University of Groningen

Structural, electronic, and magneto-optical properties of YVO3Tsvetkov, AA; Mena, FP; van Loosdrecht, PHM; van der Marel, D; Ren, Y; Nugroho, AA;Menovsky, AA; Elfimov, IS; Sawatzky, GAPublished in:Physical Review. B: Condensed Matter and Materials Physics

DOI:10.1103/PhysRevB.69.075110

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PHYSICAL REVIEW B 69, 075110 ~2004!

Structural, electronic, and magneto-optical properties of YVO3

A. A. Tsvetkov,* F. P. Mena, P. H. M. van Loosdrecht, and D. van der MarelMaterials Science Center, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands

Y. RenExperimental Facilities Division, Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA

A. A. Nugroho†

Solid State Chemistry Lab, MSC, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands

A. A. MenovskyVan der Waals–Zeeman Institute, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands

I. S. Elfimov and G. A. SawatzkyDepartment of Physics and Astronomy, The University of British Columbia, 334-6224 Agricultural Road, Vancouver,

British Columbia V6T 1Z1, Canada~Received 8 April 2003; published 26 February 2004!

Optical and magneto-optical properties of YVO3 single crystal were studied in the far-infrared, visible, andultraviolet regions. Two structural phase transitions at 75 K and 200 K were observed and established to be offirst and second order, respectively. The lattice has an orthorhombicPbnmsymmetry both above 200 K as well

as below 75 K and is found to be either dimerized monoclinicPb11 or triclinic P1 in between. We identifyYVO3 as a Mott-Hubbard insulator with an optical gap of 1.6 eV. The visible spectrum shows threed-bandexcitations at 1.8, 2.4, and 3.3 eV, followed by charge-transfer transitions at about 4 eV. The observed structureis in good agreement with LSDA1U band structure calculations. By using ligand field considerations, weassigned these bands to the transitions to the4A2g , 2Eg1 2T1g , and 2T2g states. The strong temperaturedependence of these bands is in agreement with the formation of orbital order. Despite the small net magneticmoment of 0.01mB per vanadium, a Kerr effect of the order of 0.01° was observed for all threed bands in themagnetically ordered phase (TNeel5116 K). A surprisingly strong enhancement of the Kerr effect was foundbelow 75 K, reaching a maximum of 0.1°. This effect is ascribed to the nonvanishing net orbital magneticmoment.

DOI: 10.1103/PhysRevB.69.075110 PACS number~s!: 71.20.2b, 78.20.2e, 78.30.2j

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I. INTRODUCTION

The interplay between the kinetic energy and Coulointeraction in strongly correlated electron systems enasmall external or internal perturbations to manipulateelectronic and magnetic properties of matter. If, in additiothere is a ground-state degeneracy, further interestingnomena, like an orbital ordering, can arise.1

In yttrium orthovanadate, YVO3, spin and orbital order-ing was suggested to be responsible for at least one oftemperature-induced sign reversals of the magnetization2 Inthe magnetically ordered phase, YVO3 is a canted antiferro-magnet, where a net ferromagnetic moment arises duesmall angle between the antiferromagnetically~AFM! ori-ented spins of the V31 ions. The transition from the roomtemperature paramagnetic phase to the antiferromagnstate occurs at the Ne´el temperatureTN5116 K. Upon fur-ther lowering the temperature, the magnetic moment graally changes sign around 90 K. It has been argued thatmagnetization reversal is due to the opposing effects ofDzyaloshinsky-Moriya interaction and the single-ion manetic anisotropy on the spin canting direction.2 The magne-tization switches sign again around 77 K. At this temperatthe antiferromagnetic order changes from high-tempera

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C type to low-temperatureG type.3 A C-type AFM ordercorresponds to an AFM arrangement in planes and a femagnetic arrangement between the planes. AG-type AFMorder implies a completely antiferromagnetic arrangemeboth within planes and between them. Renet al.2 argued thatalong with the spin order~SO! there is an orbital order~OO!on the vanadium sites. According to the proposed pictuone of two 3d electrons always occupies thexy orbital, whileanother electron occupies alternatingly either thexz or yzorbital on different atoms, thus forming orbital order. In oder to minimize the exchange energy aC-type spin order isaccompanied by aG-type orbital order and vice versa. Thonset temperature of the orbital order was reported tomuch higher than the Ne´el temperature,TOO5200 K.4

The proposed picture of the electronic structure stillquires confirmation from, for instance, spectroscopic expments. The strength of optical transitions involving a chatransfer between orbitals of different ions should be higsusceptible to the orbital order between ions. Indeed, onthe aims of the present research is to study the influencorbital ordering on optical transition strengths and use ttechnique to study orbital ordering in YVO3. In this paperwe present, among others, optical and magneto-optical msurements of electronic excitations in YVO3 single crystals.

©2004 The American Physical Society10-1

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A. A. TSVETKOV et al. PHYSICAL REVIEW B 69, 075110 ~2004!

The observed electronic spectra are discussed using ligfield theory considerations and compared to LDA1U calcu-lations. In addition, magneto-optical Kerr effect experimeare used to elucidate the spin orientation.

The crystal structure of YVO3 was initially reported tohave an orthorhombicPbnm (D2h

16 in Schoenflies notation!symmetry at all temperatures.5,6 Recent synchrotronmeasurements4,7 report the observation of an additional~401!reflection below 200 K, inconsistent with thePbnmsymme-try. The authors concluded4 that the crystal structure wamost likely P21 /a, the highest-symmetry subgroup oPbnm. However, the intensity of thePbnmforbidden reflec-tion was four orders of magnitude weaker than the allowreflection,4 which made the refinement of the x-ray data dficult. Far infrared~FIR! spectroscopy is a very sensitive toto study crystal structure variations. Minor atomic displacments leading to a symmetry breaking, which may be dicult to elicit from x-ray analysis, manifest themselvthrough the appearance of new phonon lines in the FIR strum. Recently, Ulrichet al.8 proposed that YVO3 may besubjected to a new sort of Peierls instability, where the nground state involves a dimerization along thec axis. Fromthe crystallographic and optical points of view this dimeriztion removes the inversion center, and IR- and Raman-acphonons become mixed. Thea-axis-polarized modes stanevertheless independent from theb- or c-axis modes if thedimerization affects only thec axis. We use FIR vibrationaspectroscopy to follow temperature-induced variations ofphonon spectrum and to refine the crystal structure of YV3.

