the material [34].

2.2 Intensity calibration

Experimentally, one measures the count rate Nis of detected photons for a certainwavelength of the scattered light, corresponding to a certain Raman shift Ω.

8

Page 15: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

2.2 Intensity calibration

abA2g + B1g

RRA1g + A2g

abA2g + B2g

RLB1g + B2g

aaA1g + B2g

aaA1g + B1g

~~

~~

Figure 2.2: Selection rules in tetragonal iron chalcogenides. Red spheres depict theiron atoms. The projected symmetries are given with respect to the 1-Fe cell whichis drawn as solid lines. The 2-Fe unit cell is shown as dashed lines. Blue and redarrows denote the polarizations of the incident and scattered light, respectively [60].

The physical property of interest is the susceptibility χ′′,

Rχ′′is(Ω, T ) =Nis

Pi · s(ωs)

ω2i

ωsω

[1− exp

(− hΩ

kBT

)](2.2)

In this equation Pi is the absorbed laser power of the incident light and ωi,s are the en-ergies of the incident or scattered photons, respectively. ω = 20000 is used to achievenormalization close to one. To correct the data the energy-dependent sensitivity ofthe instrument s(ωs) needs to be taken into account to calculate χ′′. This sensitivitywas determined by calibration [62]. During this thesis the sensitivity curve for asecond spectroscopic setup (lab Raman II) was determined experimentally (see Ap-pendix A). The constant R includes temperature- and energy-independent factors.The complete derivation can be found in Refs. [34] and [56].

9

Page 16: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

Chapter 2 Raman spectroscopy

2.3 Experimental set-up

Basically, the set-up for Raman spectroscopy consists of a source of monochromaticpolarized (P) light. The desired polarization states of the scattered light can be se-lected by the analyzer (A). The spectrometer with a detector analyses the scatteredlight as a function of wavelength.

A simplified schematic of the setup used during this thesis is shown in Fig. 2.3. Amore detailed description can be found in Ref. [34].

cryostat1.8-350 K

samplespectrometer

CCDPC0 200 400 600 800 1000

0

1

2

3 x'x' (A1g +B2g)

x'y' (B1g)

Rχ'

' (Ω

,T) (

coun

ts s

-1 m

W-1)

Raman shift Ω (cm-1)

χ '' σ'Ω

8 cm-1 ≈ 1 meV

BaFe2As2

T = 140 K

P

A

Figure 2.3: Simplified scheme of the experimental set-up in lab Raman I. P andA are polarizer and analyzer, respectively. The incident light (green) is polarized(P) and focussed on the sample, which is mounted inside the cryostat and can beset to temperatures between 1.8K and 350K. The polarization state of the collec-ted scattered light (red) is selected, and the intensity is recorded as a function ofwavelength using the spectrometer and CCD detector. Adapted from [34].

10

Page 17: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

Chapter 3

Sample preparation

From a set of FeSe1−xSx samples having various S concentrations x the materialwith x = 0.3 was selected since it is supposed to be very close to the concentrationwhere Ts vanishes.

3.1 SQUID magnetometry

The critical temperature Tc was found to be a sensitive probe to the sample stoi-chiometry in iron chalcogenides [63, 64]. To determine Tc the sample’s magnetizationwas measured as a function of temperature using a Quantum Design MPMS XL-7SQUID magnetometer.The results are shown in Fig. 3.1. First the sample was cooled in zero field (zfc)to 2K. Then the magnetization was determined upon warming at 0.1 K/min in a

0 2 4 6 8 1 0 1 2 1 4

- 1 0

- 5

0

F e S e 0 . 7 S 0 . 3 # 1 f c z f c

Magn

etic M

omen

t (10-4 em

u)

T e m p e r a t u r e T ( K )

T o nc = 8 . 0 K

Figure 3.1: Magnetic moment of FeSe0.7S0.3 as a function of temperature: The redcurve (fc) is obtained by cooling down the crystal in an external magnetic field,while the black curve shows the magnetization after cooling without magnetic field(zfc).

11

Page 18: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

Chapter 3 Sample preparation

field of H = 10Oe. Second, the sample was cooled to 2K in an applied field ofH = 10Oe (fc) and was measured upon warming.The zfc curve shows a strong decrease of the magnetic moment when supercon-ductivity sets in. In contrast, virtually no change is seen in the fc which indicatesstrong pinning of the magnetic flux. A similar result was seen previously for FeSsamples [28]. Taking the point where both curves start to deviate from each otheras the transition temperature yields T on

c ≈ 8K as expected from the phase diagram(Fig. 1.2).

3.2 Sample orientation

The correct orientation of the sample with respect to the light polarizations is crucialto obtain the selection rules (Fig. 2.2). Usually the polarizations are set in thelaboratory coordinate system. To this end the orientation of the crystal axes wasdetermined by X-ray diffraction using the Laue camera of the crystal laboratory ofthe TUM.The Laue diffraction image is shown in Fig. 3.2. Two sets of four diffraction pointseach can be recognized. They project the fourfold symmetry of the tetragonal crys-tal and originate from the quadratic arrangement of the Fe and the Se/S atoms,respectively. As can be seen the sample is well oriented with its axes pointing alongthe vertical and horizontal direction of the detector.To test this orientation the selection rules can be used. For crossed light polariz-ations along the Fe-Fe bonds, (ei, es) = (a, b), the out of phase vibration of ironatoms is projected [32]. By rotating the polarizations by 45 the phonon peak mustvanish. This is shown in Fig. 3.3 and confirms that the sample is oriented with thecrystallographic axes a and b parallel to the horizontal and vertical axes, x and y,of the laboratory frame.

12

Page 19: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

3.2 Sample orientation

Figure 3.2: Laue diffraction of the FeSe0.7S0.3 sample. The fourfold symmetry resultsin two sets of four points, stemming from the Fe and Se/S atoms, respectively, whichare rotated by 45.

1 5 0 1 6 0 1 7 0 1 8 0 1 9 0 2 0 0 2 1 0 2 2 0 2 3 001234567

p o l a r i z a t i o n ( e i , e s ) y x = b a x ' y ' = a b

Rχ'' (Ω

,T) (c

ounts

s-1 mW -1

)

R a m a n S h i f t Ω ( c m - 1 )

F e S e 0 . 7 S 0 . 3T = 3 1 6 KP a b s = 4 m Wλi = 5 7 5 n m1 5 0 1 8 0 2 1 0 2 4 00

1

Figure 3.3: Test of the sample orientation using the Raman selection rules. Forlight polarized along the Fe-Fe bonds a and b (green line) the phonon at 200 cm−1

is visible. By rotating the polarizations by 45 (red line) the phonon peak vanishes.The inset zooms in on the ba spectrum to highlight that no leakage from the phononpeak occurs.

13

Page 20: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8
Page 21: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

Chapter 4

Results

This chapter presents the results of the Raman scattering experiment on FeSe0.7S0.3.These results will be discussed in the subsequent chapter. All spectra shown arefully corrected according to Eq. 2.2.Typically spectra were measured in steps of ∆Ω = 5 cm−1 and a resolution of ∆ν ≈5 cm−1 up to Ω = 250 cm−1 to resolve narrow features. Spectra extending to higherenergies were measured using bigger step widths and a reduced resolution as nosharp lines are expected. The absorbed power of the incident laser was typically setat Pabs = 4 mW. Temperatures as given were measured at the sample holder.

