Orbital moments of CrO2 and Fe3O4 studied by MCD in soft X-ray absorption

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Orbital moments of CrO

2

and Fe

3

O

4

studied by MCD

in soft X-ray absorption

D.J. Huang

a,b,∗

, C.F. Chang

a

, J. Chen

c

, H.-J. Lin

a

, S.C. Chung

a

, H.-T. Jeng

d

,

G.Y. Guo

a,e

, W.B. Wu

a,b

, S.G. Shyu

f,g

, C.T. Chen

a

a_{National Synchrotron Radiation Research Center, Hsinchu 300, Taiwan, ROC} b_{Department of Electrophysics, National Chiao-Tung University, Hsinchu 300, Taiwan, ROC}

c_{Department of Physics, National Chung Cheng University, Chia-Yi 621, Taiwan, ROC} d_{Physics Division, National Center for Theoretical Sciences, Hinchu 300, Taiwan, ROC}

e_{Department of Physics, National Taiwan University, Taipei 106, Taiwan, ROC} f_{Institute of Chemistry, Academia Sinica, Nankang, Taipei 115, Taiwan, ROC} g_{Department of Chemistry, National Central University, Tao-Yuan 320, Taiwan, ROC}

Available online 2 April 2004

Abstract

We present studies of orbital magnetic moments of CrO2 and Fe3O4 by measuring magnetic circular dichroism (MCD) in soft X-ray absorption. The results show that Fe3O4 exhibits large orbital moments, as a consequence of the strong Coulomb interactions of Fe 3d electrons. In contrast, orbital moments of Cr in CrO2are nearly quenched, revealing that Cr 3d electrons are strongly hybridized with O 2p electrons and more delocalized as compared with those of Fe in Fe3O4. Comparing the MCD data with the band structure calculations based on local spin density approximation with on-site Coulomb energy U taken into account, we conclude that to include the on-site Coulomb interactions of 3d electrons is essential for adequately describing the electronic structure of CrO2and Fe3O4.

1. Introduction

Transition metal oxides, which are interesting for fundamental research and important for technological applications, exhibit anomalous and interesting physical properties [1]. These interesting properties are determined by the coupling between charge, orbital characters and spin of valence electrons, and the lattice degrees of freedom in transition-metal oxides. For instance, magnetic oxides such as Fe3O4, manganates and CrO2 have drawn much

attention because of metal-to-insulator transition, colossal magnetoresistance, and half-metallic behavior.

Orbital magnetism is closely related to many novel phenomena, such as magneto-optical effect, magnetostric-tion, and magnetocrystalline anisotropy. Orbital magnetic

∗_{Corresponding author.}

E-mail address: [email protected] (D.J. Huang).

moments of 3d transition metals are generally quenched because of crystal field. Some 3d transition metal oxides exhibit large unquenched orbital magnetic moments, which arises mainly from spin-orbit interaction in the localized 3d orbital whereby the atomic field is deformed in a rela-tively slight manner by the crystal field. In addition, strong Coulomb repulsion of 3d electrons localizes 3d orbitals and reduces the ligand field on the metal atoms, leading to large unquenched orbital moments[2,3]. For instance, results of magnetic X-ray scattering indicate that the orbital magnetic moment of NiO is rather large[4].

Measurements of orbital moments provide us with an opportunity to explore the localized nature of 3d electrons in transition metal oxides[2,3]. Several experimental tech-niques, such as neutron scattering, magnetic X-ray scat-tering, and magnetic circular dichroism (MCD) in X-ray absorption spectroscopy (XAS) are useful in studying or-bital moments. Element-specific separation of spin and orbital magnetization can be achieved by MCD in X-ray

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relation of spin and orbital moments to integrated XAS and integrated MCD spectra [5–10]. For example, the orbital and spin magnetic moments of Fe and Co obtained on applying the MCD sum rules to high resolutionL2_,3-edge XAS and MCD data agree well with those obtained from Einstein-de Haas gyromagnetic ratio measurements [9]. Direct transmission is the most reliable method to obtain accurate orbital magnetic moments [9], but this method is technically inapplicable to epitaxial thin films or single crystals. However indirect X-ray absorption measurement techniques, like the total electron yield (TEY) method for some transition metals, suffer typically from saturation and self-absorption effects that can produce inaccurate val-ues of orbital magnetic moment. To correct indirect XAS measurements for saturation and self-absorption effects is particularly crucial in measuring orbital moments[11].

