Orbital-Ordering-Induced Ferroelectricity in SrCrO3

Kapil Gupta,1 Priya Mahadevan,1,* Phivos Mavropoulos,2 and Marjana Lezaic2

1S. N. Bose National Centre for Basic Sciences, Block JD, Sector-III, Saltlake, Kolkata 700 098, India2Peter Grunberg Institut and Institute for Advanced Simulation, Forschungszentrum Julich and JARA, D-52425 Julich, Germany

(Received 1 February 2012; revised manuscript received 7 May 2013; published 15 August 2013)

Using density functional theory calculations, ultrathin films of SrVO3ðd1Þ and SrCrO3ðd2Þ on SrTiO3

substrates have been studied as possible multiferroics. Although both are metallic in the bulk limit, they

are found to be insulating as a result of orbital ordering driven by lattice distortions at the ultrathin limit.

While the distortions in SrVO3 have a first-order Jahn-Teller origin, those in SrCrO3 are ferroelectric in

nature. This route to ferroelectricity results in polarizations comparable with conventional ferroelectrics.

DOI: 10.1103/PhysRevLett.111.077601 PACS numbers: 77.80.�e, 71.15.Mb, 75.85.+t

Recent advances in the growth of oxide thin films haveallowed one to engineer both electronic and magneticfunctionalities in oxides, very different from their bulkcounterparts [1–5]. This additional dimension of oxideresearch has opened up the possibility of generatingcross-correlated electronic couplings which could be inter-changeably controlled by both electric as well as magneticfields, generating new classes of multiferroics. In contrast,there are very few examples among bulk materials whichare both magnetic as well as ferroelectric. This is becauseferroelectricity (FE) is usually found in d0 systems andd0-ness is not compatible with magnetic order [6]. Thereare examples of systems which exhibit both orders amongfinite dn systems; however, the magnitudes of polarizationare usually small in such cases.

An avenue that has been quite successful as a route tonew ferroelectrics in thin films is one where substrate strainand overlayer thickness have been used as handles tomodify properties, resulting in behavior very differentfrom the bulk. The work by Haeni et al. [7] showed thatsubstrate strain could be used to engineer a ferroelectricground state in SrTiO3, a d

0 paraelectric. While it was notobvious that this route should also work for multiferroics,first-principles calculations [8] predict that the straininduced by merely depositing the room-temperature ferri-magnetic double perovskites Bi2NiReO6 and Bi2MnReO6

on a substrate should turn their antipolar bulk ground stateinto a ferroelectric one. S. Bhattacharjee et al. [9] showedtheoretically that by increasing the lattice constant ofCaMnO3, a polar mode becomes soft and almost degener-ate with an antipolar mode. Similar observations weremade in epitaxially strained simple binary oxides such asBaO and EuO [10] as well as BaMnO3 [11], SrMnO3 [12],and EuTiO3 [13,14], none of which are examples of bulkferroelectric materials. All these examples were band insu-lators. Therefore, Jahn-Teller effects were irrelevant inthese systems, allowing, under strain, for the manifestationof the pseudo-Jahn-Teller effects, which are usually asso-ciated with noncentrosymmetric distortions. An importantconsequence of these studies was that ferroelectric

polarization as large as that found in d0 ferroelectricswas predicted in these oxides. In contrast, the observedferroelectric polarization in most multiferroics is at least 1or more orders of magnitude lower [15–17]. This route to ahigh polarization and possibly magnetism associated withthe same atom opens up interesting possibilities.Orbital ordering has recently emerged as an alternate

route to FE. This was recently realized in films of dopedmanganites on a high-index surface of the substrate [18],where orbital ordering with an axis tilted away from thesubstrate normalwas found. This led to off centering. Again,in this case, the examples considered were bulk insulators,which we show in the present work need not be a limitationin the choice of materials. We start by considering theexample of SrVO3 and SrCrO3, both of which are metallicin the bulk. In this work, we explore a new route to non-d0