4.1 Spectra at 310 K

Fig. 4.1 shows spectra with different polarizations at T = 310 K measured using theλi = 575 nm laserline. All spectra, except for the spectrum in ba polarization have

0 500 1000 1500 2000 2500 3000 35000.0

0.5

1.0

1.5 FeSe0.7S0.3

T = 310KPabs = 4 mWλi = 575nm

bb ba RR

RL aa ab

Rχ'

'(Ω

,T)(

coun

tss-1

mW

-1)

Raman Shift Ω (cm-1)

Fe

Se/S

a

ba~b~

Figure 4.1: Spectra of FeSe0.7S0.3 at 310K measured with polarizations as given inthe legend. The inset shows the crystal axes in the ab-plane.

15

Page 22: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

Chapter 4 Results

0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 00

5

1 0

1 5

F e S e 0 . 7 S 0 . 3b a p o l .

l a s e r w a v e l e n g t h λi 4 5 8 n m 4 5 8 n m 5 1 4 n m 5 7 5 n m

'' (Ω,T)

(cou

nts s-1 m

W -1)

R a m a n S h i f t Ω ( c m - 1 )

( a ) T = 4 0 K

0 5 0 0 1 0 0 0 1 5 0 00

1

2

3 ( b )

Rχ'' (Ω

,T) (c

ounts

s-1 mW -1

)

R a m a n S h i f t Ω ( c m - 1 )

Figure 4.2: Spectra of FeSe0.7S0.3 in ba polarization at T = 40 K measured withwavelenghts of the incident light as given in the legend. Panel (b) highlights the lowenergy part of the spectra.

a strong peak around 200 cm−1. This peak includes the A1g and B1g phonon lines,which are not resolved.Spectra with parallel polarizations show another sharp peak at around 350 cm−1.The spectra with aa, ba, and RL polarizations are dominated by a broad peak witha maximum at around 600 cm−1 and decrease to higher energies. For ab, RR, andbb polarizations, the spectra continuously increase to higher energies above around500 cm−1. All spectra flatten above 2500 cm−1.

4.2 Resonance at 40 K

The spectra in Fig. 4.2 were recorded in ba polarization at a temperature of 40K usingwavelengths of 458 nm (blue), 514 nm (green), and 575 nm (olive) for excitation. Themeasurement with a excitation wavelength of 458 nm was repeated (dashed and solidblue line). The range below 1200 cm−1 can be reproduced, whereas above 1200 cm−1

the spectra vary between the measurements. Below 1200 cm−1, as highlighted inFig. 4.2(b), a broad peak at around 460 cm−1 can be seen in all spectra. Towardsshorter wavelengths, the peak gains in intensity. In addition, a small peak apearsat about 200 cm−1 for λi = 514 nm and gains intensity for λi = 458 nm. Above1200 cm−1, all spectra show a broad excitation, the maximum of which shifts tohigher energies upon decreasing the wavelength.

16

Page 23: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

4.3 Temperature dependence in B1g symmetry

0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 2 5 0 0 3 0 0 0 3 5 0 00 . 0

0 . 5

1 . 0

1 . 5

2 . 0

2 . 5

3 . 0 F e S e 0 . 7 S 0 . 3b a p o l a r i z a t i o nP a b s = 4 m Wλi = 5 7 5 n m

T ( K ) 1 0 2 0 3 0 4 0 5 0 6 0 7 0 9 0 1 1 0 1 3 0 1 5 0 2 0 0 2 5 0 3 1 0

'' (Ω,T)

(cou

nts s-1 m

W -1)

R a m a n S h i f t Ω ( c m - 1 )

0 1 0 0 2 0 00 . 00 . 51 . 01 . 5

Figure 4.3: Raw data of FeSe0.7S0.3 in ba polarization at temperatures as indicated.The spectra were measured at a wavelength λi = 575 nm of the incident light andan absorbed power of Pabs = 4mW.

4.3 Temperature dependence in B1g symmetry

Fig. 4.3 shows measurements in ba polarizations at temperatures as indicated. Inall spectra a peak centered at roughly 500 cm−1 can be seen. Above 1200 cm−1,many spectra also exhibit a broad peak with a maximum in the range of 2000-2500 cm−1. The inset in 4.3 highlights the low-energy region. Here, with decreasingtemperature, the emergence of an increasingly sharp peak can be seen, which shiftsto lower energies during cooling.

4.4 Phonons

Fig. 4.4 shows Raman spectra in aa polarization as a function of temperature. Thepeak found at Ω ≈ 170 cm−1 for T = 310K shifts to 177 cm−1 at lowest temperatures.This peak can be identified as the c-axis in-phase vibration of the Se and S atomssimilar to FeSe [24, 65]. The second peak, which shifts from 200 cm−1 at 310K to210 cm−1 at 20K, stems from the out-of-phase vibration of the iron atoms [24, 65].This phonon has B1g symmetry in the 2-Fe crystallographic cell and hence appearsin B2g symmetry when the 1-Fe cell is used as basis as those cells are rotated by

17

Page 24: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

Chapter 4 Results

160 180 200 220 2400

5

10

15

20

25 FeSe0.7S0.3

aa polarizationPabs = 4mWλi = 575nm

T (K)20407090

150200250310

Rχ'

'(Ω

,T)(

coun

tss-1

mW

-1)

Raman Shift Ω (cm-1)

Fe

Se/S

a

b

Figure 4.4: Raman spectra of FeSe0.7S0.3 in aa polarization projecting A1g +B1g

symmetry at temperatures as given in the legend. Two peaks can be seen whichharden and sharpen monotonously upon cooling.

45 with respect to each other [34]. A weak peak is seen at 237 cm−1 for the lowesttemperatures. As the aa polarization entails no projection onto the c-axis [28, 34]it cannot be one of the two Eg phonon modes which exist in tetragonal IBS [32].

4.5 Spectra in B2g symmetry

Fig. 4.5 shows Raman spectra of FeSe0.7S0.3 in ab polarization. The spectra weremeasured using the 575 nm laserline at T = 40K and T = 310K as indicated.The continuum at T = 310K increases from 5 to about 150 cm−1 and is flat athigher energies. At 40K a weak broad peak appears which is centered around 2000-2500 cm−1 similar to what is seen in some spectra in ba polarizations (Fig. 4.5).Superposed on the continuum is a phonon line at Ω ≈ 200 cm−1. This is the Fe B1g

phonon [24, 65]. At 310K the line is symmetric. Upon cooling it shifts to higherenergies (cf. Fig. 4.4). Additional spectral weight is found at the high energy sideof the phonon line (see inset) at 40K but not at 310K.

18

Page 25: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

4.5 Spectra in B2g symmetry

0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 2 5 0 0 3 0 0 0 3 5 0 00

2

4

6

8 F e S e 0 . 7 S 0 . 3a b p o l a r i z a t i o nP a b s = 4 m Wλi = 5 7 5 n m

T ( K ) 4 0 3 1 0

Rχ'' (Ω

,T) (c

ounts

s-1 mW -1

)

R a m a n S h i f t Ω ( c m - 1 )

0 4 0 0 8 0 0 1 2 0 00 . 0

0 . 5

1 . 0

Figure 4.5: Raman spectra of FeSe0.7S0.3 measured in ab polarization using the575 nm laserline at temperatures as indicated. The inset highlights the continuumat low to medium energies. At 310K the continuum increases up to 100 cm−1 andis flat otherwise. At T = 40K a weak broad peak centered around 2000-2500 cm−1

is visible. Superposed onto the continuum is the line of the Fe B1g phonon at about200 cm−1 which hardens upon cooling and acquires an asymmetric line shape.

