Cation- and lattice-site-selective magnetic depth profiles of ultrathin Fe3O4(001) films

Tobias Pohlmann,1, 2, ∗ Timo Kuschel,3 Jari Rodewald,1 Jannis Thien,1 Kevin Ruwisch,1 Florian

Bertram,2 Eugen Weschke,4 Padraic Shafer,5 Joachim Wollschläger,1, † and Karsten Küpper1, ‡

1Department of Physics, Osnabrück University, Barbarastr. 7, 49076 Osnabrück, Germany2DESY Photon Science, Notkestr. 85, 22607 Hamburg, Germany

3Center for Spinelectronic Materials and Devices, Department of Physics,Bielefeld University, Universitätsstr. 25, 33615 Bielefeld, Germany

4Helmholtz-Zentrum Berlin für Materialien und Energie,Wilhelm-Conrad-Röntgen-Campus BESSY II, Albert-Einstein-Strasse 15, 12489 Berlin, Germany

5Advanced Light Source, Lawrence Berkeley National Laboratory, 6 Cyclotron Rd, Berkeley, CA, 94720, USA(Dated: May 5, 2020)

A detailed understanding of ultrathin film surface properties is crucial for the proper interpretationof spectroscopic, catalytic and spin-transport data. We present x-ray magnetic circular dichroism(XMCD) and x-ray resonant magnetic reflectivity (XRMR) measurements on ultrathin Fe3O4 filmsto obtain magnetic depth profiles for the three resonant energies corresponding to the differentcation species Fe2+oct, Fe

3+tet and Fe

3+oct located on octahedral and tetrahedral sites of the inverse spinel

structure of Fe3O4. By analyzing the XMCD spectrum of Fe3O4 using multiplet calculations,the resonance energy of each cation species can be isolated. Performing XRMR on these threeresonant energies yields magnetic depth profiles that correspond each to one specific cation species.The depth profiles of both kinds of Fe3+ cations reveal a 3.9 ± 1 Å-thick surface layer of enhancedmagnetization, which is likely due to an excess of these ions at the expense of the Fe2+oct species inthe surface region. The magnetically enhanced Fe3+tet layer is additionally shifted about 3 ± 1.5 Åfarther from the surface than the Fe3+oct layer.

Introduction.−Magnetite, Fe3O4, is one of the mostfrequently investigated transition-metal oxides, since it isa key material in spintronics [1], spin caloritronics [2] andmaterial chemistry [3]. Fe3O4 thin films were consideredhighly suitable as electrode material for magnetic tunneljunctions [4, 5] due to their predicted half-metallic behav-ior with 100% spin polarization [6]. However, the promisewas never quite met, with modest tunnel magnetoresis-tance ratios ranging from -26% to 18% [4, 5, 7]. In or-der to test its half-metallicity, spin-resolved x-ray photo-electron spectroscopy on Fe3O4(111) films found a spin-polarization of about 80% [8], while on Fe3O4(001) thesame technique yielded polarizations of only≈ 40%−70%[9–11].

Both the reduced tunnel magnetoresistance and thedeviations from 100% spin-polarization in spin-resolvedXPS were argued to emerge from interface and surfaceeffects, respectively [4, 5, 8, 10, 11]. For Fe3O4(111)films deposited on semiconducting ZnO(0001), lattice-site-selective depth profiles obtained by x-ray resonantmagnetic reflectivity (XRMR) and electron energy lossspectroscopy did not find a notable surface modifica-tion apart from a Feoct termination [12]. Reduction ofthe spin-polarization measured at the Fe3O4(001) sur-face was typically considered to originate from a sur-face reconstruction, the existence of which has long beenknown but only recently has been resolved as a subsur-face cation vacancy (SCV) structure [13]. This revela-tion highlights the issues that might arise from general-izing results from surface-sensitive techniques, such asx-ray absorption spectroscopy (XAS) in total electronyield (TEY) mode and x-ray photoelectron spectroscopy

(XPS), to explain the behavior of the bulk material [14].