Half-metallic oxides such as CrO2have recently drawn

re-newed attention due to their interesting magnetic and electri-cal properties. These properties are potentially important for future spintronics which takes full advantage of electrons’ spins as well as their charge in information circuits. In a half-metallic material[12], one spin channel is conductive, but the other spin channel is insulating. Based on band struc-ture calculations, many materials have been predicted to be half-metallic. However, experiments performed on some predicted half-metals do not show 100% spin polarization of the conduction electrons. One of the main reasons is that electron correlation effects prevent the conduction electrons from being 100% spin polarized. One therefore can mea-sure orbital moments to explore the localized nature of 3d electrons in half-metallic oxides[2,3]. For instance, exam-ining whether orbital moments are quenched is important in revealing the electronic nature of Fe3O4.

In this paper, we present measurements of MCD in soft X-ray absorption to study orbital magnetic moments of CrO2

and Fe3O4. MCD in X-ray absorption spectroscopy were

performed with correction for saturation effects. We also compare measurements of orbital moments with band struc-ture calculations based on local spin density approximation with on-site Coulomb energy U taken into account (LDA

+ U).

The rest of this paper is organized as follows. In the next section, we briefly describe the experimental methods in-cluding MCD methods and epitaxial growth of CrO2 and

Fe3O4thin films. Results and discussion of MCD

measure-ments are presented inSection 3, followed by the conclu-sions.

2. Experimental

2.1. Epitaxial CrO2and Fe3O4thin films

Epitaxial CrO2 films were grown on TiO2(1 0 0)

sub-strates by chemical vapor deposition (CVD) [13]. The

1,1,1-trichloroethane, 10% hydrofluoric acid and distilled water before air-drying. The deposition was at 400◦C by using CrO3as the precursor. X-ray diffraction results reveal

that CrO2 films are single crystalline and epitaxial;

mea-surements of magneto-optical Kerr effect show a square magnetic hysteresis loop, indicating high magnetic rema-nence of CrO2films.

Thin films of Fe3O4 were grown on MgO(0 0 1)

sin-gle crystals which provide an ideal template for epitaxial growth. The lattice constant of Fe3O4, 8.396 Å, is close to

twice of the MgO lattice constant, 4.211 Å, resulting in an epitaxial growth with a small lattice mismatch. Both the rocksalt structure of MgO and the inverse spinel structure of Fe3O4are based on a f.c.c. oxygen anion lattice, allowing a

continuation of the oxygen sublattice over the MgO/Fe3O4

interface. We achieved to grow epitaxial 100-monolayer (ML) (i.e. 210 Å thick) Fe3O4 thin films with

evaporat-ing Fe from an effusion cell at the presence of oxygen. Before film growth, the MgO(1 0 0) substrate was cleaved ex situ and annealed at a temperature around 650◦C with an oxygen pressure of 5× 10−8Torr for 1–2 h to remove contamination such as hydrocarbons. The cleanliness and the structure of MgO(1 0 0) surface were characterized by photoemission and reflection high energy electron diffrac-tion (RHEED), respectively. The growth rate of Fe3O4thin

films was ∼1 ML per minute. Structure of the thin films was real-time monitored by RHEED and its thickness was calibrated with the intensity oscillation of the RHEED spec-ular beam, as shown inFig. 1(a). The results reveal that the growth of Fe3O4thin films on MgO(0 0 1) is in an epitaxial

layer-by-layer mode. The film and its epitaxy were fully characterized by X-ray diffraction. The composition of the film was examined by core-level photoemission andL-edge X-ray absorption of Fe; the results are identical to those obtained from Fe3O4single crystals. In addition, the

resis-tance measurement shown inFig. 1(b)reveals that our film has a well-defined Verwey transition temperature which is also a good indication of the quality of our Fe3O4 thin

films.