19

Page 26: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8
Page 27: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

Chapter 5

Discussion

5.1 Symmetry analysis at 310 K

Fig. 5.1 shows spectra for all four main symmetries of the tetragonal crystal. Thespectra are extracted as linear combinations of the raw data shown in Fig. 4.1according to the selection rules (see Fig. 2.2). A1g and B2g symmetry show a sharppeak at around 200 cm−1. Both the A1g and B1g (2 Fe) phonon lines appear inthis energy range, similar to FeSe [24], but can not be resolved here. The spectrumin A1g symmetry has a second peak at around 350 cm−1. No phononic mode isexpected at this energy [24, 28]. In earlier experiments on BaFe2As2, a similar peakwas observed at this energy and found to stem from contamination of the sample

0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 2 5 0 0 3 0 0 0 3 5 0 0

0 . 2

0 . 4

0 . 6

0 . 8

0

F e S e 0 . 7 S 0 . 3T = 3 1 0 K

A 1 g A 2 g B 1 g B 2 g

Rχ'' (Ω

,T) (c

ounts

s-1 mW -1

)

R a m a n S h i f t Ω ( c m - 1 )

Figure 5.1: Symmetry analysis of FeSe0.7S0.3 at 310K. Raman spectra of FeSe0.7S0.3

at T = 310K for the four symmetries given in the legend. The spectra in A1g and B2g

symmetry comprise phonon modes at Ω ≈ 200 cm−1. An additional peak is found at350 cm−1 in A1g. All spectra except B1g show a monotonous increase towards higherenergies. The B1g response is dominated by the broad asymmetric peak centeredaround 550 cm−1.

21

Page 28: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

Chapter 5 Discussion

surface at low temperatures [66]. Given that the spectra shown here were taken atT = 310K this explanation seems unlikely.De Faria et al. found that maghemite (γ − Fe2O3), lepidocrocite (γ−FeOOH),and feroxyhyte (δ−FeOOH) show peaks in their Raman spectra at this energy [67].Therefore the peak at 350 cm−1 may indicate sample degradation by oxidation.In B1g symmetry, a broad asymmetric peak with a maximum between 500-550 cm−1

dominates the spectrum. This peak was identified in FeSe as the response of frus-trated order of localized spins [24]. The spectrum in A2g symmetry shows thesmallest intensity. Only above around 2000 cm−1 it becomes comparable to theresponse of the other symmetries. For this reason, the A2g response is neglected forthe following considerations where Ω < 2000 cm−1.Overall, the spectra of all symmetries are comparable to similar measurements inFeSe [24, 34]. This suggests that the high temperature phase undergoes no significantchange of the magnetic and electronic properties upon sulphur substitution fromFeSe to FeSe0.7S0.3.

5.2 Resonance at 40 K

Fig. 5.2(a) shows spectra measured at T = 40K for three different energies ωi ofthe incident light as indicated. The spectra were multiplied to match the peakheight at Ω ≈ 460 cm−1. Only the intensity, but not the spectral shape, of thisresponse depends on ωi. This illustrates that the resonance condition for the Ramanscattering process (cf. Fig. 2.1) is only met for the incident light. A resonancefor ωs would affect the line shape. A similar situation was found previously forFeSe [34, 68], indicating that the electronic structure is largely unaffected by thesulphur substitution up to x = 0.30.At higher energies the spectra exhibit a broad maximum, the peak energy of whichdepends on ωi. To analyze this feature Fig. 5.2(b) shows the intensity as a functionof the energy of the scattered photons. These spectra are corrected according toEq. 2.2 except for the Bose factor and were multiplied to match at the lowest energyof the scattered photons. Besides the putative two-magnon excitation, marked byasterisks, two additional peaks can be identified. The low energy peak is markedby a dashed line. This excitation occurs at a fixed absolute energy ωs suggestingluminescence as a possible origin.The second broad maximum shows a weak dependence of the peak energy on ωi

as highlighted by the grey shaded area. An excitation with similar peak energieswas found in FeSe [34] and was tentatively identified as a luminescence with strongsymmetry dependence. However, in FeSe the main contribution was found in B2g

symmetry and not B1g symmetry, indicating that the two excitations are differentin origin.

22

Page 29: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

5.3 Magnon and luminescence

0 2000 4000 6000 80000

2

4

6

8

14 16 18 20 22

1.7 2.0 2.2 2.5 2.7

0

2

4

6

8FeSe0.7S0.3

B1g

T = 40K

Rχ''(2.71eV)Rχ''(2.41eV) ×1.3Rχ''(2.16eV) ×2.4R

χ''(Ω

,ωi)

(cou

nts

s-1m

W-1

)

Raman Shift Ω (cm-1)

(a)

**

(b)

I(ωi=2.71eV)I(ωi=2.41eV) ×1.5I(ωi=2.16eV) ×4

Energy ωs (eV)

I(ω

s)(c

ount

ss-1

mW

-1)

Energy ωs (103 cm-1)

*

Figure 5.2: Spectra of FeSe0.7S0.3 in B1g symmetry at T = 40K measured withincident photon energies as given in the legend. (a) Raman susceptibility Rχ′′ as afunction of the Raman shift. The spectra are multiplied by factors as indicated tomatch the peak height at Ω ≈ 460 cm−1. The shape of this peak does not depend onthe incident energy. At higher shifts a broad peak appears with increasing photonenergy, the maximum of which shifts to higher energies. (b) Intensity of the scatteredlight as a function of ωs. The spectra are multiplied to match at the lowest energy.At ωs ≈ 1.8 eV a small peak is found for all laserlines (dashed vertical line). A broadhump develops and shifts to higher energies for shorter wavelengths of the incidentlight. Its approximate maximum is marked by the grey shaded area. Asterisks markthe putative two-magnon response.

5.3 Magnon and luminescence

Fig. 5.3 shows spectra in the B1g channel at temperatures ranging from 310K to10K. The spectra can be divided into two main parts. Above 1200 cm−1 the contri-bution from presumably luminescence dominates. Therefore the raw data displayedin Fig. 4.3 were multiplied to match at 1200 cm−1. The factors of this multiplica-tion are listed in Appendix C. The luminescence peak shows no clear temperaturedependence, but varies between the different measurements, likely depending on theexact spot position on the sample (cf. Fig.4.2).At lowest energies (Ω < 100 cm−1) a sharp peak emerges below T = 60K. A secondexcitation which also gains intensity at low T is found at Ω ≈ 200 cm−1. Thedominating effect in the mid-energy range is the asymmetric peak around 500 cm−1.To identify these excitations a comparison to the parent compound FeSe is benificial.To this end Fig. 5.4 shows spectra in B1g symmetry of FeSe0.7S0.3 and of FeSe at

23

Page 30: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

Chapter 5 Discussion

0 1 0 0 0 2 0 0 0 3 0 0 00 . 0

0 . 5

1 . 0

F e S e 0 . 7 S 0 . 3B 1 g

T ( K ) 1 0 2 0 3 0 4 0 5 0 6 0 7 0 9 0 1 1 0 1 3 0 1 5 0 2 0 0 2 5 0 3 1 0

'' (Ω,T)

(cou

nts s-1 m

W -1)

R a m a n S h i f t Ω ( c m - 1 )

Figure 5.3: Temperature dependence of the B1g channel. Full set of spectra attemperatures as indicated. The spectra are multiplied to match at Ω ≈ 1200 cm−1.Multiple excitations having different temperature dependences overlap.