II. EXPERIMENTAL DETAILS

The samples were made in a two-stage process. In thestage a polycrystalline powder of YVO3 was prepared fromYVO4 powder. The YVO4 powder was produced by a hightemperature solid-state reaction from appropriate mixturepredried Y2O3 ~99.998%! and V2O5 ~99.995%, metal basis!.The oxygen in YVO4 was reduced by annealing the powdin a flow of pure H2 at 1000 °C. The second crystal growstage was carried out by the floating zone technique usinfour-mirror furnace in a flow of Ar gas.9 Single-crystallineboules of about 6 mm in diameter and 60–70 mm in lenwere obtained from the growth. The crystallinity of the bouused in our experiments was checked by Laue x-ray diffrtion. The elemental composition of the crystal was checusing an electron probe microanalyzer~EPMA!, and the re-sults showed that the molar ratios were given by Y:V51.00:1.00:3.02. A separate check of the composition usa chemical analysis method showed that the cation ratio oover V was 1.0060.01 and that the oxygen stoichiometwas 3.0360.02. Both results are in good agreement.

The dielectric function for near-infrared, visible, and utraviolent spectral ranges was obtained directly by usinglipsometry. Because ellipsometric measurements aresensitive to contamination of the surface, we usedultrahigh-vacuum cryostat with a residual pressure less t1028 mbar. The cryostat was specially designed to minimthe movements of the sample due to the thermal expanof the cold finger. To minimize the mechanical stress on

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windows, the latter were mounted on long stainless stubes. The windows were proved to give no artificial effeon the measured spectra at room temperature. The spwere measured with a VASE32 ellipsometer from J.Woollam Co., Inc., covering a spectral range fro6000 cm21 to 36 000 cm21 ~0.75–4.5 eV!. During the mea-surements, the samples were aligned in such a way that ctallographic axes were parallel to the normal of the planeincidence (y direction!, the normal of the sample surface (zdirection!, and the intersection of these two planes (x direc-tion!, respectively. Such a symmetrical arrangement simfies the calculations of the dielectric tensor.10 The opticalresponse is mainly determined by thex component of thetensor. We performed the measurements on a set of samwhere all three crystallographic axes were successivaligned along thex direction. Inversion of the ellipsometricdata in the assumption of an isotropic sample gives a vgood initial approximation for thex component of the dielectric tensor. Further refinement of the dielectric tensor is doby an iterative procedure.

Far-infrared and midinfrared reflectivity spectra wemeasured by Fourier transform infrared reflection spectrcopy using a Bruker IFS-113v. The intensity of the reflectlight from the sample was referenced to that from a gmirror for every measured optical surface at each polartion. The sample was mounted on the cold finger of a heliflow cryostat, whose temperature was varied from 300down to 4.2 K. Kramers-Kronig transformation was usedcalculate the dielectric function and optical conductivfrom the reflectivity data in the infrared region. For thecalculations we extrapolated the reflectivity below 50 cm21

with a pure ionic insulator response. For the high-frequenextrapolation we used the reflectivity calculated from thelipsometric data.

The magneto-optical properties were measured usinhomebuilt Kerr spectrometer. We used an electro-optmodulation technique, similar to Ref. 11, to obtain simulneously the Kerr rotation and ellipticity induced by thsample. The combination of a xenon arc lamp, the windoa Si detector, and other optical components limited our sptral range to 350–800 nm~1.55–3.5 eV!.

III. STRUCTURAL PHASE TRANSITIONS

The orthorhombicPbnm crystal structure of YVO3 isshown in Fig. 1. It can be considered as a distorted perskite structure. When compared to the perovskite unit cthe orthorhombica andb axes lay along the diagonals of thperovskite unit cell and the corresponding translational vtors are approximatelyA2 times longer. Thec-axis dimen-sion of the orthorhombic unit cell is twice as large. ThYVO3 unit cell contains thus four formula units. Vanadiuions have an octahedral surrounding. The octahedronsdistorted, rotated, and tilted with respect to each other,illustrated in Fig. 1.

In the present work we use optically active phononstrack changes in the crystal symmetry. As yttrium orthovadate is an insulating compound, its optical response inFIR region is determined purely by lattice vibrations. In F

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STRUCTURAL, ELECTRONIC, AND MAGNETO-OPTICAL . . . PHYSICAL REVIEW B 69, 075110 ~2004!

2 the room-temperature reflectivity for all three polarizatiois shown together with the optical conductivity. As canseen, there are nine, nine, and seven optically active mofor thea, b, andc axes, respectively. The positions of the Tphonon frequencies are shown by vertical lines and thequencies are given in Tables I and II. Some resonancesvery weak. For example, the mode of highest frequencythec axis is hardly visible in the conductivity and appearsa shoulder on the reflectivity curve. It gains intensity astemperature is lowered and reaches its maximum in the ltemperature orthorhombic phase. Shown in Fig. 3 is the tperature dependence of the reflectivity for all three polaritions. The number of the phonons stays the same betwroom temperature and 200 K. Below 200 K a number ofadditional phonons gradually emerge. We illustrate thispicturing some of the new modes for theb andc axes in Fig.4. As can be seen from the figure, the intensity of the nmodes evolves continuously and monotonically as the tperature decreases, reaching its maximum at 75 K. Thetical strengths remain, however, one or two orders of magtude weaker than that of the original main modes. BelowK the new phonons discontinuously disappear. As anample, the temperature dependence of the oscillator streof the new 522 cm21 mode is shown in Fig. 4.