2.2. MCD sum rules

The sum rules of MCD in X-ray absorption permit element-selective separation of spin and orbital contribu-tions to the total magnetic moment of materials[5,6,9,8,10]. Calculations on the basis of a tight-binding approximation show that K-edge MCD spectra is generated mainly by the 3d orbital moment on the neighboring sites through the p–d hybridization [14]. MCD spectra of an s-level absorption reflect the p-projected orbital magnetization density of unoccupied states. According to X-ray MCD sum rules, orbital magnetic moments morb in units of µB per atom can be obtained from K-edge XAS and MCD spectra. Sum rules of K-edge absorption relate orbital magnetic moments to K-edge XAS and MCD spectra as

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Intensity (arbi. units)

1000 500

0

Deposition Time (seconds)

104 105 106 Resistance ( Ω) 250 200 150 100 Temperature (K) (a) (b)

Fig. 1. (a) Intensity oscillation of RHEED specular beam and (b) temperature dependence of resistance measurement of 100 ML Fe3O4 thin films grown on MgO(1 0 0). [5,7,8]: morb= −2 3 K(σ+− σ−) dω K(σ++ σ−) dω(6 − np), (1)

where npandω are the electron occupation number in the

2p states and the photon energy, respectively; σ₊ and σ₋ are cross sections for absorption taken with the projection of the spin of the incident photons parallel and anti-parallel to the spin of the majority electrons in transition metals, respectively. K denotes the integration range across the

K-edge of the spectra.

With X-ray MCD sum rules, L2_,3-edge XAS and MCD spectra also provide information on the orbital morb and spinmspinmagnetic moments of transition metals as in the following equations: morb= −4 3 L2,3(σ+− σ−) dω L2,3(σ++ σ−) dω (10 − nd), (2) and mspin+ 7Tz = − 6_L 3(σ+− σ−) dω − 4_L₂_,3(σ+− σ−) dω L2,3(σ++ σ−) dω × (10 − nd), (3) wherendis the 3d electron occupation number of transition metals.L2_,3denotes the integration range acrossL2andL3 absorption edges. T_z is the expectation value of magnetic dipole operator. For cubic materials,T_z is typically negli-gible. Thus the ratio morb/morb of orbital to spin moments can be expressed as morb mspin ≈ 2_L 3+L2(σ+− σ−) dω 9_L 3(σ+− σ−) dω − 6 L3+L2(σ+− σ−) dω . (4) WithEq. (4), MCD spectra provide us with a measurement ofmorb/mspin, requiring no information on the background of XAS spectra, the average number of 3d holes, and the degree of circular polarization of incident photons.

2.3. MCD measurements

We carried out MCD measurements in soft X-ray ab-sorption with the elliptically polarized undulator (EPU) beamline [15,16] and the Dragon beamline of the Na-tional Synchrotron Radiation Research Center in Taiwan. The EPU can generate circularly polarized light or lin-early polarized light with the polarization in the horizontal or vertical direction with respect to the storage ring. The Dragon beamline delivers circularly polarized light via a bending magnet. All soft X-ray absorption measurements were taken with photons of an energy resolution 0.2 eV. The incident angle was 45◦off the sample normal. During the measurements, the thin films were at the magnetically remanent state and kept at a temperature of 80 K. Sample drain current was detected as the absorption signal.

For measuring L-edge XAS of Fe with the TEY method, there exists significant saturation effects. To extract the cor-rect value of orbital moments by applying the sum rules to the MCD data obtained with a TEY measurement, one needs to examine carefully the saturation effects. When sat-uration occurs, the measured TEY signal is no longer uni-formly proportional to the absorption cross section, leading to an inaccurate measurement of orbital magnetic moments

[11]. The degree to which saturation occurs in the TEY sig-nal depends on the relative photon penetration depthλ_xand electron sampling depth λe. The measured absorption sig-nalITEYin a TEY measurement is reduced by a correction factorf = 1/(1 + λe/λ_xcosθ), where θ is the incidence angle of X-ray with respect to the surface normal[11], i.e.,

ITEY= fCσ, in which C and σ are a proportion constant and

the absorption cross section, respectively. Theλe of Fe3O4

was estimated to be 50 Å, andλ_xat theL3andL2edges, re-spectively, were 170 and 525 Å[21]. One thus would expect to have 37 and 16% reduction in the TEY signal of Fe3O4

at theL3andL2peaks, respectively, if the saturation effects were not corrected.