0 5 0 0 1 0 0 0 1 5 0 00 . 0

0 . 5

1 . 0F e S e 0 . 7 S 0 . 3B 1 g

T ( K ) 2 0 9 0 3 1 0

Rχ'' (Ω

,T) (c

ounts

s-1 mW -1

)

R a m a n S h i f t Ω ( c m - 1 )

( a )

0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0

( b ) F e S eB 1 g

Figure 5.4: B1g spectra of (a) FeSe0.7S0.3 and (b) FeSe at three characteristic temper-atures. The data of FeSe are taken from Refs. [24, 34]. In FeSe0.7S0.3 the peak withmaximum at 550 cm−1 at 310K continuously softens upon cooling but gains intensityonly for T = 20K. In pristine FeSe the same excitation softens from about 550 cm−1

at 310K to 460 cm−1 at 90K but hardens again to 530 cm−1 at 20K. Sharp peaksbelow 100 cm−1 originating from fluctuations are seen in FeSe0.7S0.3 at T = 20K andin FeSe at T ≤ 90K, respectively. An additional excitation at 200 cm−1 is found inFeSe0.7S0.3 at 20K and in FeSe at 90K.

24

Page 31: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

5.4 Fluctuations

three characteristic temperatures. For both compounds the spectrum at T = 310Kincreases linearly at low energies and forms a broad maximum centred at about550 cm−1 which softens upon cooling. In FeSe0.7S0.3 [Fig. 5.4(a)] this softeningcontinous to lowest temperatures where a peak energy of 460 cm−1 is reached. Thisis similar to the spectrum found in FeSe [Fig. 5.4(b)] at T = 90 K ≈ Ts. Inthe pristine material below Ts the peak hardens again, reaching 530 cm−1 at 20K.The continuous gain in peak height found in FeSe is not observed in the sulphursubstituted compound, where an increase is only seen at T = 20K. This may be,however, an effect of the multiplication of the spectra. In FeSe this excitation wassimulated using a Heisenberg model [68] and, due to the agreement between theoryand experiment, was identified as response from localized spins. In FeSe0.7S0.3 asimilar line shape is found. Additionally, the softening upon cooling to 20K inFeSe0.7S0.3 is comparable to what is observed in FeSe above Ts. This leads to thecorollary that the response from localized spins persists in FeSe0.7S0.3 whereby thetemperature dependence is compatible with a shift of Ts → 0.

5.4 Fluctuations

Fig. 5.5 zooms in on the low energy part of the spectra presented already in Fig. 5.3.With decreasing temperature the initial slope of the spectra increases and a peakforms, becoming discernible below T ≤ 60K . Upon further cooling the peaksharpens, gains intensity and shifts to lower energies. Its approximate positionis indicated by the grey shaded area.In FeSe the Se A1g phonon at 180 cm−1 appears in the B1g spectra for T < Ts [32, 34].The energy range where the phonon is found in FeSe0.7S0.3 (cf. Fig. 4.4) is incasedby the dotted black box. No peak is observable here which is consistent with thefact that no nematic transition is found in the observed temperature range (see Fig1.2).The behaviour of the low energy peak (grey shade) is known from fluctuations inBaFe2As2, Ba(Fe1−xCox)2As2, and pristine FeSe. There the intensity of the fluctu-ations becomes maximal at the nematic transition at Ts. In the Ba-122 compoundsthey vanish immediately at the nearby (or even coincident) magnetic phase trans-ition, indicating their spin nature. In FeSe they persist down to lowest temperaturesand may be similar to the spin fluctuations in BaFe2As2 when the magnetic trans-ition is suppressed, Tm → 0. Alternatively they were interpreted as charge nematicfluctuations [69]. The evolution in FeSe0.7S0.3 is qualitatively similar to that in FeSefor Ts → 0, indicating that the fluctuations may be of the same origin. The rela-tionship of these fluctuations and the nematic phase is accentuated by their similarsuppression with increasing sulphur content in FeSe1−xSx as shown in Fig. 5.6. HereTmax

fluc is the temperature where the peak from fluctuations in the spectra achieves itsmaximum intensity before decreasing again. The values for x = 0.05 and x = 0.20

25

Page 32: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

Chapter 5 Discussion

0 50 100 150 200 2500.0

0.5

1.0

FeSe0.7S0.3

B1g

T (K)1020304050607090

110130150200250310

Rχ'

'(Ω

,T)(

coun

tss-1

mW

-1)

Raman Shift Ω (cm-1)

Figure 5.5: Spectra in B1g symmetry highlighting the low energy region. Uponcooling a peak at Ω ≈ 30 cm−1 becomes discernible below T ≈ 60K which softensand gains intensity. Its approximate temperature dependence is shown by the greyshaded area. The black dashed box indicates the energy range where the Se/Sphonon is found in A1g symmetry. No peak appears in the B1g spectra shown here.

are taken from the analysis which will appear in the master’s thesis of L. Peis [70].In FeSe0.7S0.3, Tmax

fluc = 10 K is given by the lowest temperature where fluctuationscould be observed and Ts(x = 0.3) = 0 is extrapolated from the data in Fig. 1.2.Both characteristic temperatures are almost identical over the studied range of x.To facilitate a quantitative study of the temperature dependence of the fluctuationsa decomposition of the spectra is necessary.

5.5 Decomposition

As shown above the spectra in B1g symmetry comprise several different excitations.At all temperatures the two-magnon response from localized spins is superimposedon a continuum of electron-hole excitations. Additionally at low temperatures ahump around 200 cm−1 arises and the fluctuation peak dominates the low energyregion.An attempt to isolate the various contributions to the spectra can be made alongthe lines of Refs. [24] and [34] and is shown in Fig. 5.7. To describe the electron-holecontinuum for each temperature a phenomenological function used previously inBaFe2As2 [71, 72] is fitted to the corresponding B2g spectra (excluding the phononline), as shown in the insets. Here no factor is applied to either the B1g or the B2g

spectra as the latter cannot be matched at any energy.For T = 310K [Fig. 5.7(a)] this function (dashed blue line) is then subtracted from

26

Page 33: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

5.5 Decomposition

0 . 1 0 . 2 0 . 3 0 . 4002 04 06 08 0

1 0 0F e S e 1 - x S x T m a x

f l u c t T s

Te

mpera

ture T

(K)

S u l p h u r c o n t e n t x

Figure 5.6: Evolution of the fluctuations with sulphur substitution. Tmaxfluc denotes

the temperature where the peak from fluctuations reaches its maximum intensity.Ts is the nematic transition temperature taken from Fig. 1.2. Both exhibit a similarsuppression when S is substituted for Se and vanish around x = 0.30.

the B1g data (black line) and directly yields an approximation to the spectral shapeof the two-magnon peak (green dashed line).At T = 40K [Fig. 5.7(b)] the peak from fluctuations at Ω ≈ 24 cm−1 is describedbased on Aslamazov-Larkin diagrams [24, 73] which can model both charge and spinfluctuations. Subtracting this contribution (red dashed line) and the electron-holecontinuum (dashed blue line) from the B1g spectrum (black line) then yields thetwo-magnon peak and the excitation around 200 cm−1 (green dashed line) whichcurrently can not be separated.This purely qualitative decomposition indicates that the spectra for FeSe0.7S0.3 canbe treated in a similar way as those of FeSe, although the additional contributionsat 200 cm−1 and from putative luminescence increase the uncertainty and remainhard to explain.

27

Page 34: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

Chapter 5 Discussion

0 4 0 0 8 0 00 . 0

0 . 5

1 . 0

1 . 5

0 4 0 0 8 0 0 1 2 0 0

Rχ'' (Ω

,T) (c

ounts

s-1 mW -1

)

R a m a n S h i f t Ω ( c m - 1 )

( b ) T = 4 0 KB 1 g

( a )F e S e 0 . 7 S 0 . 3T = 3 1 0 KB 1 g

4 0 0 8 0 000 . 0

0 . 4B 2 g

0 4 0 0 8 0 0

0 . 4

0 B 2 g

Figure 5.7: Contributions to the B1g spectra for (a) T = 310K and (b) T = 40K.Experimental spectra are shown as black solid lines. The insets show the B2g spectraat the corresponding temperature and an analytic approximation to the electron-holecontinuum (dashed blue line), which is assumed to be symmetry independent anda good approximation for B1g symmetry. The low energy peak in (b) at T = 40Kis modelled via AL-type diagrams (red). Substracting these two contributions fromthe experimental B1g spectra recovers the approximate shape of the response fromlocalized spins (green) [34].

