Orbital-selective confinement effect of Ru 4d orbitals in SrRuO 3 ultrathin film
Soonmin Kang, Yi Tseng, Beom Hyun Kim, Seokhwan Yun, Byungmin Sohn, Bongju Kim, Daniel McNally, Eugenio Paris, Choong H. Kim, Changyoung Kim, Tae Won Noh, Sumio Ishihara, Thorsten Schmitt, Je-Geun Park
OOrbital-selective confinement effect of Ru 4 d orbitals in SrRuO ultrathin film Soonmin Kang,
1, 2
Yi Tseng, Beom Hyun Kim, Seokhwan Yun,
1, 2
Byungmin Sohn,
1, 2
Bongju Kim,
1, 2
Daniel McNally, Eugenio Paris, Choong H. Kim,
1, 2
ChangyoungKim,
1, 2
Tae Won Noh,
1, 2
Sumio Ishihara, Thorsten Schmitt, ∗ and Je-Geun Park
1, 2, † Center for Correlated Electron Systems, Institute for Basic Science (IBS), Seoul 08826, Korea Department of Physics and Astronomy, Seoul National University, Seoul 08826, Korea Swiss Light Source, Paul Scherrer Institut (PSI), CH-5232 Villigen, Switzerland Korea Institute for Advanced Study (KIAS), Seoul 02455, Korea Department of Physics, Tohoku University, Sendai 980-8578, Japan (Dated: December 27, 2018)The electronic structure of SrRuO thin film with thickness from 50 to 1 unit cell (u.c.) is in-vestigated via the resonant inelastic x-ray scattering (RIXS) technique at the O K-edge to unravelthe intriguing interplay of orbital and charge degrees of freedom. We found that orbital-selectivequantum confinement effect (QCE) induces the splitting of Ru 4 d orbitals. At the same time, weobserved a clear suppression of the electron-hole continuum across the metal-to-insulator transition(MIT) occurring at the 4 u.c. sample. From these two clear observations we conclude that QCEgives rise to a Mott insulating phase in ultrathin SrRuO films. Our interpretation of the RIXSspectra is supported by the configuration interaction calculations of RuO clusters. PACS numbers: fill in later
I. INTRODUCTION
Orbital degree of freedom (DOF) is relatively less wellunderstood among the four fundamental DOF of solid:charge, spin, lattice, and orbital. The role of the orbitalDOF was originally recognized by the now famous Kugel-Khomskii model [1]. It has since taken another decadebefore its full consequence was experimentally observedfrom numerous studies on so-called colossal magnetore-sistance (CMR) manganites [2]. The most direct effect oforbital DOF can be found in the so-called orbital order-ing and the associated metal-insulator transition (MIT)with unique magnetic or structural transitions [3, 4]. Amore recent breakthrough in an understanding of orbitalDOF is in the discovery of orbital-selective mechanism. Itis now believed that several Ru and V oxides exhibit thephenomena that arise from the orbital-selective physics[4–7]. One notable example is the orbital-selective Motttransition [8].The role of orbital DOF is typically enhanced for lo-calised systems, i.e. with a larger U term. So it becomesmore prominent in 3 d transition metal oxides, which iswhy CMR manganite was the first system that was iden-tified with orbital physics. Nevertheless, several Ru com-pounds were also reported to have rather unique featuresdue to the orbital physics. Despite the progress of our un-derstanding of orbital physics for Ru, an orbital-selectiveprocess still remains pretty much unexplored for Ru com-pounds although it was already suggested for the doping-dependent MIT of (Ca,Sr) RuO [5, 9, 10].SrRuO is a well-known member of the ruthenates fam-ily with a ferromagnetic phase below the Curie tempera-ture of 165 K. Unlike other ferromagnetic materials, con-ductivity of bulk SrRuO is high enough to make it a popular choice of electrode for various thin film sampleswith a stable perovskite structure [11]. At the same time,it is one of the rare itinerant ferromagnetic oxides, whichhas attracted significant interest in its own right [12, 13].For example, it has long been suspected that some kindof coupling between the lattice and spin degrees of free-dom works for the ferromagnetic ground state. It was alsofound both theoretically and experimentally that RuO octahedra of SrRuO undergoes quite irregular ‘plastic’distortion below the ferromagnetic transition tempera-ture [14, 15]. More recently, the unusual temperature