FE through ultrathin films of transition-metal oxides which,as discussed earlier, were found to be insulating. In contrastto the examples listed above, in the cases we investigate, thetransition-metal cation is Jahn-Teller active in bulk. A fur-ther important difference is that strain (although it could bepresent) does not play a crucial role in the induced FE.Ultrathin films [just two monolayers (MLs)] of SrVO3

on SrTiO3 (001) as well as films comprising two MLs ofSrCrO3 on SrTiO3 (001) are considered. Examining theelectronic structure theoretically, we find both systems tobe insulating, both arising from an orbital ordering at thesurface, driven primarily by structural distortions. WhileSrVO3 favors Jahn-Teller distortions, SrCrO3 favors aferroelectric ground state, with a large contribution to theenergy lowering in the insulating state derived from thesedistortions. Our detailed analysis shows that the modifica-tions of the crystal field at the surface associated with amissing apical oxygen allow for the observed FE in SrCrO3

(and possibly in other non-d0 transition-metal com-pounds). These distortions at the surface survive even forthe thicker films. The calculated polarization is found to belarge, comparable to that in bulk d0 ferroelectrics.We consider a symmetric slab (see, for instance,

Ref. [19]) consisting of 13 layers of SrO-TiO2, terminating

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in a TiO2 layer, to mimic the substrate. The in-plane latticeconstant is fixed at the experimental value (3.905 A) forSrTiO3, while the out-of-plane lattice constant was varied.We allowed for tilts of the TiO6 as well asMO6 octahedra,a distortion observed in low-temperature SrTiO3 [20]. Theelectronic structure of these systems was calculated withinVASP [21] using a k-point mesh of 6� 6� 1 using a

generalized gradient approximation ðGGAÞ þU scheme[22,23] with a Ueff of 2:2=2:5 on V=Cr [24]. A vacuumof 15 A was used to minimize interaction between slabs inthe periodic supercell geometry. Internal positions wereallowed to relax to their minimum energy value. We con-struct maximally localized Wannier functions and use theshifts of their centers in the ferroelectric phase with respectto the paraelectric one to calculate the ferroelectric polar-ization [25]. For this purpose, the electronic ground statefor the relaxed structure was converged with the full-potential linearized augmented plane wave method-basedcode FLEUR [26], in film geometry, on a 7� 7 k-pointmesh. The maximally localized Wannier functions wereconstructed with the WANNIER90 code [27] and the interfacebetween FLEUR and WANNIER90 [28]. The advantage of theWannier functions approach (over the Berry phase one) inthe specific system where the ferroelectric polarization isnot uniform is that the contributions of every layer oratom (see Ref. [28]) to the electronic polarization can beextracted.

We started by calculating the electronic structure of bulkSrVO3 and SrCrO3 within GGAþU. Both compoundswere found to be metallic, consistent with experiment.Next, we performed similar calculations for two MLs ofSrMO3 (M ¼ V, Cr) on SrTiO3, and the ground state wasin both cases found to be insulating.

Let us first examine in more detail the case of SrVO3.EachVO5 unit at the surface has in-plane V-O bond lengths(1.95 A) longer than the out-of-plane one (1.91 A). Thiscould in principle result in a lower energy for the dxyorbital than for the doubly degenerate dyz and dxz orbitals

[Fig. 1(a)]. As there is just one electron associated with theV4þ ion, in this case, an insulating ground state isexpected. However, since one of the apical oxygens ismissing at the surface, this could result in a reversed order-ing of the levels leading to a metallic state [Fig. 1(b)]. Ourcalculations find the scenario discussed in Fig. 1(b) real-ized. However, on performing a complete structural opti-mization, one finds an orbital-ordering transition which hasa Jahn-Teller origin with two elongated V-O (2.18 A) andtwo contracted V-O bond lengths (1.78 A) [see Fig. 1(c)].A ferromagnetic state is found to be favored by 60 meV=Vat the two-ML limit, in contrast to the bulk, which isparamagnetic.