28

Page 35: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

Chapter 6

Summary

In this thesis FeSe0.7S0.3, a compound of the selenium-sulphur series of iron chal-cogenide superconductors, was studied using Raman spectroscopy with the focusplaced on magnetism and fluctuation phenomena. To this end Raman spectra wereacquired as a function of temperature, excitation energy, and polarization. Sym-metry resolved spectra at 310K closely resemble those from the parent compoundFeSe, where phonons and a two-magnon peak from frustrated order of localizedspins are superposed on a continuum of electron-hole excitations. Measurementswith various excitation energies reveal two contributions putatively from lumines-cence between 1.8 eV to 2 eV. For the two-magnon excitation the line shape does notdepend on the energy of the incident light as in FeSe.The response in the B1g channel shows a softening of the two-magnon mode andthe emergence of a peak ascribed to fluctuations when the temperature is lowered.The qualitative temperature dependence of both excitations is found to be similarto that of pristine FeSe above the nemato-structural transition temperature Ts. Nosign of such a transition was seen from the phonon modes in FeSe0.7S0.3.The comparison of FeSe0.7S0.3 with its parent compound FeSe shows no indicationfor substantial changes to the magnetic and electronic configuration by sulphur sub-stitution, even though a zero-temperature phase transition was supposed at slightlylower sulphur levels. The results acquired in this work suggest than FeSe0.7S0.3 canbe seen similar to pristine FeSe whereby Ts is zero.Scheduled measurements on samples with higher sulphur content are supposed toclarify whether this behaviour is due to Ts indeed being fully suppressed in FeSe0.7S0.3

or whether a vestigial nematic phase below the experimentally accessible temperat-ure range remains.

29

Page 36: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8
Page 37: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

Appendix A

Sensitivity of the optical set-up oflab Raman II

Measurements of the Raman scattered light over a wide energy range require energydependent corrections with respect to the sensitivity of the setup s(ω) according toEq. 2.2. For the setup Raman I used in this thesis this sensitivity was determinedexperimentally [34, 62].As measurements were also intended in lab Raman II a sensitivity curve was requiredfor this setup. Recently new gratings were inserted into the spectrometer (Jobin-Yvon T64000) as well as a new CCD detector (Jobin-Yvon Symphony II) as theprevious one was found to be defective [74]. Therefore the transmission of thespectrometer with its new gratings and the quantum efficiency (QE) of the newCCD had to be determined. A detailed description of the calibration process andthe whole optical setup can be found in Ref. [74].To determine the transmission of the spectrometer the laser beam is directed throughthe spectrometer where all gratings are set to −1st order and the light is polarizedparallel to the grating’s dispersion direction (perpendicular to the lines) and exitsat the monochannel exit after the third monochromator. The ratio of its powerbefore the entrance slit and after the monochannel exit is the transmission. Thisquantity, determined for all available laserlines, is shown in Fig. A.1(a). It exhibitsa maximum in the green range and drops rapidly towards both shorter and longerwavelengths, and agrees well with similar measurements of the old gratings [75].To determine the QE of the CCD this beam is directed on the CCD, and its intensityis measured by the detector. To avoid overflow of the CCD the beam needs to beattenuated sufficiently using neutral density (ND) filters to keep the number ofregistered counts below 216 = 65536 being the maximum capacity of the analog-to-digital converter (ADC). As, in turn, the optical density (OD) of the ND filters alsodepends on the wavelength it needs to be measured. This can be done by directlymeasuring their transmission using a power meter (method 1).Alternatively, the intensity of the beam on the CCD can be measured for differentcombinations of ND filters (method 2). By solving a set of equations [74] the ODand the QE can be determined. The results obtained via the two independent

31

Page 38: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

Appendix A Sensitivity of the optical set-up of lab Raman II

4 0 0 5 0 0 6 0 0 7 0 0 8 0 0

0 . 0 5

0 . 1 0

0 . 1 5

0 . 2 0

0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0

0 . 20 . 40 . 60 . 81 . 0

0

T JY

64k(λ

)

W a v e l e n g t h λ ( n m )

( a ) ( b )

N D f i l t e r d i r e c t l y m e a s u r e d N D f i l t e r c a l c u l a t e d C C D s p e c i f i c a t i o n s

QE(λ)

W a v e l e n g t h λ ( n m )

Figure A.1: Optical sensitivity of the setup in lab Raman II. (a) Transmis-sion through the Jobin-Yvon T64000 spectrometer as a function of wavelength.(b) Quantum efficiency (QE) of the Jobin-Yvon Symphony II CCD as a function ofwavelength. To determine the QE the optical densities (ODs) of a set of neutraldensity (ND) filters must be determined. For the black curve this was achieved byindividually measuring the transmission of a laser beam through the ND filters. Forthe grey curve the intensity of the beam was measured using the CCD and the ODswere calculated from a set of equations [74]. The red curve is the QE taken fromthe CCD’s datasheet.

methods (1) and (2) are shown in Fig. A.1(b) together with the QE as given inthe CCD’s datasheet. The QE determined with the ODs measured by transmissionagrees reasonably with the specifications. In contrast,the QE determined using theCCD only is lower over the whole accessible range and varies strongly. Additionally,for some laser lines unrealistically low values such as < 10% were obtained. Possiblythe set of equations is numerically ill defined.

32

Page 39: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

Appendix B

Superconductivity

Fig. B.1 shows two spectra at temperatures below (T = 4 K, magenta) and rightabove (T = 10K, grey) the superconducting transition Tc ≈ 8 K (see chapter 3.1) ofthe FeSe0.7S0.3 sample. The normalconducting spectrum exhibits a maximum below10 cm−1 which was identified as response from fluctuations (see chapter 5.4). Thestrong increase of the superconducting spectrum towards zero Raman shift can likelybe attributed to elastic scattering due to an accumulation of surface layers at lowtemperature. Above 60 cm−1 the progression of both spectra is virtually identical.The superconducting spectrum exhibits a peak at Ω ≈ 32 cm−1. A similar peak atthis energy was observed in FeSe [24, 69] below Tc ≈ 8.8 K and was resolved as twoexcitations [69]. This peak was identified as one or two pairbreaking peaks of thesuperconducting state with an energy of 2∆ ≈ 4.5 kBTc which is similar to what

0 5 0 1 0 0 1 5 0 2 0 00 . 0

0 . 5

1 . 0

F e S e 0 . 7 S 0 . 3B 1 g

T ( K ) 4 1 0

Rχ'' (Ω

,T) (c

ounts

s-1 mW -1

)

R a m a n S h i f t Ω ( c m - 1 )

Figure B.1: Spectra of FeSe0.7S0.3 in B1g symmetry at temperatures below (magenta)and above (grey) the superconducting transition at Tc ≈ 8 K. The peak centeredbelow 10 cm−1 in the 10K spetrum was assigned to fluctuations. The superconduct-ing spectrum exhibits a peak at 30 cm−1. Above 60 cm−1 the progression of bothspectra is virtually identical.