de-pendence of the spin gap found by inelastic neutron scat-tering was attributed to a possible magnetic monopole inthe k -space [16]. Interestingly, it is known too that themetallic phase of bulk SrRuO is close to a transition be-tween Fermi-liquid and non-Fermi-liquid states [12, 17].Another interesting point, more relevant to our work, isthat SrRuO thin films undergo MIT with decreasingthickness, whose origin is to date not well understood[18–20]. Thus, SrRuO thin films can be a fertile groundfor exploring some of the fundamental physics related toMIT and correlation physics with the orbital DOF.In addition, first-principle LDA+U calculations foundthat the Ru orbitals of SrRuO thin films exhibit ratherunusual quantum confinement effects (QCE) when reduc-ing thickness [20]. As the thickness of film gets reduced,the proportion of RuO octahedra exposed to the sur-face increases, which makes Ru t g orbitals like d xz or d yz to prefer to form one-dimensional (1D) strips. As aresult of the geometrical restriction, enhanced QCE wastheoretically predicted to induce a distinctive change inthe electronic structures for Ru 4 d orbitals. To be morespecific, density of states (DOS) for a 2D square latticewith a tight-binding model has a van Hove singularity a r X i v : . [ c ond - m a t . s t r- e l ] D ec at the band center whereas DOS for a 1D line case hastwo separate singularities at the each edge of the band[21]. For example, the 2D-type van Hove singularity of d xy DOS persists down to monolayer SrRuO . However, d xz and d yz orbitals in monolayer limit do not have elec-tron hopping along the z-axis due to spacial confinement,which induces the 1D-type singularities of their DOS.This orbital-selective QCE was theoretically suggested tobe the main driving force of the intriguing paramagneticphase found for very thin SrRuO samples [20]. We alsonote that QCE was used to explain the Mott insulatingphase of LaNiO /LaAlO thin films [22].The purpose of this study was twofold. First, we in-vestigated the proposed QCE by measuring the orbital-dependent charge transfer with the high-resolution RIXSstudies as a function of thickness. Second, we studied howthe charge dynamics changes across the MIT by exam-ining low energy excitations across the critical thickness.Furthermore, we tried to find correlation between thosetwo distinct characteristics of SrRuO thin film. II. EXPERIMENTAL METHODS
Epitaxial SrRuO thin films were deposited on TiO -terminated SrTiO (001) substrates by pulsed laser de-position (PLD) at 670 ◦ C with oxygen pressure of 100mTorr. Ultraviolet light coming from the excimer laserwith power of 2.1
J/cm is applied to the target witha spot size of 2 mm . We optimized the growth con-dition by measuring the resistivity of our samples andthereby monitoring the quality in addition to the usualinspection of the reflection high-energy electron diffrac-tion (RHEED) patterns. The RHEED pattern in timevariation implies good surface quality, which shows aclear change in the growth mode from a layer-by-layergrowth to a step flow growth as a function of time. Onthe other hand, the high residual resistivity ratio of 8.2obtained for the samples testifies the high quality of oursamples. In addition to the resistivity measurement, weverified the roughness of the samples in atomic force mi-croscopy (AFM) images, another sign of the high qualityof surface in thin films (Fig. 1).We carried out O K-edge resonant inelastic x-ray scat-tering (RIXS) at the ADRESS beamline of Swiss LightSource [23, 24]. RIXS is a powerful tool to study thecharge dynamics related to orbital physics as one cantune the energy to a specific absorption resonance of ele-ments. Energy of ruthenium L-edge ( ∼ d orbitals while varying the FIG. 1 (color online) In-situ RHEED pattern andtopography image with AFM. The sample growth startsfrom 10 seconds. Growth mode change that occurs at 40 and60 seconds shows the good surface quality of thin films.Inset figures show RHEED patterns before and after thesample growth. AFM image indicates the clean surface andthe apparent steps with the height of 4 ˚A, which is the sizeof 1 u.c. for SrRuO . thickness of thin film samples.The proper energy of the incident beam was chosenthrough x-ray absorption spectroscopy (XAS) with dif-ferent thickness from 1 to 33 u.c. as shown in Fig. 2. Thefirst peak at around 529.8 eV gets weaker as the thicknessof the samples becomes reduced. From the fact that therelative intensity changes for different samples and alsobased on the previous XAS studies in SrTiO [25, 26],we conclude that peaks at above 530 eV are due to ab-sorptions from the substrates. Therefore we chose 529.8eV as an incident energy for our RIXS experiment withhigh statistics, which is slightly lower than the pure O K-edge. The energy difference between pure O K-edge andabsorption from our sample comes from the hybridizationenergy. We verified the energy resolution to be less than70 meV by checking the full width at half maximum ofthe elastic line from diffuse scattering at a carbon tapereference.All our samples were aligned with a grazing angle( θ = 15 ◦ ) to increase the scattering cross section es-pecially for ultrathin samples. The scattering angle fromincident beam to detector was fixed to 130 ◦ , with thecorresponding momentum transfer of q (cid:107) = 0.28 [2 π/a ].We employed two different polarizations for our experi-ments: σ polarization is parallel to the sample plane and π polarization is nearly perpendicular to the plane. Thus,the former is more sensitive to p x ( p y ) orbital while thelatter is so to p z orbital due to the incident angle. Allexperiments were performed at 20 K.Fig. 3 shows RIXS results for all seven samples withdifferent thickness. To explain the RIXS spectra, we di-vided the spectra into two groups depending on the char-acteristic energy of the peaks and their apparent rele-vance to our two main questions: QCE and MIT, respec-tively. For example, in the high energy side ranging from FIG. 2 (color online) XAS results as a function of thethickness of the sample. The energy of 529.8 eV was used forour RIXS experiments because other peaks mainly originatefrom the SrTiO substrate. p to Ru 4 d orbitals and so reflect the expectedchange in the Ru 4 d orbitals. On the other hand, thereare two relatively weaker peaks below 2 eV with strongthickness dependence. These low-energy excitations canbe interpreted as arising from d-d excitations or coherentpeaks connected to quasiparticle states that are closelyrelated to the metallic phase of SrRuO . In the remainingpart of the paper, we would like to focus on the chargetransfers to explain QCE first and then move on to thelow energy part for MIT. III. RESULTS AND DISCUSSIONA. Configuration interaction calculation of clustermodels
In order to explain the charge transfer peaks and d-d excitations in detail, we performed the configurationinteraction (CI) calculations using two cluster modelsof RuO and Ru-O-Ru (see Fig. 4a) to find that eachof the calculations with different clusters shows distinctfeatures of SrRuO . We note that our model calculationsuits for t g orbitals of more localized character. For in-stance, this calculation with the RuO cluster model hasadvantage in explaining the charge transfer between O2 p and Ru d orbitals because the cluster consists of sixoxygen atoms. On the other hand, the calculation withthe Ru-O-Ru cluster gives a better description of inter-site d-d excitations. These calculations can also reflectthe QCE by the extra control of adjusting the amount ofRu d splitting. For example, we can set Ru d orbitalsto split into ε xy = 2 / t g , ε xz = ε yz = − / t g , FIG. 3 (color online) (a, b) RIXS spectra at the O K-edgewith σ and π polarizations for SrRuO thin films. Upperfigures show the overall features of RIXS spectra dependingon the thickness of the samples and the polarization ofincident beam. As the thickness decreases, the peak at thelow energy side (dot line) becomes weaker while the peak at5 eV(dashed line) gets stronger for both polarizations. Inaddition to the 5 eV peak, the peak around 4.5 eV(dash-dotline) also appears for the σ polarization. Note that this 4.5eV peak becomes stronger below 5 u.c. sample and shiftstowards higher energy as decreasing the thickness. (c) Thelower