To determine the energy-dependent correction factorf of Fe3O4, we measured the energy-dependent X-ray

penetra-tion depth λ_x with a new quasi-transmission technique in XAS. The underlying concept of this technique is shown in

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hν hν' hν MgO Fe₃O₄ detector substrate overlayer

Fig. 2. Schematic diagrams of (a) direct transmission and (b) quasi-transmission for soft X-ray absorption measurements. Filled and open circles shown in the substrate represent the composition atoms Mg and O, respectively. In quasi-transmission, O fluorescencehν from the substrate is detected.

Fig. 2. For incident photons with energyhν greater than the energy of OK-edge fluorescence, the transmitted photons through the Fe3O4 overlayer stimulate O K-edge

fluores-cencehνfrom the substrate MgO. The dependence of Ohν intensity on the incident photon energy accordingly provides an avenue for detecting relatively the transmitted photon in-tensity. The O atoms in substrate MgO can serve as detectors for transmission measurement of XAS. The contribution of O fluorescence from the Fe3O4 overlayer is negligible as

compared to that from the substrate, since the penetration depth of O fluorescence is much larger than the thickness of Fe3O4 overlayer. A plot of O K-edge fluorescence hν

intensity versus incident photon energyhν in the region of the FeL-edge absorption therefore gives rise to a measure-ment of transmission spectrum for FeL-edge absorption of Fe3O4overlayer.

The validity of this quasi-transmission technique was ex-amined by measuring the X-ray penetration depth of 80 Å thick pure Fe thin films in the region of theL2_,3-edge ab-sorption, as shown inFig. 3. A semiconductor fluorescence

1.0 0.9 0.8 0.7 0.6

Transmission (arb. units)

σ₊ σ₋ 1500 1000 500 0 λx (Angstroms) 740 730 720 710 700

Photon energy (eV) (a)

(b)

Fig. 3. (a)L2,3-edge quasi-transmission measurements and (b) average X-ray penetration depthλx of 80 Å thick pure Fe thin films grown on MgO(0 0 1).σ+andσ−are defined in the text.

fluorescence. Our measured λ_x of Fe thin film is in good agreement with that of previous direct transmission results

[9,11]. These test results establish unambiguously that a quasi-transmission measurement is as accurate as a direct transmission measurement in obtaining X-ray penetration depthλ_xof Fe.

3. Results and discussion

3.1. Orbital moments of CrO2

Fig. 4 presents the O K-edge XAS and MCD of CrO2

[17]. After correction for the incomplete polarization and the incident angle of soft X-ray, i.e. multiplying (σ₊ −

σ−) by 1/[ cos 45◦×0.6] for MCD spectra while keeping

XAS=(σ₊+ σ₋) unchanged, we found that the MCD to XAS ratio at the pre-peak position of O K-edge absorp-tion is 4.1%, which is larger than that, 3%, observed on La1−xSrxMnO3 single crystals[18]. For q and r as the

in-tegrated intensities of MCD and XAS spectra across the

Intensities (arb. units)

536 534

532 530

528

Photon energy (eV)

r q (σ₊+σ₋)/2 integrated (σ₊+σ₋) x 1/100 σ₊ σ₋ XAS background MCD integration x 1/2 MCD x 5

Fig. 4.K-edge XAS and MCD spectra of O in CrO2(after[17]). Top: XAS spectra with spin of photons parallel (denoted as σ+) and anti-parallel (denoted asσ−) to that of Cr 3d majority electrons, respectively; middle: MCD, i.e. (σ+− σ−)/[ cos 45◦×0.6], and MCD integration of the O

K-edge absorption; bottom: XAS integration spectra with an XAS

back-ground (thin broken line). Ther and q denote the integration of XAS and MCD spectra across theK-edge, respectively.

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K-edge, the orbital magnetic moment per O atom is morb = −(2/3)(q/r)(6−np). To quantitatively obtain the O 2p hole

density, we compared the spectrum of O 1s XAS of CrO2

with that of O2 molecules. The average number of O 2p

holes per atom in CrO2is estimated to be 0.5[17]. With an

arctangent-like edge-jump function for the background of the XAS spectra, the O orbital magnetic moment is there-fore estimated to be−(0.003 ± 0.001)µB. The large

uncer-tainty originates mainly from our estimate of the number of O 2p holes, the background functions of XAS spectra, and the uncertainty from the degree of circular polarization of incident photons.