In particular, drawing conclusions about the cation dis-tribution of magnetite requires caution, because the bulkmaterial of the inverse spinel Fe3O4 should contain di-valent Fe2+oct, as well as trivalent ions in both octahedraland tetrahedral coordination, Fe3+tet and Fe

3+oct. However,

the DFT+U calculations of the SCV structure predictthe first four atomic layers to only contain Fe3+ ions andto have a formal stoichometry of Fe11O16, in agreementwith earlier reports on an excess of Fe3+ at the (001)surface [15]. A subsequent study of how the magneticproperties of Fe3O4 are affected at the surface used x-raymagnetic circular dichroism (XMCD) with varying prob-ing depth and found a reduced magnetic moment at thesurface of a natural magnetite crystal [16].

In this letter we report an investigation of the mag-netic surface properties of ultrathin Fe3O4(001) films, incontrast to the bulk, by recording magnetooptical depthprofiles of the three cation species in Fe3O4. Using pho-tons with resonant energies, we employed XRMR to de-termine the magnetooptical depth profiles at the energiescharacteristic for Fe2+oct, Fe

3+tet and Fe

3+oct in magnetite’s

L2,3 XMCD spectrum individually for three ultrathinFe3O4/MgO(001) films of varying thicknesses. We find a≈ 3.9 Å layer of enhanced magnetooptical absorption atthe surface at the resonant energies of both Fe3+ speciesbut not for Fe2+, suggesting an Fe3+-rich surface.

Experimental and theoretical details.−We preparedthe Fe3O4/MgO(001) samples in a multichamber ultra-high-vacuum system using reactive molecular beamepitaxy (RMBE). Their chemical composition and(√

2×√

2)R45◦ superstructure was confirmed by in-situ

arX

iv:2

005.

0165

7v1

[co

nd-m

at.m

es-h

all]

4 M

ay 2

020

2

XPS and low-energy electron diffraction (LEED), respec-tively. For details on the deposition and characterizationmethods please see Refs. [17] or [18].

For the XAS and XMCD study, the samples weretransfered from our lab under ambient conditions to theSuperconducting Vector Magnet Endstation at beamline4.0.2 of the Advanced Light Source (ALS). All sampleswere measured in a magnetic field of 4 T along the x-raybeam at room temperature. The incidence angle of thex-rays was 30◦ from the [100] direction of Fe3O4, andthe degree of circular polarization was 90%. The XASand XMCD spectra were measured across the Fe L2,3absorption edges (690 − 750 eV). All XAS spectra weremeasured in the TEY mode, which has a probing depthin magnetite of about 3 nm.

The XAS and XMCD data were analyzed by apply-ing the sum rules [19–21] and charge-transfer multipletcalculations using the Thole code [22] with assistance ofCTM4XAS [23, 24]. For the sum rules, we took into ac-count a correction factor of 1.142 derived by Teramuraet al. for Fe2+ [21] and assumed 14 holesf.u. . For the mul-tiplet calculations, we assumed the three-cation model,using crystal field and charge-transfer parameters as de-scribed in Ref. [17]. The parameters and more detailsregarding the multiplet calculations can also be found inthe Supplemental Materials [25] (Chapter A, includingRefs. [17, 26, 27]). The multiplet states resulting fromthese calculations were compared to the data by assum-ing a Gaussian instrumental broadening of 0.2 eV, and aLorentzian lifetime broadening of 0.3 eV at L3 and 0.6 eVat L2.