To contrast the results for SrVO3 films, we have alsoconsidered two MLs of SrCrO3 on a SrTiO3 substrate.Here, the degeneracy lifting of the Cr t2g levels is also a

consequence of the missing apical oxygen with the dxz and

dyz levels at lower energy than the dxy level. As there are

two electrons in the d levels of the Cr4þ ion, they occupythe doubly degenerate dxz and dyz levels, leading to a band

insulator. Interestingly, we find that carrying out completestructural optimization results in a strong modification ofthe in-plane Cr-O bond lengths from their starting values:while two of the bond lengths contract, the other twoextend [Fig. 1(d)] [29]. The effect of this structural dis-tortion is that the system has no inversion symmetry nowand possesses a finite electric polarization. While in bothSrVO3 and SrCrO3 the dominant energy lowering comesfrom the in-plane distortions, note the important differ-ence: in SrCrO3, the Jahn-Teller effect is quenched dueto one additional electron on the Cr4þ cation and to themodified crystal field at the surface (with respect to that ofthe bulk material), so the pseudo-Jahn-Teller effectsbecome operative, driving the system ferroelectric or polar.These results put ultrathin films of SrCrO3 in the samecategory of band insulators turned ferroelectrics whereorbital ordering drives the system insulating. Now, everyband insulator does not turn ferroelectric, so this immedi-ately brings up the question of the microscopic interactionsthat are responsible for FE here. In the following,

FIG. 1 (color online). Distortions and crystal field splitting ofthe t2g orbitals for (a) aMO6 octahedron under tensile strain and

(b) a surface MO5 unit, where M ¼ transition-metal atom. TheM-O network in the x-y plane found in the presence of (c) Jahn-Teller distortions (seen in SrVO3) and (d) pseudo-Jahn-Tellerdistortions (seen in SrCrO3). Large (small) and gray (red)spheres denote M (O) atoms.

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we investigate the origin of the observed ferroelectricdistortions.

In Fig. 2(a), we have plotted the partial density of Cr-dstates for the structure in which the film is constrained to becentrosymmetric. A band gap barely opens up in thisstructure between the majority spin Cr dyz=dxz states and

the dxy states. The bandwidths associated with the dxz and

dyz orbitals are a factor of 2 less than the bandwidths

associated with the dxy orbitals as a result of broken

periodicity along the positive z direction. Allowing forthe constraint of centrosymmetry to be relaxed, we findthat two of the in-plane Cr-O bond lengths become shorterand are equal to 1.78 A while two others become longerand are equal to 2.15 A, in contrast to their undistortedvalues of 1.95 A. A part of the energy lowering in theprocess comes from the increased hopping interaction dueto shorter Cr-O bonds. This is clearly seen in the increasedseparation of the bonding and antibonding states withdominant contribution from the dxy orbitals [Fig. 2(b)].

The shorter Cr-O bond lengths also result in an increasedrepulsion between the electrons on Cr and O. This is partlyovercome by the presence of the vacuum in the z direction,which allows the dxz and dyz orbitals to extend into the

vacuum region. This may be seen from the charge densityplot associated with the antibonding states with dxz=dyzcharacter plotted in the inset of Fig. 2(b). The lobe of the dorbital closer to the longer Cr-O bond extends further intothe vacuum to compensate for the increased repulsionassociated with the shorter Cr-O bonds. These resultsalso provide us with design principles for generating multi-ferroic materials in which one hasMO5 structures resulting

fromMO6 octahedra. In-plane distortions as well as largerspacings in one of the z directions in which the oxygen isabsent could result in ferroic distortions.In Fig. 3, we show the calculated values of the layer-