To analyze the observed phonon spectra, we applgroup theory analysis. The primitive cell of YVO3 containsfour formula units, yielding 60 phonon modes in total. In tPbnm lattice the four yttrium atoms and four vanadium aoms occupy equivalent sites 4c and 4b in Wyckoff notationwith site symmetryCs

xz andCi , respectively. The 12 oxygeatoms are distributed between two inequivalent sites 4c and

FIG. 1. Pbnmorthorhombic crystal structure of YVO3.

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8d with site symmetryCsxz and C1, respectively. Using the

usual procedure,12 we find that the phonon normal modetransform according to

G57Ag18Au15B1g110B1u17B2g

18B2u15B3g110B3u .

The total representationG can be subdivided into threacoustic vibrational modesB1u1B2u1B3u , 24 Raman-active modes 7Ag15B1g17B2g15B3g , eight silent Au

FIG. 2. Room-temperature reflectivity and corresponding optconductivity for the three crystallographic directions. Dashed linindicate positions of the phonon modes. There are nine, nine,seven modes for thea, b, and c axes, respectively, in agreemewith the Pbnmsymmetry.

TABLE I. TO phonon modes for thea and b axes at roomtemperature.

B1u ~a! B3u ~b!

v (cm21) g (cm21) Sa v (cm21) g (cm21) Sb

162.2 3.2 0.08 144.3 15.5 0.73211.6 8.5 5.4 237.4 5.5 2.0328.5 9.9 1.6 280.1 8.4 0.64359.2 15.0 0.56 318.7 7.8 0.35420.8 10.4 1.4 374.5 6.3 0.22446.8 17.3 2.6 390.7 16.5 4.21494.5 10.0 0.005 471.7 13.3 1.2517.5 15.5 0.06 543.7 9.8 0.86572.4 22.6 0.91 559.8 17.5 0.21

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A. A. TSVETKOV et al. PHYSICAL REVIEW B 69, 075110 ~2004!

modes, and 25 infrared-active modes. The infrared vibratiare split into 9B1u(Euua), 9B3u(Euub), and 7B2u(Euuc)modes with the electric dipole moment aligned along thea,b, andc axes, respectively.

A similar group theory analysis is applied to the lowesymmetry structuresP21 /a, P1, andPb11, which are sub-groups of thePbnm symmetry. Table III illustrates whichsymmetry elements are inherited in different symmetries.also show the relation between the widely used notaPbnm, adopted also in this paper, and the standard notaPnma. The monoclinicP21 /a symmetry is postulated fromx-ray measurements.7 The triclinic P1 symmetry, secondhighest possible symmetry afterP21 /a, was proposed by usbased on indications that the center of inversionconserved.13 Both x-ray7 and optical13 measurements showthat the symmetry cannot be higher than monoclinic. Recneutron experiments indicated the possibility of a dimerizstate.8 Dimerization displaces the middle VO2 plane~see Fig.1! away from its central position. It removes the inversicenter and screw axis from the symmetry operations

TABLE II. c-axis phonons at 75 K.B2u modes originate fromthe room-temperature phase. New vibrational modes, appearinlow 200 K, are designated asA.

Mode Frequency Sa Sb Sc

B2u 180.2 - - 7A 199 - 0.037 0.008

B2u 205.6 - 0.006 0.78B2u 333.0 0.19 0.008 2.9A 350 - 0.67 0.003

B2u 359.8 - 0.02 0.37B2u 420.5 1.6 0.076 1.6A 522 - 0.024 0.018

B2u 564.9 - 0.014 1.2B2u 699.2 - - 0.002

FIG. 3. Temperature dependence of the FIR reflectivity for thpolarizations.

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P21 /a. The remaining symmetry group includes only a gliplaneb and is referred to asPb11.

As the x-ray measurements do not reveal any multiplition of the unit cell,4 the number of atoms in the unit cell inot changed. For monoclinicP21 /a (C2h

5 ) symmetry groupone expects 16Bu IR-active and 2 acoustic modes in thebcplane and one acoustic and 17Au IR modes along thea axis.In the case of triclinicP1 (Ci

1) symmetry, there should be33Au IR modes, which can have components along all thaxes. MonoclinicPb11 (Cs

2) symmetry splits phonons intotwo irreducible representations 30A8(Euubc)130A9(Euua),where Raman and IR modes are mixed. How the phomode irreducible representations transform into each odue to the descent in symmetry is depicted in Fig. 5. Bmonoclinic C2h

5 and triclinic Ci1 crystal lattices have an in

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FIG. 4. Left panels: ‘‘leakage’’ of theb-axis B3u mode into thec-axis response. Right panels: appearance of a new previously sAu mode in theb andc responses. Inset: temperature dependencthe optical strength of the new mode.

TABLE III. Possible symmetries and symmetry operationsthe intermediate phase (75 K,T,200 K).

N Pnma Pbnm P21 /a P1 Pb11

D2h16 D2h

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STRUCTURAL, ELECTRONIC, AND MAGNETO-OPTICAL . . . PHYSICAL REVIEW B 69, 075110 ~2004!

version center. As a result the IR and Raman modes domix with each other for these symmetries. In point groC2h , because theb andc axes are not orthogonal anymorthe corresponding phonons mix and form theBu representa-tion 7B2u19B3u→16Bu . The modeAu , silent inD2h

16 sym-metry, becomes optically active and together with theB1umode gives theAu representation 8Au19B1u→17Au . Apossible twinning in theb-c plane cannot be a reason foleaking theb-c phonons to thea axis and vice versa. Alternatively, in the lowestCi

1 symmetry all the phonons mixtogether, as seen in Fig. 5. In thePb11 symmetry, RamanAgmodes become visible in thebc plane and together with thIR Bu phonons form theA8 representation 12Ag118Bu→30A8. Similar, RamanBg modes can be observed in tha-axis response together with IRAu modes 12Bg118Au

→30A9. An important difference betweenP1 and Pb11symmetries is that inP1 the same modes can be observedall three polarizations, while inPb11, a eigenmodes on oneside andb andc eigenmodes on the other side remain serate.