The samples were transfered to BESSY II under ambi-ent conditions and x-ray reflectivity (XRR) and XRMRwere performed in the XUV Diffractometer at beamlineUE46 PGM-1 [28]. The samples were placed betweentwo permanent magnets in a magnetic field of 200 mTat room temperature, with a degree of circular polariza-tion of 90%. First, we characterized the structural prop-erties of the sample (thickness d, roughness σ) by XRRat off-resonant energies (680 eV, 1000 eV). Second, XASand XMCD were measured in order to select suitableenergies for XRMR. Finally, θ − 2θ scans in the range2θ = 0◦ − 140◦ at resonant energies Ei with extremain the XMCD signal (maximum at 708.4 eV, minimumat 709.5 eV, maximum at 710.2 eV) were performed withboth right and left circularly polarized x-rays, to obtainthe XRMR asymmetry ratios ∆I(Ei, qz). These curveswere then fitted with the Zak matrix formalism using thesoftware ReMagX [29] to determine the depth profilesof the magnetooptical absorption ∆β(z) and dispersion∆δ(z) along the film height z. A detailed review of theXRMR method and the software is given in Ref. [29],and a conclusive recipe for fitting XRMR data can befound in Refs. [30, 31].

Results.−Structural parameters obtained from the off-resonant XRR measurements are displayed in Tab. I.

7 0 0 7 1 0 7 2 0 7 3 0- 0 . 4

- 0 . 2

0 . 0

XMCD

(arb.

units)

e n e r g y ( e V ) F e2 +o c t F e 3 +t e t F e 3 +o c t

0 . 0

0 . 5

1 . 0 ( c )( a )

( b )

d a t a s i m u l a t i o n F e 2 +o c t F e 3 +t e t F e 3 +o c t

B = 4 T

XAS (

arb. un

its) 2 5 n m F e 3 O 4

051 01 52 02 53 03 54 0

cation

stoich

ometr

y (%)

3 3 % 3 1 %3 5 %

FIG. 1. (a) XAS and (b) XMCD spectrum at the Fe L2,3 edgefor the 25 nm Fe3O4 film, taken at 4 T external magnetic field,at room temperature and in TEY mode. A step function wassubtracted from the XAS spectrum. Black dots representdata; green, red and blue spectra are multiplet calculationsfor the three cation species of Fe3O4, the grey line is theirsum. The cation spectra are offset for better visibility. (c)Cation stoichometry used to obtain the fit in (a) and (b).

Figure 1 shows the XAS and XMCD spectra of the 25 nmFe3O4 film, recorded at ALS. Corresponding data mea-sured at BESSY II, under the same conditions in whichthe XRMR was performed, can be found in the Supple-mental Material [25] (Chapter A). The spin and orbitalmoments µspin and µorb obtained from the sum rules aregiven in Tab. I. Their sum is slightly reduced comparedto the bulk value of magnetite of µ = µspin + µorb =4.07µB [32]. They also show a tendency toward a slightlyhigher moment for the thicker films. This behavior ofmagnetite films has also been observed previously [17],and can be explained by a higher density of anti-phaseboundaries (APBs) for thinner films due to the antifer-romagnetic coupling of APBs reducing the average mag-netic moment of the film [33–35].

Additionally, multiplet simulations of the three-cationmodel are fitted to the XMCD data (cf Fig. 1). By

TABLE I. Thicknesses d, surface roughnesses σsurf and inter-face roughnesses σint of the investigated samples as obtainedby fitting off-resonant XRR curves, as well as their spin mo-ments µspin and orbital moments µorb from the sum-rule anal-ysis.

sample 13 nm 25 nm 50 nmd (nm) 13.5 ± 0.5 25.2 ± 0.3 52.8 ± 0.3

σsurf (nm) 0.22 ± 0.05 0.33 ± 0.05 0.34 ± 0.05σint(nm) 0.35 ± 0.05 0.35 ± 0.05 0.37 ± 0.05

µspin (µB/f.u.) 3.2 ± 0.3 3.5 ± 0.3 3.7 ± 0.3µorb (µB/f.u.) 0.07 ± 0.02 0.09 ± 0.02 0.11 ± 0.02µ (µB/f.u.) 3.27 ± 0.3 3.59 ± 0.3 3.81 ± 0.3

3

weighting the individual spectra with respect to thecation stoichometry given in Fig. 1(c), the XAS andXMCD data can be described well by our model (cf. greyline). Thus, the cation distribution on different sites al-most follows the ideal stoichiometry of 1:1:1.