33

Page 40: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

Appendix B Superconductivity

is found in Ba(Fe0.939Co0.061)2As2 [76]. In FeSe0.7S0.3 the peak energy of 32 cm−1

corresponds to 2∆ ≈ 6 kBTc which is closer to what is found in the potassium dopedBa-122 [77].

34

Page 41: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

Appendix C

Correction factors of the B1gchannel

Here the correction factor applied to the B1g spectra is given. For the T = 310 Kspectrum the factor was chosen as unity and the other spectra were multiplied tomatch at Ω ≈ 1200 cm−1. Fig. C.1 shows this factor as a function of the temper-ature T of the sample holder. While no clear dependency is discernible it appearsthat larger and more varying corrections were needed for spectra at temperaturesbelow 150K. The same factors are shown in Fig. C.2 depending on the date of themeasurement. The labels give the temperature of the sample holder which is alsoreflected in the color scale. A drift with time is found which may result from changesof the lab temperature, possibly induced by changes to the outside temperature.

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 00 . 0

0 . 5

1 . 0

1 . 5

factor

T e m p e r a t u r e T ( K )

Figure C.1: Correction factor applied to the B1g spectra as a function of the tem-perature of the sample holder. The factor is chosen as unity at 310K. Correctionsclose to unity are found for temperatures above 150K, but larger corrections andstronger deviations are found at lower temperatures.

35

Page 42: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

Appendix C Correction factors of the B1g channel

1 6 . 7 2 3 . 7 3 0 . 7 6 . 8 1 3 . 8

0 . 5

1 . 0

1 . 5

0

44 4

1 01 0 2 0

2 03 03 04 0

4 01 1 0

5 04 04 0

6 06 0

5 0 7 0 9 0

1 3 0

1 3 01 5 0

7 0

2 0 0

2 0 02 5 0

3 1 0 4

1 01 0

5 0

factor

D a t e ( 2 0 1 9 )

Figure C.2: Evolution of the correction factor for B1g spectra over time. The labelsand color code correspond to the temperature of the sample holder. A slow variationof the factor with time can be seen.

36

Page 43: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

Bibliography

[1] K. Ishida, Y. Nakai, and H. Hosono. To What Extent Iron-Pnictide New Su-perconductors Have Been Clarified: A Progress Report. J. Phys. Soc. Jpn. 78,062001 (2009).

[2] H. Hosono and K. Kuroki. Iron-based superconductors: Current status of ma-terials and pairing mechanism. Physica C: Superconductivity 514, 399 (2015).Superconducting Materials: Conventional, Unconventional and Undetermined.

[3] H. Hosono, A. Yamamoto, H. Hiramatsu, and Y. Ma. Recent advances iniron-based superconductors toward applications. Mater. Today 21, 278 (2018).

[4] A. E. Böhmer and A. Kreisel. Nematicity, magnetism and superconductivityin FeSe. J. Phys.: Condens. Matter 30, 023001 (2018).

[5] J.-H. Chu, J. G. Analytis, C. Kucharczyk, and I. R. Fisher. Determinationof the phase diagram of the electron-doped superconductor Ba(Fe1−xCox)2As2.Phys. Rev. B 79, 014506 (2009).

[6] S. Jiang, H. Xing, G. Xuan, C. Wang, Z. Ren, C. Feng, J. Dai, Z. Xu, andG. Cao. Superconductivity up to 30 K in the vicinity of the quantum criticalpoint in BaFe2(As1−xPx)2. J. Phys.: Condens. Matter 21, 382203 (2009).

[7] D. Johrendt and R. Pöttgen. Superconductivity, magnetism and crystal chem-istry of Ba1−xKxFe2As2. Physica C 469, 332 (2009).

[8] D. N. Basov and A. V. Chubukov. Manifesto for a higher Tc. Nat. Phys. 7, 272(2011).

[9] A. Chubukov. Pairing Mechanism in Fe-Based Superconductors. Annu. Rev.Cond. Mat. Phys. 3, 57 (2012).

[10] M. D. Lumsden and A. D. Christianson. Magnetism in Fe-based superconduct-ors. J. Phys.: Condens. Matter 22, 203203 (2010).

[11] N. Mannella. The magnetic moment enigma in Fe-based high temperaturesuperconductors. J. Phys.: Condens. Matter 26, 473202 (2014).

[12] P. Dai. Antiferromagnetic order and spin dynamics in iron-based superconduct-ors. Rev. Mod. Phys. 87, 855 (2015).

37

Page 44: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

[13] M. Yi, Y. Zhang, Z.-X. Shen, and D. Lu. Role of the orbital degree of freedomin iron-based superconductors. npj Quantum Mater. 2, 57 (2017).

[14] A. E. Böhmer and C. Meingast. Electronic nematic susceptibility of iron-basedsuperconductors. C. R. Phys. 17, 90 (2016).

[15] A. I. Coldea and M. D. Watson. The Key Ingredients of the Electronic Structureof FeSe. Annu. Rev. Cond. Mat. Phys. 9, 125 (2018).

[16] J. Schilling, N. Hillier, and N. Foroozani. What have we learned from high-pressure experiments on Cu-oxide and Fe-based superconductors? J. Phys.Conf. Ser. 449, 012021 (2013).

[17] A. S. Sefat and D. J. Singh. Chemistry and electronic structure of iron-basedsuperconductors. MRS Bull. 36, 614 (2011).

[18] S. Hosoi, K. Matsuura, K. Ishida, H. Wang, Y. Mizukami, T. Watashige,S. Kasahara, Y. Matsuda, and T. Shibauchi. Nematic quantum critical pointwithout magnetism in FeSe1−xSx superconductors. Proc. Natl. Acad. Sci. 113,8139 (2016).

[19] T. M. McQueen, A. J. Williams, P. W. Stephens, J. Tao, Y. Zhu, V. Kseno-fontov, F. Casper, C. Felser, and R. J. Cava. Tetragonal-to-OrthorhombicStructural Phase Transition at 90 K in the Superconductor Fe1.01Se. Phys.Rev. Lett. 103, 057002 (2009).

[20] S.-H. Baek, D. V. Efremov, J. M. Ok, J. S. Kim, J. van den Brink, and B. Büch-ner. Orbital-driven nematicity in FeSe. Nat. Mater. 14, 210 (2015).

[21] A. V. Chubukov, M. Khodas, and R. M. Fernandes. Magnetism, Superconduct-ivity, and Spontaneous Orbital Order in Iron-Based Superconductors: WhichComes First and Why? Phys. Rev. X 6, 041045 (2016).

[22] Q. Wang, Y. Shen, B. Pan, X. Zhang, K. Ikeuchi, K. Iida, A. D. Christianson,H. C. Walker, D. T. Adroja, M. Abdel-Hafiez, X. Chen, D. A. Chareev, A. N.Vasiliev, and J. Zhao. Magnetic ground state of FeSe. Nat. Commun. 7, 12182(2016).

[23] Q. Wang, Y. Shen, B. Pan, Y. Hao, M. Ma, F. Zhou, P. Steffens, K. Schmalzl,T. R. Forrest, M. Abdel-Hafiez, X. Chen, D. A. Chareev, A. N. Vasiliev,P. Bourges, Y. Sidis, H. Cao, and J. Zhao. Strong interplay between stripespin fluctuations, nematicity and superconductivity in FeSe. Nat Mater 15,159 (2016).

38

Page 45: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

[24] A. Baum, H. N. Ruiz, N. Lazarević, Y. Wang, T. Böhm, R. Hossein-ian Ahangharnejhad, P. Adelmann, T. Wolf, Z. V. Popović, B. Moritz, T. P.Devereaux, and R. Hackl. Frustrated spin order and stripe fluctuations in FeSe.Commun. Phys. 2, 14 (2019).