Fig. 5 displays the Cr L-edge XAS and MCD spectra of CrO2 [17]. For q and r as the integrated intensities of

MCD and XAS spectra across theL2_,3edges, respectively, as shown inFig. 5, the orbital magnetic moment of Cr ismorb =

−(4/3)(q/r)(10 − nd). With an appropriate arctangent-like

edge-jump function for the XAS background andnd∼1, our MCD data indicate that the orbital magnetic moment of Cr is−(0.06 ± 0.02)µB[17]. Unlike the case of Fe3O4, MCD

data of CrO2are not severely affected by saturation effects,

because the difference in intensity between absorption at the CrL3andL2edges is significantly smaller than that of Fe. In our MCD measurements on CrO2, saturation effects have

been corrected by normalizing the XAS spectra to the normal

Intensity (arb. units)

605 600 595 590 585 580 575 570

Photon energy (eV)

σ₊ σ₋ (σ ₊ + σ ₋)/2 (σ₊− σ₋) x 2 integrated (σ₊ + σ ₋)/200 integrated (σ₊− σ₋)/100 r q

Fig. 5.L2,3-edge XAS and MCD spectra of Cr in CrO2(after[17]). Top: XAS spectra with incident photon of different spin directions; middle: XAS integration spectra with an arctangent-like edge-jump function of background (thin broken line); bottom: MCD and MCD integration spectra. The descriptions of the figure correspond to those ofFig. 4.

incidence data. In contrast, our MCD and XAS data do not provide quantitatively information on the spin moment of Cr because one can not uniquely define which part of the spectra belongs to theL3 or the L2 edges. This is due to the large multiplet splitting in the XAS final states relative to the Cr 2p core-level spin-orbit splitting. Nevertheless, the integration spectrum of our MCD data indicates that the orbital moment of Cr is opposite to its spin moment[17].

MCD measurements presented above, nevertheless, pro-vide valuable qualitative information on element specific or-bital magnetic moment. Our measurements reveal that Cr orbital moments of CrO2 is opposite to its spin moment,

but parallel aligned to O orbital moment. We found that the measured Cr orbital moment of−(0.06±0.02)µBis

consis-tent with those of LDA+ U calculations with U = 3–4 eV

[17,19].

3.2. Orbital moments of Fe3O4

Fig. 6 shows Fe L2_,3-edge XAS and MCD spectra of Fe3O4 thin films obtained with TEY measurements.

Be-fore obtaining the orbital moments, we first discuss the multiplet structure of the spectra. The 2p XAS spectrum reflects directly the nature of the 3d electronic ground state. The local ground state of Fe ions is a mixture of configu-rations 3dn, 3dn+1L, and 3dn+2L2 withn = 5 and 6 for Fe3+and Fe2+ions, respectively, whereL denotes a ligand hole. The final state inL-edge absorption is predominantly a mixture of configurations 2p3dn+1 and 2p3dn+2L. The 2p3dn+1 configuration exhibits multiplet structure as a consequence of the 2p–3d exchange interaction, whereas

TEY intensity (arb. units.)

735 730 725 720 715 710 705 700

Photon energy (eV) σ+

σ

MCD X4

Fig. 6. FeL2,3-edge XAS and MCD spectra of Fe3O4thin films obtained with TEY measurements.σ+andσ−are defined in the text.

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3000 2000 1000 0 λx( Angstroms) 740 730 720 710 700

Photon energy (eV) 0.9

0.8 0.7 0.6 0.5

Transmission (arb. units)

(a)

(b)

Fig. 7. Fe L2,3-edge X-ray absorption in quasi-transmission mode (a) and penetration depth λx (b) of Fe3O4 taken with quasi-transmission measurements.

a broad band feature exists in the configuration 2p3dn+2L resulting from the bandlike character of the ligand hole. The MCD measurements suggest that the leading edge of the L3 absorption (i.e. at photon energy 707.5 eV) with a negative MCD peak results mainly from 2p → 3d transi-tion in the B-site Fe2+ ions. Another negative MCD peak at photon energy 709.4 eV is derived predominately from the B-site Fe3+ions. The energy difference between these two MCD peaks is∼(Udd− Udc), where Udd andUdc are

the Coulomb interaction energies between 3d electrons and between 3d electrons and 2p core holes, respectively. In addition, the positive MCD peak at photon energy 708.6 eV predominantly results from the A-site Fe3+ions.