One feature of this kind of modelling is the fact thateach of the three extrema observed in the XMCD spec-trum can mainly be attributed to one cation spectrum.Table II shows the contributions rcation(Ei) of each cationspectrum at the resonant energies Ei in the XMCD spec-trum, according to

rcation(Ei) =Ication(Ei)

|IFe2+oct(Ei)|+ |IFe3+tet(Ei)|+ |IFe

3+oct(Ei)|

,

(1)with Ication(Ei) being the XMCD signal of the corre-sponding cation spectrum in Fig. 1(b) at energies Ei =708.4 eV, 709.5 eV, 710.2 eV. While there still is a con-siderable mixing, at least 64% of each extremum can beattributed to its dominant cation.

The distinction between the Fe2+oct and Fe3+oct ions is a

noteworthy issue for several reasons. Above the Ver-wey transition temperature, these ions should be ran-domly distributed on octahedral sites as shown by neu-tron diffraction [36]. Thus, the model could potentiallybe simplified by describing them as Fe2.5+oct , effectively re-ducing the number of cation species. However, only mul-tiplet calculations based on a three-cation model describeroom-temperature spectra from XPS, XAS and XMCDat the Fe L absorption edge with sufficient agreement[17, 37–40]. Note that this extremum-cation assignmentqualitatively also holds true in LSDA+U calculations,but they predict a stronger overlap of the three cationspectra [41]. A possible explanation for this behaviormay well be the different electronic structure at the sur-face of magnetite. In that case, we would expect differentspectra from the surface and the bulk. In fact, a re-cent study using hard x-ray photoelectron spectroscopy(HAXPES) reported on a bulk-exclusive state not ob-servable in surface-sensitive soft XPS [42].

Accordingly, the strategy to obtain cationic depth pro-files is to pick the three corresponding XMCD resonantenergies and perform XRMR measurements at these res-onances. Figure 2 shows the asymmetry ratios andtheir fits at the three XMCD resonant energies for the25 nm Fe3O4 film. Corresponding figures for the other

TABLE II. Contributions of the three cation species to theextrema in the XMCD spectrum in Fig. 1(b), as obtained bythe multiplet analysis using Eq. (1).

Energy Fe2+oct Fe3+tet Fe

3+oct

708.4 eV 73 ± 5% −8 ± 3% 19 ± 5%709.5 eV 18 ± 3% −64 ± 3% 18 ± 3%710.2 eV 4 ± 3% −16 ± 8% 80 ± 10%

0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6- 2 00

2 0- 2 0

00

2 04 06 08 0 2 5 n m F e 3 O 4

7 0 8 . 4 e V

d a t a f i t

asymm

etry r

atio ∆I

(%)

s c a t t e r i n g v e c t o r q z ( 1 / Å )

7 1 0 . 2 e V7 0 9 . 5 e V

FIG. 2. XRMR data (open circles) and corresponding fits(solid lines) from the 25 nm Fe3O4 film, recorded at thethree resonant energies of the XMCD L3 edge, using themodeled magnetooptical depth profiles of Fig. 3(a). Datawere recorded with a magnetic field of 200 mT along theFe3O4(001) direction at room temperature.

two samples can be found in the Supplemental Mate-rial [25] (Chapter B). The magnetooptical depth profiles∆β(z) that produce the fits are shown in Fig. 3(a). Themost striking feature of all three samples is the behaviorat the surface: at the Fe2+oct resonance energy (708.4 eV,green), the magnetooptical depth profiles in fact appearto be just homogeneous for all samples. However, at boththe Fe3+tet and the Fe

3+oct resonance energies, there are no-

ticeable changes to the ∆β depth profiles. In order to fittheir asymmetry ratios, we must include a thin surfacelayer of enhanced magnetooptical absorption. The twothinner Fe3O4 films - 13 nm and 25 nm - are quantita-tively very similar for the Fe3+oct and Fe

3+tet magnetoopti-

cal depth profiles, with only minor differences in the en-hanced amplitude at the surface, and the ∆β in the bulkmatches between the samples. In contrast, the 50 nmFe3O4 film shows slightly higher ∆β at the Fe

3+oct res-

onance, and smaller ∆β at the Fe3+tet resonance. Also,the magnetooptical absorption at the Fe2+oct resonance be-comes larger with increasing film thickness, in agreementwith our results from the sum-rule analysis (see Tab.I). The obvious choice of magnetooptical depth profileswhich are simply homogeneous through the entire filmdid not provide satisfactory fits to the data. This is dis-cussed in more detail in the Supplemental Material [25](Chapter C).