At room temperature we observed nine, nine, and sephonons for thea, b, andc axes, respectively~see Fig. 2!.The TO phonon frequenciesv, broadeningG, and opticalstrengthS are presented in Tables I and II. Our observatconfirms the orthorhombicPbnm symmetry of the crystalattice at room temperature. At lower temperatures, as fathe crystal structure is concerned, we can conclude from4 that thePbnm symmetry is transformed to a lower onbelow 200 K and is restored again below 75 K. The tempeture evolution of the optical strength of the new phonoindicates that the phase transition at 200 K has a secorder nature and that the one at 75 K has a first-order naShown in Table II are the phonon mode frequenciesstrengths observed in thec-axis spectrum at 75 K. The lineactive also in the high-temperature phase are in boldfaceassigned toB2u ; those appearing only in the intermediatemperature phase are labeled byA. Although much morenew phonons are seen for all three axes, only the activc-axis modes, having a counterpart in the other axes,shown in the table. First, one can see that the originalc-axis

FIG. 5. Transformations of the phonon irreducible representions due to the descent in lattice symmetry.

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phonon lines give rise to phonon absorptions along thbaxis. The reverse is also valid. The phonons from theb axis‘‘leak’’ in the intermediate phase to thec axis, which isshown in Fig. 4. This agrees with all three symmetries unconsideration. However, there are a number of newly avated absorption peaks~199, 350, and 522 cm21) in the bandc polarizations, which do not have parents in other plarizations. The fact that these new modes are exactly atsame frequency in bothb andc polarizations—as shown inthe right panels of Fig. 4—excludes the possibility of tdoubling of the unit cell as their origin. The appearancenew modes is forbidden in theP21 /a symmetry~see alsoFig. 5!. This observation rules outP21 /a symmetry for theintermediate phase. Because these modes are not seen ipolarization above 200 K or below 75 K, we can ascrithese phonons either to the previously silent modeAu acti-vated in P1 symmetry or to the high-temperature Rammodes activated inPb11 symmetry. We did not observe ancorrelation of phonons betweenb andc on the one side anda on the other side, apart from the modes already presboth in a and c polarizations above 200 K~333 and420 cm21 modes in Table II!. This could imply that the tri-clinic distortions are extremely small, in particular for theaaxis. However, thePb11 symmetry gives a more naturaexplanation, as it keeps thea andbc modes apart, consistenwith the observation. All in all, these facts draw us to tconclusion that the crystal structure of YVO3 in the interme-diate phase most likely has a monoclinicPb11 symmetry. Afurther test of this conclusion could be a comparison to Rman measurements, when data become available.

Finally, we remark on the relation between the electroand crystal structure changes. From Fig. 6 one can seethe main modes evolve smoothly through the second-o

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FIG. 6. Temperature dependence of the TO frequencies forc-axis B2u phonon modes. For comparison purposes, the vertscale in each square comprises 6% of the central frequency.

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A. A. TSVETKOV et al. PHYSICAL REVIEW B 69, 075110 ~2004!

phase transition, where the appearance of orbital ordereported.4,7 However, a number of phonon frequencichange substantially at the first-order phase transition, whspins and orbitals switch their ordering. The frequenchange is found to be particularly strong for the modaround 400 cm21. From lattice dynamical calculations14 forthe isostructural compound LaMnO3 we conclude that the400 cm21 modes mainly involve vanadium-oxygen bond vbrations. Therefore, it seems that the main structural chanat the first-order transition involve a distortion of the VO6octahedra.

IV. ELECTRONIC STRUCTURE

The yttrium Y31 and vanadium V31 ions in YVO3 bothcarry a formal charge 31. Yttrium has a complete shell, anit can be excluded from consideration for the electronic trsitions. Vanadium has two 3d electrons in the outer shell. Wcan thus expect two types of optical transitions in the visirange:d-d transitions between vanadium ions with the chacteristic energy of the Mott-Hubbard gap@Mott-Hubbard~MH! transitions# and the charge-transfer~CT! transitionsfrom the oxygen 2p band to the free states in the vanadiu3d band.

Shown in Figs. 7 and 8 are the real and imaginary part

FIG. 7. Temperature dependence of the real and imaginary pof the b-axis dielectric function for YVO3. The vertical lines indi-cate locations of the band maxima.

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the YVO3 dielectric function,«5«81 i«9, measured at vari-ous temperatures. The optical response at low temperatis determined by three bands with their maxima located1.8, 2.4, and 3.3 eV, followed by a sharp upturn above 4The optical gap is found at 1.6 eV. It is quite remarkableobserve that the intensity of some bands, located in thegion of a few electron volts, changes by as much as 50%temperature variations as small askBT<26 meV.

Recently Miyasakaet al.15 reported reflectivity measurements on YVO3, where the optical conductivity, obtainethrough the Kramers-Kronig relations, revealed only twpeaks. Also the temperature dependence and the reporteisotropy of the conductivity were different. Since«9 is ap-proximately 5 times smaller than«8 in the visible part of thespectrum, the reflectivity is mainly determined by the repart of «. The d-band structure in«8 and «9 gives rise toreflectivity variations of only a few percent and thtemperature-induced changes of the reflectivity are aro1% or less. This together with the close vicinity of the strocharge-transfer transitions places heavy demands on thecuracy of the measurements. A small error can substantaffect an interpretation of the electronic spectrum. Therefowe used the ellipsometry technique to determine«8 and «9directly at each particular photon energy, excluding thecessity of reference measurements. In addition we took scial precautions to perform measurements in ultrahvacuum in order to avoid surface contamination at low teperatures. We trust that these measures substantially mmize a possible error.

Let us first discuss the origin of the bands. Following tgeneral classification scheme,16 YVO3 is a Mott-Hubbard in-sulator. The lowest excitations aredi

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FIG. 8. Real and imaginary parts of the dielectric function fthe a andc axes of YVO3.