graph shows the whole spectrum for the 1 u.c. samplewith the σ polarization. Altogether seven Gaussian fittingfunctions are needed to fit the spectra based on the CI andDFT calculations. Different types of peak are marked bydifferent alphabet in the lower graph. ε z = 10 Dq − / e g , and ε x − y = 10 Dq + 1 / e g . It isto be noted that we used an unusually large energy split-ting between d xy and d xz ( d yz ) orbitals (∆ t g =0.8 eV)from the results of first-principle calculation in ref. [20],which is the energy difference between the 2D-type sin-gularity of d xy and the 1D-type singularity of d xz ( d yz ).We also take into account both the spin-orbit coupling( λ ) and the Kanamori-type Coulomb interaction ( U and J H ) among d orbitals [27]. The energy levels of oxygen p orbitals in the valence band can depend on whether theyare hybridized with Ru d orbitals or not [28–30]. For ex-ample, O p orbitals are assumed in our calculations tobe non-interacting and their energy levels are given as e p for non-bonding and e p − ∆ p for bonding p orbitals,respectively. e p is determined as e p = 4 U − J H − ∆, TABLE. I
Physical parameters used for the cluster calculations in units of eV.10 Dq ∆ t g ∆ e g λ U J H ∆ ∆ p V pdσ V pdπ FIG. 4 (color online) (a) RuO cluster used in the CIcalculation. (b, c) Schematic view of charge transfer and d-dexcitations. Oxygen 1 s electrons are excited to vacant 2 p levels which are hybridized with Ru t g orbitals. The energylosses should be different depending on orbitals from whichthe relaxation occurs. Top figure in (c) shows t g − e g excitations and the bottom one indicates the charge transferfrom O 2 p to Ru 4 d levels. where ∆ is the charge transfer energy in the cubic sym-metry defined as the energy difference between lowest d L and d states. The hopping integrals between p and d orbitals are parameterized with V pdπ for t g and V pdσ for e g orbitals according to the Slater-Koster theory [31].We used the parameters shown in Table I in order to fitthe experimental RIXS spectrum.For more details of our calculations, let | Ψ g (cid:105) and E g be the ground state and its energy, respectively. In thedipole and fast collision approximation, the oxygen K-edge RIXS intensity at zero momentum is given as I ∼ − π Im (cid:104) Ψ g | ˆ R ( (cid:15) , (cid:15) (cid:48) ) 1 ω − H + E g + iδ ˆ R ( (cid:15) , (cid:15) (cid:48) ) | Ψ g (cid:105) . (1)And ˆ R ( (cid:15) , (cid:15) (cid:48) ) is the RIXS scattering operator given asˆ R ( (cid:15) , (cid:15) (cid:48) ) = 13 (cid:88) imm (cid:48) σ (cid:15) m (cid:15) (cid:48) m (cid:48) c im (cid:48) σ c † im (cid:48) σ , (2)where c † im (cid:48) σ is the creation operator of oxygen p electronwith m = ( x, y, z ) orbital and σ spin at an i -th site, and (cid:15) and (cid:15) (cid:48) are the polarizations of incident and outgoingx-rays, respectively[27]. δ is the Lorentz broadening andwe set δ = 0 . p orbital states, they can be expressed with a linearcombination of bonding and non-bonding states like c † imσ = (cid:88) α ( U Bα,im ) ∗ c † ασ + (cid:88) µ ( U Nµ,im ) ∗ c † µσ , (3)where U Bα,im and U Nµ,im are the coefficients of m orbitalat the i -th site for bonding and non-bonding states α and µ , respectively. Because non-bonding p orbitals are fullyoccupied in the ground state, only annihilation opera-tion is allowed. We can then get the scattering operatorassociated with non-bonding orbitals as followingˆ R N ( (cid:15) , (cid:15) (cid:48) ) = (cid:88) αµσ R Nαµ ( (cid:15) , (cid:15) (cid:48) ) c µσ c † ασ , (4)where R Nαµ = (cid:80) imm (cid:48) U Nµ,im (cid:48) ( U Bα,im ) ∗ (cid:15) (cid:48) m (cid:48) (cid:15) m . The RIXSintensity attributed to non-bonding p orbitals is given as I N = − π Im (cid:88) αα (cid:48) µ R Nα (cid:48) µ ( (cid:15) , (cid:15) (cid:48) ) ∗ R Nαµ ( (cid:15) , (cid:15) (cid:48) ) × (cid:104) Ψ g | c α (cid:48) σ ω − H + E g + e p + iδ c † α (cid:48) σ | Ψ g (cid:105) . (5)The RIXS intensity attributed to the bonding p orbitalscan then be calculated using the following relation I B = − π Im (cid:104) Ψ g | ˆ R B ( (cid:15) , (cid:15) (cid:48) ) 1 ω − H + E g + iδ ˆ R B ( (cid:15) , (cid:15) (cid:48) ) | Ψ g (cid:105) , (6)whereˆ R B ( (cid:15) , (cid:15) (cid:48) ) = 13 (cid:88) αβσimm (cid:48) U Bβ,im (cid:48) ( U Bα,im ) ∗ (cid:15) (cid:48) m (cid:48) (cid:15) m c βσ c † ασ . (7)In case of the CI calculation of a Ru-O-Ru cluster,mainly explaining the low energy excitations, we directlyused Eqs. (1) and (2) instead of considering bonding andnon-bonding states. In addition, we restricted the Hilbertspace with the following assumption that the oxygenatom between two Ru atoms has three possible statesof p , p , and p electron configurations. The result ofthis calculation is shown in Fig. 5.The peaks in the O K-edge RIXS spectrum can also becategorized according to Ru 4 d orbitals that participatein the RIXS process as shown in Fig. 4. Electrons inthe core oxygen levels are excited to vacant O 2 p levels FIG. 5 (color online) Low energy RIXS spectra of 1 u.c.SrRuO with the CI calculation of a Ru-O-Ru cluster. Thesymbols represent the experimental results while the linesshow the theoretical results with different color used for thedifferent polarization of the incident beam. The peak at 2eV shows intersite d-d excitations. that are hybridized with Ru 4 d orbitals as seen in theO K-edge RIXS and subsequent relaxation occurs fromthe occupied 2 p states. We can, in principle, determinethe origin of each peak by examining the energy of theemitted photons. For example, if the electrons are relaxedfrom 2 p level hybridized with t g levels that are locatedright below the Fermi level, the process can be consideredas d-d excitations. In the case of charge transfers between2 p and 4 d orbitals, however, the relaxation starts from 2 p states not participating in the hybridization. B. Quantum confinement effects
According to our CI calculations, the charge transferscorrespond to the peaks C and D as observed from 2to 10 eV. Peak C, for instance, represents the chargetransfer between non-bonding O 2 p states and Ru t g orbitals while peak D mainly originates from bonding O2 p states and Ru e g orbitals. As shown in top graphsof Fig. 6, both peaks C and D undergo a considerablechange depending on the thickness of the sample and thepolarization of incident beam. The remarkable changeof peak C is clearly seen around 4.4 eV. It is notablethat this variation only occurs for the σ polarization.Meanwhile, an additional peak emerges around 5 eV thatis most likely due to the charge transfer between O 2 p and Ru e g levels in both polarization channels, but theposition of the peak is slightly different depending on thepolarization (see Fig. 6).The splitting of both peaks shown in Figs. 3 and 6 FIG. 6 (color online) RIXS spectra with the results of CIcalculation for monolayer SrRuO . The symbols representthe experimental results while the lines show the theoreticalresults with different color used for the different polarizationof the incident beam. (Left) Calculation results withnon-bonding p orbitals: (right) calculation results withbonding states. can be taken as the evidence of QCE, which is more pro-nounced for the thinner samples. The splitting of peaksaround 4 and 5 eV reflects the energy splitting of Ru t g and e g , respectively. Of interest, the QCE in mono-layer SrRuO modifies the electronic structure, whichsubsequently induces the separate orbital energy levelsdepending on the geometrical characteristics of each or-bital. We comment that the energy difference betweeneach singularity of the 2D-type band for d xy and the1D-type band of d xz ( d yz ) corresponds quite well to theamount of peak splitting in peak C [20]. It should alsobe noted that 0.8 eV of t g energy splitting cannot beobtained in the cases of the usual Jahn-Teller distortion:which is typically about 0.1 eV for t g of ruthenates [32].A further interesting point is the polarization depen-dence of the peaks. In our explanation, the QCE pushesthe energy levels of d xz ( d yz ) or d z down so that theenergy of charge transfer related to those orbitals getsshifted towards lower energy. On the other hand, orbitalssuch as d xy or d x − y move in the opposite direction. Inthe case of the charge transfer between d xz ( d yz ) and p orbitals, the same amount of energy shift compensatesfor the hopping integral V pdπ . Thus the additional peakat 4.4 eV appears only with the orbitals parallel to thesurface of the samples and the one around 5 eV emergesat different energy depending on the polarization of theincident beam. Because each polarization excites differ-ent O p orbitals, we believe the ‘orbital-selective’ charac-teristic of the QCE results in the observed polarizationdependence. C. Metal-insulator transition