resolved ferroelectric polarization for the case of two MLsof SrCrO3 on SrTiO3. The bars with the vertical (violet)pattern show the total (ionic plus electronic) polarization inCrO2=TiO2 layers, while the ones with the horizontal(green) pattern show the total polarization in SrO layers.The (gray) bars outlined with violet (CrO2=TiO2 layers) orgreen (SrO layers) indicate the electronic contribution tothe total polarization in the respective layers. Note that theelectronic contribution in CrO2=TiO2 layers is rather large.It constitutes about 50% of the total polarization, while inSrO layers it is smaller and negative. The polarizationpoints in the h110i direction (in plane) and is calculatedper layer; i.e., instead of the unit cell volume that would beused to evaluate it in a bulk system, we use the volume ofeach layer, calculated as the product of the area of thein-plane unit cell and the sum of the half-distances to theneighboring layers on either side. The volume of the sur-face layer is taken to be equal to the one beneath it. Whilenot ferroelectric in bulk, we find that a significant polar-ization is induced in high-k SrTiO3 by the ferroelectricshifts of Cr4þ ions at the surface. Note that the polarizationin the center of the film is constrained to zero by the chosengeometry (in the calculation, the Cr4þ ions move in theopposite directions on the opposite sides of the film), andits decay with the distance from the surface need not be asrapid in the case of a thicker substrate. A rough estimate ofthe energy for switching is found to be 42 meV [30],similar to other displacive ferroelectrics [31].

0

0.5

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0

0.5

1

1.5

2dxy

dyz

dxz

DO

S(/e

V/a

tom

)

(a)

(b)

FIG. 2 (color online). The majority spin dxz, dyz, and dxyprojected partial density of states for a Cr atom (a) in bulklikegeometry and (b) in the optimized ferroelectric geometry for twoMLs of SrCrO3 films on SrTiO3. The charge density associatedwith the antibonding states with dxz and dyz character is shown in

inset of (b). Vertical dashed lines indicate the valence bandmaximum and conduction band minimum of SrTiO3. The zeroof energy indicates the Fermi energy.

CrO

2

SrO

TiO

2

SrO

TiO

2

SrO

TiO

2

SrO

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40

60

80

100

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ariz

atio

n [µ

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m2 ]

FIG. 3 (color online). The layer resolved polarizations for twoMLs of SrCrO3 on SrTiO3: The bars with a vertical violet patternshow the total (ionic plus electronic) polarization in CrO2 layers,while the ones with the horizontal green pattern show the totalpolarization in SrO layers. The gray bars outlined with violet(CrO2 layers) or green (SrO layers) indicate the electroniccontribution to the total polarization in the respective layers.

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In SrCrO3, the observed ferroelectric distortions wereassociated with the two-ML limit. However, when anadditional SrO ML was added, this led to the out-of-planedistortions becoming the largest distortions. The differingenvironments on either side of the surface CrO6 octahedralead to unequal bond lengths of 1.88 and 1.95 A along thepositive and negative z directions. As a result, a finitedipole moment develops (although it is unswitchable byan electric field). Similar observations have been made onother interfaces [32]. The system still remains insulatingat this limit. Adding another layer, we find that the surfaceCrO2 layer sustains ferroelectric distortions in addition tocharge ordering. The Cr in CrO2 is found to have anegative charge transfer energy [33]. Here, we also findthis to be the case, and consequently, some of the holes arelocalized on the oxygens. The surface Cr atoms are foundto have a valency of d1þ� and d2 [Figs. 4(a) and 4(b)],while the subsurface Cr atoms have a breathing-mode-type distortion which leads to a valency of d3�� and d2 onthese Cr atoms [Figs. 4(c) and 4(d)]. By comparing thetotal energy of several configurations, we find a ferromag-netic coupling parameter in the surface Cr layer and anantiferromagnetic coupling in the subsurface layer andbetween the layers.

In the preceding discussion, the substrate imposed atensile strain on the SrCrO3 overlayers. It is impressive,however, that one finds that as a consequence of the largestabilization energy for the in-plane ferroelectric distor-tions, the films can sustain these distortions even for 2%compressive strain.