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STRUCTURAL, ELECTRONIC, AND MAGNETO-OPTICAL . . . PHYSICAL REVIEW B 69, 075110 ~2004!

between different vanadium ions,i andj. The upturn above 4eV is due to charge-transfer excitations. This general picalso follows from our LSDA1U calculations and agreewith previous room-temperature measurements.17,18 The finestructure of the MH band observed here has not beenported previously and will be discussed using ligand fitheoretical considerations and LSDA1U calculations.

Because the orthorhombic distortion of the oxygen ochedron is small, we can neglect any on-sited-d excitations.For the same reason we can, considering the energy diagrestrict ourselves in the first approximation to Oh symmetryon the vanadium site. Theeg orbitals can be excluded, because due to the large crystal field splitting, 10Dq, the mix-ing betweeneg andt2g orbitals is expected to be small. Thuin the strong-field approximation the twod electrons occupyt2g orbitals.

If we take into account the Coulomb interaction, thet2glevel is split into 3T1g , 1Eg , 1T2g , and1A1g levels, asshown in Fig. 9~a!. The 1Eg and 1T2g levels are degeneratin the Oh symmetry. In the ground state thed electrons oc-cupy the lowest-energyS51 state3T1g , in agreement withHund’s rules. The MH excitations occur from the initial stawith two vanadium atoms in thed2 state to the final statewith the first atom in thed1 (V41) and the second in thed3

(V21) states. In the final state the wave function of the sinelectron follows obviously only one irreducible represention 2T2g , while the d3 state splits into four levels4A2g ,2Eg ,2

T1g , and 2T2g , with 2Eg and 2T1g again being degenerate. The energy diagram of the final state is depicted in9~b!. The three observed bands in Fig. 7 correspond to tsitions to these three energy levels. According to the msurements, these bands span the energy range of 1.5 eV1.8 eV to 3.3 eV. With the crystal field splitting of 10Dq'2 eV, our assumption of a small admixture ofeg orbitalsis justified.

The picture obtained with the ligand field theory isgood agreement with our LSDA1U calculations. LSDA1Uband structure calculations have been performed in the linmuffin-tin orbital ~LMTO! calculation scheme.19,20 Vana-

FIG. 9. Energy diagram for~a! the ground state of the vanadiumions and~b! excited states of two vanadium sites.

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e-

-

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e-

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ar

dium 3d partial densities of states were obtained in tLDA1U calculation withU53.4 eV andJ50.85 eV for thelow-temperature crystal and magnetic structure of YVO3.The results are consistent with previous calculations ofelectronic structure.21 As can be seen from the electron desity of states in Fig. 10, the highest occupied states formnarrow d band, with both electrons in a spin-up state. TAFM-ordered neighboring vanadium ion should accordingbe in a spin-down state. The lowest unoccupied band cosponds to the addition of an electron with spin up. Thagrees with the lowest excited4A2g state, which indeed putselectrons in the high-spin stateS53/2. Two consequent excitation bands are formed by the transfer of spin-down eltrons, again in agreement with the lowS51/2 spin states inthe 2Eg , 2T1g , and 2T2g representations found from thligand field theory. Higher electron-addition bands wiequal spin-up and spin-down populations have aneg origin.From the energy distribution of the bands in Fig. 10 one csee that YVO3 is indeed a Mott-Hubbard insulator.16 Thelowest excitations ared-d transitions d2d2→d3d1. Thecharge-transfer transitionsd2→d3L occur at higher energiethan thed-d transitions.

The temperature dependence of the optical responsYVO3 is shown in Figs. 7 and 8. There is only a smtemperature dependence between 70 K and 5 K, as caseen in Fig. 8, and the corresponding data are omitted infurther consideration. To clarify the temperature dependeof the MH bands, Fig. 11 shows a differential dielectric funtion for Euub, where the 250 K data are subtracted from tcurves in Fig. 7. In order to quantify temperature variatioof the optical strength of the bands, we fitted simultaneouthe real and imaginary parts. The differential dielectric funtion turned out to be well fitted with three Gaussians in timaginary part and with its Hilbert transform, the Dawso

FIG. 10. Vanadium 3d partial density of states for spin-up anspin-down electrons, obtained in local spin-density approximatwith the Hubbard potentialU taken into account.N21 andN11correspond to the electron removal and electron addition starespectively.

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A. A. TSVETKOV et al. PHYSICAL REVIEW B 69, 075110 ~2004!

function, in the real part. The fitted curves for 80 K ashown along with the experimental data in Fig. 11. The fdielectric function shown in Fig. 7 was also fitted in the saway, but an additional fourth Gaussian was necessary tocount for the CT band. In this way the position of the banwas confirmed to be temperature independent. Howevewas not possible to determine accurately the absolute opstrength of the MH bands due to an additional non-Gauscontribution. It was also impossible to determine the positof the 3.3 eV band at high temperatures because of its vishing presence in the spectra. The band positions and opstrengths obtained from the fits are plotted in Fig. 12. Tdielectric function reveals minimal variations between rootemperature and the second-order structural phase transat 200 K. Below 200 K a strong growth of the 3.3 eV band

FIG. 11. The dielectric functions from Fig. 7 after subtractionthe 250 K data. The fit curve shows a simultaneous fit to theand imaginary parts for the 80 K data.

FIG. 12. Temperature dependence of the position of the elecbands~left! and their optical strength together with the total specweight of the three bands~right!.

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lec-sitaln

nn-cale

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observed, which is accompanied by a decrease of the 1.82.4 eV bands. The total integrated change of the optstrength of these MH bands remains virtually zero downthe Neel temperatureTN5116 K. In the magnetically or-dered state the 3.3 eV band acquires additional strength.additional spectral weight transfer should come from higenergies, most probably from theeg states, as the decreasethe low-energy bands cannot account for it. Indeed,lowest-energy state in thet2g

2 eg configuration is obtained byadding aneg electron to the ground state3T1g . Four irre-ducible representations,4T1g , 4T2g , 2T1g , and 2T2g can beformed from this configuration, where the latter represention descends also from thet2g

3 configuration. Antiferromag-netic order favors transitions to the low-spin states and tgives additional optical strength to the2T2g state.