In order to highlight this phenomenon, Fig. 3(b) showsthe surface region of the 25 nm Fe3O4 film, together withthe density depth profile obtained from off-resonant XRR(grey line). The edge of the magnetooptical depth pro-file of the Fe2+oct resonance roughly matches the location ofthe magnetically enhanced Fe3+tet layer. The thickness ofthe magnetically enhanced layers is about 3.5 Å for both

4

4.5 Å

3.5 Å

(a)

(c)

(b)

Fe2+oct

O2-(001)

(010

)

3.5 Å

Fe3+octFe3+tet

FIG. 3. (a) ∆β(z) depth profiles for all three samples at thethree resonant energies, extracted from the XRMR fits. (b)Close-up of the surface magnetooptical depth profile of the25 nm Fe3O4 film, together with the optical density obtainedfrom off-resonant XRR fits (grey line). (c) (Bulk-terminated)model of the magnetite unit cell, in scale with Fig. 3(b).Comparison with the model in (c) illustrates the sizes of theenhanced regions being roughly half a unit cell of magnetite(four cation layers).

Fe3+ species. This corresponds to slightly less than halfa bulk unit cell of magnetite (a/2 = 4.2 Å), as illustratedby Fig. 3(c). Furthermore, the magnetically enhancedlayers are not colocated at the same depth: the magnet-ically enhanced Fe3+tet layer is shifted about 4.5 Å deeperinto the film than the magnetically enhanced Fe3+oct layer.Table III summarizes the individual thicknesses of themagnetically enhanced layers denh and their offset fromone another for the different samples. All three samplesshow comparable, but not quite identical results. Whilethe model qualitatively holds up well among the sam-

TABLE III. Thicknesses denh and vertical shifts of the en-hanced magnetic layers at the Fe3+tet and Fe

3+oct resonances.

denhFe3+oct

denhFe3+tet

vertical shift

13 nm 4.7 Å 3.2 Å 2 Å25 nm 3.5 Å 3.4 Å 4.5 Å50 nm 3.8 Å 6.4 Å 2.5 Å

ples, both the thicknesses denh and the depth offsets aresimilar in magnitude to the surface roughness, making itdifficult to resolve the exact distances with any greaterprecision.

Discussion.−Within the three-cation picture, we candiscuss the magnetooptical depth profiles obtained forthe resonant energies. The magnetooptical depth pro-files are not identical with the depth distribution of thecations: As quantified in Tab. II, however, the signalon each resonance is a mixture of contributions from allthree cations. For the magnetooptical depth profile at710.2 eV approximately 80% of the signal originates fromthe Fe3+oct and can be regarded as an almost pure effectfrom that species. And since the position of the layerof enhanced magnetization at 709.5 eV does not matchthe position of the 710.2 eV layer, we can conclude it tobe a distinct physical feature, stemming from the Fe3+tetspecies.