[25] S. Holenstein, U. Pachmayr, Z. Guguchia, S. Kamusella, R. Khasanov, A. Am-ato, C. Baines, H.-H. Klauss, E. Morenzoni, D. Johrendt, and H. Luetkens. Co-existence of low-moment magnetism and superconductivity in tetragonal FeSand suppression of Tc under pressure. Phys. Rev. B 93, 140506 (2016).

[26] F. K. K. Kirschner, F. Lang, C. V. Topping, P. J. Baker, F. L. Pratt, S. E.Wright, D. N. Woodruff, S. J. Clarke, and S. J. Blundell. Robustness of su-perconductivity to competing magnetic phases in tetragonal FeS. Phys. Rev. B94, 134509 (2016).

[27] S. Kuhn, M. Kidder, D. Parker, C. dela Cruz, M. McGuire, W. Chance, L. Li,L. Debeer-Schmitt, J. Ermentrout, K. Littrell, M. Eskildsen, and A. Sefat.Structure and property correlations in FeS. Physica C 534, 29 (2017).

[28] A. Baum, A. Milosavljević, N. Lazarević, M. M. Radonjić, B. Nikolić,M. Mitschek, Z. I. Maranloo, M. Šćepanović, M. Grujić-Brojčin, N. Stojilović,M. Opel, A. Wang, C. Petrovic, Z. V. Popović, and R. Hackl. Phonon anomaliesin FeS. Phys. Rev. B 97, 054306 (2018).

[29] A. I. Coldea, S. F. Blake, S. Kasahara, A. A. Haghighirad, M. D. Watson,W. Knafo, E. S. Choi, A. McCollam, P. Reiss, T. Yamashita, M. Bruma, S. C.Speller, Y. Matsuda, T. Wolf, T. Shibauchi, and A. J. Schofield. Evolutionof the low-temperature Fermi surface of superconducting FeSe1−xS across anematic phase transition. npj Quantum Mater. 4, 2 (2019).

[30] D. J. Singh. Electronic structure and doping in BaFe2As2 and LiFeAs: Densityfunctional calculations. Phys. Rev. B 78, 094511 (2008).

[31] V. Vildosola, L. Pourovskii, R. Arita, S. Biermann, and A. Georges. Bandwidthand Fermi surface of iron oxypnictides: Covalency and sensitivity to structuralchanges. Phys. Rev. B 78, 064518 (2008).

[32] A. Baum, Y. Li, M. Tomić, N. Lazarević, D. Jost, F. Löffler, B. Muschler,T. Böhm, J.-H. Chu, I. R. Fisher, R. Valentí, I. I. Mazin, and R. Hackl. Interplayof lattice, electronic, and spin degrees of freedom in detwinned BaFe2As2: ARaman scattering study. Phys. Rev. B 98, 075113 (2018).

[33] J. Paglione and R. L. Greene. High-temperature superconductivity in iron-based materials. Nat. Phys. 6, 645 (2010).

39

Page 46: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

[34] A. Baum. Interrelation of lattice, charge, and spin degrees of freedom iniron based systems. Dissertation, Technische Universität München (2018).http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:91-diss-20181115-1453967-1-1. Dissertation.

[35] U. Pachmayr, N. Fehn, and D. Johrendt. Structural transition and supercon-ductivity in hydrothermally synthesized FeX (X = S, Se). Chem. Commun.52, 194 (2016).

[36] A. E. Böhmer, F. Hardy, F. Eilers, D. Ernst, P. Adelmann, P. Schweiss, T. Wolf,and C. Meingast. Lack of coupling between superconductivity and orthorhombicdistortion in stoichiometric single-crystalline FeSe. Phys. Rev. B 87, 180505(2013).

[37] E. Colombier, S. L. Bud’ko, N. Ni, and P. C. Canfield. Complete pressure-dependent phase diagrams for SrFe2As2 and BaFe2As2. Phys. Rev. B 79, 224518(2009).

[38] Y. Mizuguchi, F. Tomioka, S. Tsuda, T. Yamaguchi, and Y. Takano. Super-conductivity at 27K in tetragonal FeSe under high pressure. Appl. Phys. Lett.93, 152505 (2008).

[39] T. Terashima, N. Kikugawa, S. Kasahara, T. Watashige, T. Shibauchi, Y. Mat-suda, T. Wolf, A. E. Böhmer, F. Hardy, C. Meingast, H. v. Löhneysen, andS. Uji. Pressure-Induced Antiferromagnetic Transition and Phase Diagram inFeSe. J. Phys. Soc. Jpn. 84, 063701 (2015).

[40] C. Petrovic. priv. comm. (2019).

[41] M. Rotter, M. Tegel, D. Johrendt, I. Schellenberg, W. Hermes, and R. Pöttgen.Spin-density-wave anomaly at 140 K in the ternary iron arsenide BaFe2As2.Phys. Rev. B 78, 020503 (2008).

[42] F.-C. Hsu, J.-Y. Luo, K.-W. Yeh, T.-K. Chen, T.-W. Huang, P. M. Wu, Y.-C.Lee, Y.-L. Huang, Y.-Y. Chu, D.-C. Yan, and M.-K. Wu. Superconductivity inthe PbO-type structure α-FeSe. Proc. Natl. Acad. Sci. 105, 14262 (2008).

[43] X. Lai, H. Zhang, Y. Wang, X. Wang, X. Zhang, J. Lin, and F. Huang. Obser-vation of Superconductivity in Tetragonal FeS. J. Am. Chem. Soc. 137, 10148(2015).

[44] J. P. Sun, K. Matsuura, G. Z. Ye, Y. Mizukami, M. Shimozawa, K. Matsubay-ashi, M. Yamashita, T. Watashige, S. Kasahara, Y. Matsuda, J. Q. Yan, B. C.Sales, Y. Uwatoko, J. G. Cheng, and T. Shibauchi. Dome-shaped magneticorder competing with high-temperature superconductivity at high pressures inFeSe. Nat. Commun. 7, 12146 (2016).

40

Page 47: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

[45] M. He, L. Wang, F. Hardy, L. Xu, T. Wolf, P. Adelmann, and C. Meingast.Evidence for short-range magnetic order in the nematic phase of FeSe fromanisotropic in-plane magnetostriction and susceptibility measurements. Phys.Rev. B 97, 104107 (2018).

[46] T. Shimojima, Y. Suzuki, T. Sonobe, A. Nakamura, M. Sakano, J. Omachi,K. Yoshioka, M. Kuwata-Gonokami, K. Ono, H. Kumigashira, A. E. Böhmer,F. Hardy, T. Wolf, C. Meingast, H. v. Löhneysen, H. Ikeda, and K. Ishizaka.Lifting of xz / yz orbital degeneracy at the structural transition in detwinnedFeSe. Phys. Rev. B 90, 121111 (2014).

[47] F. Wang, S. A. Kivelson, and D.-H. Lee. Nematicity and quantum paramag-netism in FeSe. Nat. Phys. 11, 959 (2015).

[48] H. Kotegawa, S. Masaki, Y. Awai, H. Tou, Y. Mizuguchi, and Y. Takano.Evidence for Unconventional Superconductivity in Arsenic-Free Iron-Based Su-perconductor FeSe: A 77Se-NMR Study. J. Phys. Soc. Jpn. 77, 113703 (2008).

[49] J. K. Glasbrenner, I. I. Mazin, H. O. Jeschke, P. J. Hirschfeld, R. M. Fernandes,and R. Valenti. Effect of magnetic frustration on nematicity and superconduct-ivity in iron chalcogenides. Nat. Phys. 11, 953 (2015).