At the first-order phase transition, the optical strengththe 2.4 and 3.3 eV bands experiences jumps in oppositerections. Additionally, as can be seen in Fig. 11~a!, a newshoulder emerges at around 2.7 eV. This appears in Fig.an extended flat region, which becomes visible probablyto the narrowing of the 3.3 eV band. However, its opticstrength is very small.

The optical spectrum begins to change below the secoorder phase transition at 200 K. These changes cannodirectly related to the lower symmetry as the 3.3 eV badoes not disappear in the low-temperature orthorhomphase. The reason should rather come from some electrcorrelations and associated distortions of the VO6 octahe-drons. Renet al.2 suggested that the spin order in YVO3 isaccompanied by an orbital order. The orbital order isported to appear below the 200 K phase transition.4,7 In theproposed picture for the orbital ordering, thexy orbitals arealways occupied by one of the twod electrons, while theoccupation of thexz and yz orbitals alternates in an AFMorder. The orbital order was found to be different above abelow 77 K in agreement with the different magnetic ordAccording to Renet al.,2 there is aC-type magnetic andG-type orbital order above 77 K and aG-type magnetic andC-type orbital order below 77 K.

We now turn to a discussion of how orbital and magneordering influences the optical conductivity. We considemodel where the optical conductivity is proportional to telectron transition probability between two neighboring vnadium sites. There are in total nine independent eigenfutions in the 3T1g representation. At room temperature thelectron transition probability can be calculated by averagover arbitrary orientations of spins and orbits on two ionsi.e., by averaging over all linear combinations of these nwave functions. Magnetic or orbital order limits the choiof initial wave functions. At lower temperatures we can epect that the electron transition from theS51 state on thefirst ion to theS53/2 state on the other ion becomes leprobable due to the antiferromagnetic order. Thus, the insity of the lowest band should decrease. As can be seenFigs. 7 and 11, the optical strength of the lowest band inddecreases upon cooling. By using a more rigorous analysthe transition probabilities, we can evaluate if a particuorder is consistent with the observed temperature depdence of«(v). In this analysis we neglect the tilting of th

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STRUCTURAL, ELECTRONIC, AND MAGNETO-OPTICAL . . . PHYSICAL REVIEW B 69, 075110 ~2004!

octahedra and assume that the transition integrals betwedorbitals on the neighboring vanadium ions are the sameall directions and for alld orbitals. The conductivity is assumed to be determined by the probabilities to create aconsisting of an occupied orbital on one site and an emorbital on the neighboring site, with the constraint that ttransition be allowed. The intersited-d transitions are medi-ated by thep orbitals of the oxygen ions between the vandium sites. At room temperature all3T1g states are occupierandomly. At lower temperatures we used the magneticorbital order, suggested above.2 If we assume the transitionintegral from completely occupied to completely empty obital as unity, then the transition probabilities at room teperature are found to be 0.49, 0.84, and 0.44 for the4A2g ,2Eg12T1g , and 2T2g final states, respectively. We also caculated the transition probabilities for AFM spin order afor AFM spin order accompanied by the aforementionedbital order~see Table IV!. Both simple AFM-SO and AFM-SO1OO lead to a decrease of the lowest band and ancrease of the intensity of the highest band, consistent wthe observations.

However, none of the considered orderings gives therect sign for the intensity change for the middle band—i.edecrease of strength with decreasing temperature. Moreowe found that no combination of completely polarized sta(Sz51) can give the desired intensity decrease for the2Eg1 2T1g band. The same conclusions hold if the on-site symetry is lowered to tetragonal. If some addition of theSz50 initial wave function is allowed, as suggested by neutmeasurements,4 a large variety of possible orbitally orderestructures becomes allowed. Although different orbital ordings can indeed explain the observed intensity changes,not possible to give a preference to a particular order.22

V. MAGNETO-OPTICAL KERR EFFECT

The energy diagram shown in Fig. 9 was derived assuing a local cubic symmetry on the vanadium site. In realone axis of the octahedron is different from the other twThis tetragonal-type distortion additionally splits the multilet structure, which partially lifts the degeneracy of tground and excited states. On top of that, a spin-orbital cpling provides segregation of the states by the quantum nber MJ . The latter gives rise to the magneto-optical Keeffect ~MOKE!. The temperature dependence of the Kerrtation spectrumQK(E) is shown in Fig. 13. The curves arshifted for clarity. The measurements were performed inpolar geometry at nearly normal angle of incidence, withmagnetic field of 0.1–0.2 T parallel to thea axis, Huua. In

TABLE IV. Calculated transition probabilities at room temperture, in the AFM spin-ordered~SO! state and in the AFM spin- andorbital-ordered~SO-OO! state.

Order 4A2g2Eg1 2T1g

2T2g

Room temperature 0.49 0.84 0.44AFM SO 0.30 1.48 0.89AFM SO-OO 0.33 1.67 1.0

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the other field orientations, the magnetic moment wassmall for the Kerr rotation to be detected. No rotation of tpolarization plane was observed above the Ne´el temperaturewithin our experimental error. Below the Ne´el temperaturebut above the first-order phase transition, only a weak strture of the order ofQK'0.01° can be seen. Below 75 Kremarkable peak as large asQK50.1° is observed. In totalthere are three resonance structures. Enlarged in the insFig. 13 are two surprisingly narrow dispersion-type resnances at 1.8 and 2.2 eV that have positions approximacorresponding to the onset of the two first MH bands. Thintensity, though rather small;0.01°, is well reproduced ondifferent samples. The third broad peak appears to hmaximum at 3.5 eV, which is also confirmed by the zecrossing of the Kerr ellipticity«K(E). This band lies belowthe charge-transfer onset and corresponds to thed-d transi-tions. The maximum rotation in this band amounts to;0.1°.Such a large magneto-optical effect seems to be quiteprising, because from the electrodynamics point of viewtime-reversal symmetry, although broken on the microscoscale, is usually restored on the macroscopic scale in antromagnetic compounds. If this indeed were the caseYVO3, the Kerr rotation would mainly result from the sma0.2° spin canting and would be as minuscule as the net mnetic moment is. For comparison, the saturation magnmoment in Ni is 0.61mB per atom—i.e., approximately 60

FIG. 13. ~a! Temperature dependence of the Kerr rotation msured in the polar geometry withHuua. ~b! The Kerr rotationQK

together with the Kerr ellipticity«K in the low-temperature phaseInset: enlarged view of the resonances at 1.8 and 2.2 eV.