To extract the correct value of orbital moments by apply-ing the sum rules to these MCD data, we have obtained the correction factor for saturation effects of Fe L-edge XAS measurements by the measuring X-ray absorption length.

Fig. 7(a)shows the quasi-transmission measurements on Fe

L2,3-edge XAS of epitaxial Fe3O4 thin films of thickness

100 ML at 300 K. These quasi-transmission data give rise to a measurement on the X-ray penetration depthλ_xof Fe3O4,

as shown inFig. (b), in whichλ_xat theL3andL2absorption peaks are similar to those shown in[21]. With the measured

λx and the electron sampling depth λe = 50 Å from [21], we achieved to have MCD measurements on Fe3O4 with

correction for saturation effects, as shown inFig. 8. There is a pronounced difference (∼20%) between the L3 MCD

spectra with and without correction for saturation effects, whereas the difference in theL2 MCD is relatively small. Forp and q as the integrals of the MCD spectrum across the

L3and theL2_,3 absorption edges, respectively,morb/mspin is 2q/(9p − 6q). We found that morb/mspin of Fe3O4 per

formula unit are 0.21 and 0.17 with and without correction for saturation effects, respectively, if the 7T_z contribution is neglected. MCD (arb. units) 740 730 720 710 700

Photon energy (eV)

MCD integration (arb. units)

MCD

MCD integration p

q

Fig. 8. Fe L2,3-edge MCD and MCD integration of Fe3O4 obtained from TEY measurements. The solid and dash lines are with and without correction for saturation effects, respectively.p and q denote the integrals of the MCD spectrum across the L3 and the L2,3 absorption edges, respectively.

LSDA+ U calculations show the values of spin moment

and magnetic dipole moments of Fe3O4 are, respectively,

3.97µBand 0.155µBper formula unit[20]. The contribution of 7T_z thus gives rise to 4% of increase in the morb/mspin ratio. Therefore, we conclude thatmorb/mspinof Fe3O4per

formula unit is 0.22 ± 0.04, suggesting an average orbital magnetic moment of(0.44 ± 0.08)µB per B-site Fe atom. To unravel the origin of the unquenched orbital magnetic moments of Fe3O4, we resort to configuration interaction

approach for the ground state electronic configuration of the octahedral Fe2+ ions based on a FeO6 cluster model.

We calculated the occupation probabilities of down-spin 3d electrons of high-spin Fe2+ ions in an octahedral crystal field. With the spin-orbit interaction, but without the crystal field and the hybridization between Fe 3d and O 2p, the orbital moment of Fe2+ions maximizes, i.e.,morb= 2µBas

expected from the Hund’s coupling. If the the crystal field and the hybridization are included, the dominant down-spin

t2g state of Fe2+ is 1/√2(Idyz+ dzx), leading to an orbital moment of 1µB[22], i.e., average 0.5µBper B-site Fe atom in Fe3O4. Our MCD measurements thus indicate that 3d

electrons of B-site Fe in Fe3O4 are with a strong localized

nature even at temperature above the Verwey transition.

4. Conclusions

We have studied orbital magnetic moments of CrO2and

Fe3O4 by measuring MCD in soft X-ray absorption. The

results show that orbital moments of Cr in CrO2 are are

nearly quenched, revealing that Cr 3d electrons are strongly hybridized with O 2p electrons and more delocalized as compared with those of Fe in Fe3O4. We found that oxygen

atoms in CrO2exhibit a significant orbital magnetic moment

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CrO2are parallel coupled to that of Cr, while the spin

mo-ments are anti-parallel coupled. In addition, the magnitudes of spin and orbital moments of Cr are enhanced as on-site Cr 3d–3d Coulomb interaction increases. We also found that Fe3O4exhibits large orbital moments, in contrast to nearly

quenched orbital moments of Cr in CrO2. Large orbital

polarization of Fe in Fe3O4caused by on-site Coulomb

in-teractions of 3d electrons results in unquenched orbital mo-ments of Fe3O4. As compared with LDA+ U calculations,

our results indicate that one has to properly include on-site Coulomb interactions of 3d electrons in CrO2 and Fe3O4

in order to describe their electronic structure adequately.

Acknowledgements

This work was supported in part by the National Science Council of Taiwan.

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