One ansatz is to take into account rearranged cationdistributions due to the Fe3O4(001) surface as proposedby the SCV model [13, 14]. The SCV model predictsthat, in order to achieve polarity compensation, the firstunit cell contains only Fe3+ species, with the first Fe3+tetlayer lying about 1 Å deeper than the Fe3+oct. This modelmatches surprisingly well some aspects of our findings.The first Feoct-O layer remains stoichometric, but theFe2+oct changes valency to Fe

3+oct, effectively doubling the

Fe3+oct density. In the second layer, an additional Fe3+tet

ion is added, increasing the Fe3+tet density by 50%. How-ever, we do not observe the depletion of Fe2+oct cationsin the first 8.4 Å. This agreement is surprising becauseFe3O4 surfaces tend to hydroxilate on ambient conditionsand do not show the (

√2×√

2)R45◦ LEED pattern, butinstead a (1 × 1) pattern [14]. This, however, may beattributed to disorder at the surface with loss of long-range order while the local order of vacancies and inter-stitials is kept. Our results now suggest that at least theFe3+-enrichment of the surface remains intact under am-bient conditions. A more detailed comparison of the SCVmodel to our findings can be found in the SupplementalMaterial [25] (Chapter D).

Taking the model of occupation of octahedral sitesby Fe2.5+oct cations as an alternative, the agreement ofthe XAS/XMCD spectra with the multiplet calculationsmight be merely valid at the surface, while both octahe-drally coordinated Fe species are identical in the bulk. In

5

that case, the discrepancy between surface and bulk ofthe magnetooptical depth profiles would represent thetransition from the surface electronic structure to thebulk structure. Using bulk-sensitive HAXPES, Taguchiet al. report on a bulk feature at 708.5 eV, which is in-visible for surface-sensitive soft XPS [42]. In this picture,we could interpret the magnetooptical depth profiles andthe XMCD spectra as follows: the top 4−6 Å, consistingof Fe3+oct and Fe

3+tet ions, give rise to the XMCD extrema

at 709.5 eV and 710.2 eV, as reflected in the enhanced∆β layers at those energies. Deeper into the Fe3O4 film,the Fe3+oct species vanishes in favor of the Fe

2.5+oct species,

and consequently, the magnetic dichroism at 710.2 eVis reduced. Instead, the bulk-feature at 708.4 eV be-comes prominent, related to the Fe2.5+oct species. In theXMCD signal, it is visible as the supposed Fe2+oct peak, butstrongly suppressed due to the surface sensitivity of theTEY detection. In this interpretation, our results agreewith the more pronounced signal at 708.5 eV far from thesurface reported in Ref. [42], and can explain the obser-vation of the two distinct Feoct species at the surface,which should not be distinguishable at room tempera-ture.

Summary.−In conclusion, we fabricated threeFe3O4/MgO(001) ultrathin films of different thicknessesby RMBE. We recorded XAS/XMCD at ALS beamline4.0.2 as well as XAS/XMCD and XRMR measurementsat BESSY II beamline UE46 PGM-1, in order to obtainmagnetooptical depth profiles. By fitting multipletcalculations to the XMCD data, we disentangle thecation contributions at the three resonant energies ofthe XMCD spectrum, and use XRMR at those energiesin order to resolve the magnetooptical depth profiles ofthe three iron species in Fe3O4. We find that both Fe

3+

species show an enhanced signal in the surface-nearregion in a ≈ 3.9 ± 1 Å thick layer, with the Fe3+tet layerlocated about 3 ± 1.5 Å underneath the Fe3+oct layer.We attribute this to the first unit cell from the surfacecontaining an excess of Fe3+ cations.

Acknowledgements.−Financial support from the Bun-desministerium für Bildung und Forschung (FKZ05K16MP1) is gratefully acknowledged. We are alsograteful for the kind support from the DeutscheForschungsgemeinschaft (DFG under No. KU2321/6-1,and No. WO533/20-1). This research used resourcesof the Advanced Light Source, a DOE Office of ScienceUser Facility under contract no. DE-AC02-05CH11231,by recording XMCD at at beamline 4.0.2. (ALS-10261).We thank HZB for the allocation of synchrotron beam-time at beamline UE46 PGM-1 (181/06266ST/R) wherewe recorded the XRMR and additional XMCD measure-ments.

∗ tobias.pohlmann@desy.de† jwollsch@uni-osnabrueck.de‡ kkuepper@uni-osnabrueck.de

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Cation- and lattice-site-selective magnetic depth profiles of ultrathin Fe3O4(001) filmsAbstract References