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A. A. TSVETKOV et al. PHYSICAL REVIEW B 69, 075110 ~2004!

times larger that the net moment of 0.01 Bohr magnetonvanadium atom in YVO3. Still the Kerr rotation in Ni isquite comparable to those of the low-temperature phasYVO3 and lies between 0.1° and 0.2° in the visible rang

Antiferromagnetic compounds can have large magneoptical effects, as was shown recently,23,24 if the local spinand orbital magnetic moments are not collinear. In particuan orbital magnetic moment does not vanish in transitimetal perovskites with thePbnmstructure due to the tiltingof the octahedra.25 We can find nonvanishing ferromagnetcomponents of the net orbital magnetic momentML fromsymmetry considerations, following the guideline and notions from Ref. 25. There are four inequivalent vanadiusites i 51,2,3,4 in the YVO3 unit cell. These sites can bgenerated by four symmetry transformations, unity opera

E, and three screw axes,S2x with the shift (12 ,0,0) and coor-

dinatesx, 14 ,0; S2y(0,1

2 ,0) 14 ,y, 1

4 ; andS2z(0,0,12 ) 0,0,z. Herex, y, andz are parallel to the crystallographic axesa, b, andc,respectively. The local relation between the orbital magnmoment ML

i and the spin magnetization directione5(cosu sinf,sinu sinf,cosu) on each vanadium sitei cangenerally be written asMLa

i 5L abi eb , where the matrixL ab

i

determines the orbital magnetic moment induced by the sorbit interaction. We apply the mentioned symmetry opetions to the matrixL ab

i to obtain averaged matricesLab

5( i 514 L ab

i for the C- and G-type spin ordering, respectively:

L C54S 0 L xy1 0

L yx1 0 0

0 0 0D , L G54S 0 0 L xz

1

0 0 0

L zx1 0 0

D .

The corresponding net orbital magnetic moments are

C: MLC54~L xy

1 sinu sinf,L xy1 sinu cosf,0!,

G: MLG54~L xz

1 cosu,0,L zx1 sinu cosf!.

The orbital magnetic momentML has the same symmetry athe gyration vectorg,26 which determines the antisymmetrpart of the dielectric tensor,«ab

a 5 ieabggg , responsible formageto-optical effects.27 Hereeabg is the unit antisymmetrictensor. In the polar measurement geometry discussedcomponents of the vectorga and, correspondingly, components ofML define the orientation of the magnetic fieldH forwhich observation of Kerr effect is possible.

For theG-type spin order, the structure ofMLG suggests

that the polar Kerr effect can exist forHuua if spins areparallel to thec axis and forHuuc if spins are aligned alongthe a axis. If the spins are along theb axis, ML

G and thecorresponding Kerr effect are zero. This does not excludepossibility for the second, weaker, type of Kerr effect, whiis directly related to the spin canting. It should be empsized here that Kerr rotation due to orbital magnetic mments can exist even if the spins are exactly antiferromnetically aligned.25 Our observation of a substantiamagneto-optical effect only forHuua shows that spins in thelow-temperature phase of YVO3 are aligned along thec axis.

07511

er

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This agrees with neutron scattering measurements.4 Theweak structure at 1.8 and 2.2 eV is most probably the scanting effect.

The C-type spin order as seen from theMLC angular de-

pendence allows a magneto-optical activity, only if spinsaligned in theab plane. The small magnitude of the expementally observed MOKE above 80 K compared to the lotemperature phase suggests that the spins are alignedthe c axis. In this case,ML

C is zero for any orientation ofH,and the Kerr effect substantially decreases, in agreemwith our experimental observations. This result contradithe neutron data, where a substantial spin component athe b axis is observed4. This, however, can reflect anotheimportant property of YVO3. As was shown in Ref. 28G-type antiferromagnetic orbital order in the form proposby Renet al.2 suppresses the orbital magnetic moment. Tcan be the reason why no substantial Kerr rotation wasserved for theC-type spin order. This conclusion requirethat the on-site magnetic moment in theG-type orbital orderbe reduced from 2mB to 1.1mB ,4 not due to the orbital magnetic moment, but due to a mixture ofSz51 andSz50 3T1gstates, in agreement with the conclusion obtained in thevious section.

VI. CONCLUSIONS

The analysis of the YVO3 phonon spectra revealed thredifferent phases. The orthorhombicPbnm structure existsdown to 200 K. At 200 K there is a second-order phatransition to a lower-symmetry structure. The orthorhomPbnm crystal symmetry is restored through a first-ordphase transition below 74 K. The most probable structurethe intermediate phase is the monoclinicPb11, where theVO6 octahedra form a dimerized chain along thec axis. Nev-ertheless, the possibility of a triclinicP1 symmetry cannotbe excluded completely.