Having established FE at the ultrathin limit, we went onto examine the magnetic properties as a function of thick-ness. The bulk is found to be an antiferromagnetic metal,

consistent with experiment. At the ultrathin limit of twoMLs, the antiferromagnetic state is more stable than theferromagnetic state by 45 meV=Cr atom, correspondingto a nearest-neighbor coupling of J ¼ 11:25 meV in aHeisenberg model. The stabilization of an antiferromag-netic state can be easily understood within a superex-change picture, as there are channels for delocalizationonly for an antiferromagnetic arrangement of spins. Thisdifference is enhanced at the three-ML limit to 52 meV=Cratom. At the four-ML limit, various magnetic configura-tions were considered, and we find that the surface layerbecomes ferromagnetic while the subsurface CrO2 layerbecomes antiferromagnetic, with the system found to beinsulating. The closely competing configuration whereboth surface layer Cr atoms as well as the subsurface layerCr atoms are coupled antiferromagnetically is found to be9 meV=Cr atom higher.From a device perspective, the important question is

whether there is a coupling between the electrical andmagnetic degrees of freedom. We compute the magneticcrystalline anisotropy for the two-ML film of SrCrO3 andfind that the spin favors an in-plane orientation over anout-of-plane one by 128 �eV per Cr atom. Within theplane, the spin favors an orientation at 90� to the directionof the electric polarization by 14 �eV. We note that asimilar arrangement was observed in BiFeO3 [34]. ByMonte Carlo simulations on a Heisenberg model basis,including single-ion anisotropy, we find that the couplingbetween electric polarization and staggered-magnetizationdirection persists up to a temperature of 70 K, after whichshort-range magnetic order is lost. Even if this temperatureis considerably lower than room temperature, the novelmechanism that is revealed here could emerge inother materials at higher temperature, provided that theexchange is stronger.Ultrathin films of d1 and d2 transition-metal oxides have

been explored as possible candidates for multiferroicity.Orbital ordering allows one to realize an insulating surfaceeven in systems where the bulk form is metallic. Whilethese have a Jahn-Teller origin in the case of SrVO3,pseudo-Jahn-Teller effects result in sizeable ferroelectricdistortions for SrCrO3 which, even in the absence of strain,also turns out to be an antiferromagnetic insulator at thislimit of two MLs. These distortions persist into thesubstrate and survive for the surface CrO5 layer even forthicker films of four MLs opening up new possibilities fornon-d0 multiferroics.We acknowledge useful discussions with D.D. Sarma, S.

Blugel, and I. B. Bersuker. K.G. acknowledges CSIR,India, and P.M. acknowledges DST, Government ofIndia, through the Indo-EU Project ATHENA for financialsupport. M. L. gratefully acknowledges the financial sup-port of the Young Investigators Group Programme ofthe Helmholtz Association, Contract No. VH-NG-409,the support of the Julich Supercomputing Centre and the

0

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dyz

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0.8

0

0.4

0.8

-6 -4 -2 0 2 40

0.4

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DO

S(/e

V/C

r)

Energy(eV)

Cr1-Surface layer (d2)

Cr2-Surface layer (d1+

)

Cr1-Subsurface layer (d2)

Cr2-Subsurface layer (d3-

)

δ

δ

(a)

(b)

(c)

(d)

FIG. 4. The majority spin dxz, dyz, and dxy projected partialdensity of states for a Cr atom belonging to (a),(b) the surfacelayer and to (c),(d) the subsurface layer of four-ML SrCrO3 filmson SrTiO3. Vertical dashed lines indicate the valence bandmaximum and conduction band minimum of SrTiO3. The zeroof energy indicates the Fermi energy.

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European Community’s Seventh Framework Programme(FP7/2007-2013) under Grant No. NMP3-LA-2010-246102. P.M. and M. L. also thank the DST-DAAD pro-gramme which funded the exchange visits.

*Corresponding author.

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