[50] D. Vaughan and M. Ridout. Mössbauer studies of some sulphide minerals. J.Inorg. Nucl. Chem. 33, 741 (1971).

[51] M. Mitschek. Magnetismus und Supraleitung in Eisenchalkogeniden. Master-arbeit, Technische Universität München (2017).

[52] B. Zimmer. Darstellung und Charakterisierung ternärer Phosphide und qua-ternärer Phosphid-Oxide der Seltenerdelemente und des Thoriums mit Über-gangsmetallen. Dissertation, Universität Münster (1996).

[53] Y. Kamihara, H. Hiramatsu, M. Hirano, R. Kawamura, H. Yanagi, T. Kamiya,and H. Hosono. Iron-Based Layered Superconductor: LaOFeP. J. Am. Chem.Soc. 128, 10012 (2006).

[54] S. Medvedev, T. M. McQueen, I. A. Troyan, T. Palasyuk, M. I. Eremets, R. J.Cava, S. Naghavi, F. Casper, V. Ksenofontov, G. Wortmann, and C. Felser.Electronic and magnetic phase diagram of β-Fe1.01Se with superconductivity at36.7K under pressure. Nat. Mater. 8, 630 (2009).

[55] J.-F. Ge, Z.-L. Liu, C. Liu, C.-L. Gao, D. Qian, Q.-K. Xue, Y. Liu, and J.-F.Jia. Superconductivity above 100 K in single-layer FeSe films on doped SrTiO3.Nat. Mater. 14, 285 (2015).

41

Page 48: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

[56] T. Devereaux and R. Hackl. Inelastic light scattering from correlated electrons.Rev. Mod. Phys. 79, 175 (2007).

[57] A. Smekal. Zur Quantentheorie der Dispersion. Naturwissenschaften 11, 873(1923).

[58] C. V. Raman and K. Krishnan. A New Type of Secondary Radiation. Nature121, 501 (1928).

[59] G. Landsberg and L. Mandelstam. Eine neue Erscheinung bei der Lichtzer-streuung in Krystallen. Naturwissenschaften 16, 557 (1928).

[60] A. Baum. Untersuchung des Spindichtewellen-Übergangs in BaFe2As2. Diplo-marbeit, Technische Universität München (2012).

[61] W. Hayes and R. Loudon. Scattering of Light by Crystals. John Wiley ansSons, New York (1978).

[62] C. Hoffmann. Diplomarbeit, Technische Universität München (1997).

[63] T. M. McQueen, Q. Huang, V. Ksenofontov, C. Felser, Q. Xu, H. Zandbergen,Y. S. Hor, J. Allred, A. J. Williams, D. Qu, J. Checkelsky, N. P. Ong, and R. J.Cava. Extreme sensitivity of superconductivity to stoichiometry in Fe1+δSe.Phys. Rev. B 79, 014522 (2009).

[64] A. Williams, T. McQueen, and R. Cava. The stoichiometry of FeSe. Solid StateCommun. 149, 1507 (2009).

[65] V. Gnezdilov, Y. G. Pashkevich, P. Lemmens, D. Wulferding, T. Shevtsova,A. Gusev, D. Chareev, and A. Vasiliev. Interplay between lattice and spin statesdegree of freedom in the FeSe superconductor: Dynamic spin state instabilities.Phys. Rev. B 87, 144508 (2013).

[66] A. Baum. priv. comm. priv. comm. (2019).

[67] D. L. A. de Faria, S. VenÃćncio Silva, and M. T. de Oliveira. Raman micro-spectroscopy of some iron oxides and oxyhydroxides. J. Raman Spectrosc. 28,873 (1997).

[68] H. Ruiz, Y. Wang, B. Moritz, A. Baum, R. Hackl, and T. P. Devereaux. Frus-trated magnetism from local moments in FeSe. Phys. Rev. B 99, 125130 (2019).

[69] P. Massat, D. Farina, I. Paul, S. Karlsson, P. Strobel, P. Toulemonde, M.-A.Méasson, M. Cazayous, A. Sacuto, S. Kasahara, T. Shibauchi, Y. Matsuda,and Y. Gallais. Charge-induced nematicity in FeSe. Proc. Natl. Acad. Sci. 113,9177 (2016).

42

Page 49: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

[70] L. Peis. Studies on FeSe1−xSx (master’s thesis) (2019).

[71] F. Kretzschmar, T. Böhm, U. Karahasanovic, B. Muschler, A. Baum, D. Jost,J. Schmalian, S. Caprara, M. Grilli, C. Di Castro, J. G. Analytis, J.-H. Chu,I. R. Fisher, and R. Hackl. Critical spin fluctuations and the origin of nematicorder in Ba(Fe1−xCox)2As2. Nat. Phys. 12, 560 (2016).

[72] T. U. Böhm. The case for Spin-fluctuation induced pairing in Ba1−xKxFe2As2.Dissertation, Technische Universität München (2017).

[73] S. Caprara, C. Di Castro, M. Grilli, and D. Suppa. Charge-Fluctuation Contri-bution to the Raman Response in Superconducting Cuprates. Phys. Rev. Lett.95, 117004 (2005).

[74] U. Zweck. Electronic and magnetic excitations in underdoped YBa2Cu3O6+x.Masterarbeit, Technische Universität München (2018).

[75] R. Nemetschek. Energielücke und Pseudogap in supraleitfähigem YBa2Cu3O6+x

Ergebnisse der elektronischen Raman-Streuung. Dissertation, Technische Uni-versität München (1998).

[76] B. Muschler, W. Prestel, R. Hackl, T. P. Devereaux, J. G. Analytis, J.-H.Chu, and I. R. Fisher. Band- and momentum-dependent electron dynamicsin superconducting Ba(Fe1−xCox)2As2 as seen via electronic Raman scattering.Phys. Rev. B 80, 180510 (2009).

[77] T. Böhm, F. Kretzschmar, A. Baum, M. Rehm, D. Jost, R. Hossein-ian Ahangharnejhad, R. Thomale, C. Platt, T. A. Maier, W. Hanke, B. Moritz,T. P. Devereaux, D. J. Scalapino, S. Maiti, P. J. Hirschfeld, P. Adelmann,T. Wolf, W. Hai-Hu, and R. Hackl. Microscopic origin of Cooper pairing in theiron-based superconductor Ba1−xKxFe2As2. npj Quantum Mater. 3, 48 (2018).

43

Page 50: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8
Page 51: Fluctuations and frustrated magnetism in sulphur substituted iron … · 2020. 4. 6. · 1.2 Phase diagram T s T c Sulphur content x Temperature T (K) 1 10 100 0.0 0.2 0.4 0.6 0.8

Acknowledgments

Last but not least I want to thank everyone who supported me during my time atthe Walther-Meißner-Institute and while writing this thesis.

Especially I want to thank

• PD Dr. Rudi Hackl not only for supervising my bachelor’s thesis but forall the interesting, informative and entertaining discussions not only aboutphysics and of course for the outstanding coffee.

• Prof. Dr. Rudolf Gross for the opportunity to write my bachelor’s thesis atthe Walther-Meißner-Institute

• Dr. Andreas Baum for his help, his knowledge, his support and of course allthe fun we had

• Prof. C. Petrovic and his group for providing the FeSe0.7S0.3 sample and thephase diagram

• Leander Peis for his arduous work in the lab which put these measurementsforth

• The whole Raman-group for the good working atmosphere and the interestingand informative discussions

• Susanne Mayr and Michael Stanger for their help in the crystal preparation

• the craftsmen of the WMI workshop

• My parents, Sybille and Roman Stumberger and my brother Robin for alwayshaving my back no matter what. I love you.

45