YVO3 is a Mott-Hubbard insulator with an optical gap o1.6 eV. There are three optical bands with energies 1.8,and 3.3 eV, which we identify with the intervanadium trasitions from the 3T1g ground state to the4A2g , 2Eg12T1g , and 2T2g states. Thesed-d excitations are followedby the charge-transfer transitions at 4 eV. The bandstructure is in agreement with the LSDA1U calculations.The d bands revealed a strong temperature dependenceing a model which includes only the nearest-neighbor trsitions, we found that the observed temperature dependdisagrees with the simple antiferromagnetic spin orderiThis indicates that orbital ordering phenomena are respsible for the observed temperature variations. However,commonly considereduxy,xzu/uxy,yzu orbital order seemsalso inconsistent with our data, if we assume a fully polized on-site state.

We observed two types of magneto-optical effects.small net magnetic moment due to the uncompensatedmoments induces a weak Kerr rotation of the order;0.01°. The effect exists in all phases below the magnordering temperature and for all active optical transitionsstrong Kerr effect appears as a consequence of the low c

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STRUCTURAL, ELECTRONIC, AND MAGNETO-OPTICAL . . . PHYSICAL REVIEW B 69, 075110 ~2004!

tallographic symmetry and ferromagnetic ordering of thebital magnetic moments. A Kerr rotation of the order;0.1° was found in the low-temperature phase for the hiestd-d transition band. It follows from symmetry consideations that the spin magnetic moment is aligned along thcaxis in both magnetic structures. However, this conclusfor theC-type AFM spin arrangement can be affected byaccompanying orbital order.

*Present address: NSRIM Institute, University of Nijmegen, Tonooiveld 1, 6525 ED Nijmegen, The Netherlands. Electronicdress: tsvetkov@sci.kun.nl

†On leave from Jurusan Fisika, Institut Teknologi Bandung,Ganesha 10, Bandung 40132, Indonesia.1K.I. Kugel and D.I. Khomskii, Zh. E´ksp. Teor. Fiz.64, 1429

~1973! @Sov. Phys. JETP37, 725 ~1973!#.2Y. Ren, T.T.M. Palstra, D.I. Khomskii, E. Pellegrin, A.A. Nu

groho, A.A. Menovsky, and G.A. Sawatzky, Nature~London!396, 441 ~1998!.

3H. Kawano, H. Yoshizawa, and Y. Ueda, J. Phys. Soc. Jpn.63,2857 ~1995!.

4G.R. Blake, T.T.M. Palstra, Y. Ren, A.A. Nugroho, and A.A. Meovsky, Phys. Rev. B65, 174112~2002!.

5D.B. Rogers, A. Ferretti, D.H. Ridgley, R.J. Arnott, and J.Goodenough, J. Appl. Phys.37, 1431~1966!.

6V.G. Zubkov, A.S. Borukhovich, G.V. Bazuev, I.I. Matveenkand G.P. Shveikin, Sov. Phys. JETP39, 896 ~1974!.

7G.R. Blake, T.T.M. Palstra, Y. Ren, A.A. Nugroho, and A.A. Meovsky, Phys. Rev. Lett.87, 245501~2001!.

8C. Ulrich, G. Khaliullin, J. Sirker, M. Reehuis, M. Ohl, S. Miyasaka, Y. Tokura, and B. Keimer, cond-mat/0211589~unpub-lished!.

9Y. Ren, T.T.M. Palstra, D.I. Khomskii, A.A. Nugroho, A.A. Menovsky, and G.A. Sawatzky, Phys. Rev. B62, 6577~2000!.

10M. Schubert, T.E. Tiwald, and C.M. Herzinger, Phys. Rev. B61,8187 ~2000!, and references therein.

11K. Sato, H. Hongu, H. Ikekame, Y. Tosaka, M. Watanabe,Takanashi, and H. Fujimori, Jpn. J. Appl. Phys., Part 132, 989~1993!.

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ACKNOWLEDGMENTS

We acknowledge useful discussion with G. R. Blake. Wthank H. J. Bron for his help with sample preparation. Thresearch was supported by The Netherlands FoundationFundamental Research on Matter~FOM! with financial aidfrom the Nederlandse Organisatie voor WetenschappeOnderzoek~NWO!.

--

l.

.

12D.L. Rousseau, R.P. Bauman, and S.P.S. Porto, J. Raman Strosc.10, 253 ~1981!.

13A.A. Tsvetkov, F.P. Mena, Y. Ren, I.S. Elfimov, P.H.M. van Loodrecht, D. van der Marel, A.A. Nugroho, A.A. Menovsky, anG.A. Sawatzky, Physica B312, 783 ~2002!.

14I.S. Smirnova, Physica B262, 247 ~1999!.15S. Miyasaka, Y. Okimoto, and Y. Tokura, J. Phys. Soc. Jpn.71,

2086 ~2002!.16J. Zaanen, G.A. Sawatzky, and J.W. Allen, Phys. Rev. Lett.55,

418 ~1985!.17M. Kasuya, Y. Tokura, T. Arima, H. Eisaki, and S. Uchida, Phy

Rev. B47, 6197~1993!.18T. Arima, Y. Tokura, and J.B. Torrance, Phys. Rev. B48, 17 006

~1993!.19O.K. Andersen, Phys. Rev. B12, 3060~1975!.20V.I. Anisimov, J. Zaanen, and O.K. Andersen, Phys. Rev. B44,

943 ~1991!.21H. Sawada and K. Terakura, Phys. Rev. B58, 6831~1998!.22For example, if we maximize the spin magnetic moment, we

tain that theuxz,yzu orbitals should be always occupied on avanadium sites. This gives correct intensity changes for thebands and all axes.

23I.V. Solovyev, N. Hamada, and K. Terakura, Phys. Rev. Lett.76,4825 ~1996!.

24L.M. Sandratskii and J. Ku¨bler, Phys. Rev. Lett.76, 4963~1996!.25I.V. Solovyev, Phys. Rev. B55, 8060~1997!.26Y.A. Uspenskii, E.T. Kulatov, and S.V. Halilov, Phys. Rev. B54,

474 ~1996!.27D.L. Landau and E.M. Lifshitz,Electrodynamics of Condense

Media ~Pergamon, New York, 1960!.28T. Jo, J. Phys. Soc. Jpn.72, 155 ~2003!.

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