While the peaks related to the charge transfer seem tosupport our scenario of the QCE process in SrRuO films,the ones in the low energy range produce the clearest ev-idence of MIT. For instance, with reducing the thicknesspeak A is suppressed rapidly but peak B gets enhancedsimultaneously below the thickness of 5 u.c. This oppo-site trend of these two peaks A and B can be easily un-derstood in terms of MIT as seen in the resistivity datashown in Fig. 7. We note that the critical thickness candepend on the growth conditions according to our fabri-cation of several SrRuO films used for this work.According to our CI calculations, peak B can be as-cribed to d-d excitations between intersite t g orbitals(Fig. 4c). Electrons are excited to O 2 p levels that hy-bridize with Ru t g levels in the valence band and after-wards relaxation occurs from the t g levels in the con-duction band. Although the process can, in principle, in-volves oxygen p levels, it is intrinsically the excitationsbetween two separate t g bands in the valence and con-duction bands.Meanwhile, the origin of peak A can be found by cal-culating the joint density of states (JDOS) from first-principle calculations with density functional theory.Joint density of states (JDOS) represents the probabil-ity of allowed interband transitions including absorptionor energy-loss functions [33, 34]. We calculated JDOS byconsidering the energy levels in the valence and conduc-tion bands. In our calculation, JDOS is given as J ( q ) = (cid:88) (cid:126)k δ ( | ε f ( k ) − ε i ( k − q ) | ) . (8)According to our experimental geometry with a grazingangle, we choose the interband transition with the fixedmomentum transfer of q (cid:107) = 0.28 [2 π/a ] and computedthe DOS of the energy difference between two levels,which represent the theoretical spectrum of electron-holeexcitations. By comparing our calculation results withthe experimental data as shown in Fig. 7, the calculatedJDOS for the electron-hole continuum is in good agree-ment with the lowest peak seen in bulk SrRuO . It meansthat peak A corresponds to itinerant quasi-particle exci-tations while peak B does to excitations between lowerand upper Hubbard bands. In this sense, the spectralweight transfer from peak A to peak B is in good agree-ment with the MIT in SrRuO thin films. We commentthat the transfer of spectral weight from peak A to peakB is also consistent with MIT as seen in the resistivitydata.Another interesting point is the connection betweenQCE and MIT, whose experimental evidence can be read-ily found in the very thin SrRuO sample. In particular,a new peak is seen to be separated from the d xy levelbelow 5 u.c. and moves towards higher energy as shownin Fig. 6. This means that QCE gets enhanced in thinnerSrRuO samples. With QCE splitting the Ru 4 d bands,MIT in SrRuO resembles that of Ca RuO , which is aclassic example of an orbital-selective Mott insulator [35]. FIG. 7 (color online) (a, b) Low energy excitations arecompared to the JDOS from DFT calculation. We clearlyobserve the electron-hole continuum in the thick sample,which arise from its metallic phase. The intensity of peak Asharply decreases below 5 u.c. and it completely disappearsfor the monolayer SrRuO . (c) Electical resistivity ofSrRuO thin films with different thickness. The resistivityincreases progressively with reducing the thickness andcrosses the theoretical Mott-Ioffe-Regel limit between 4 and5 u.c. It is notable that the critical thickness from RIXS andresistivity coincides with one another. For our thinnest sample of 1 u.c. SrRuO , QCE seems tosplit the otherwise degenerate t g orbitals leading to aMott-type insulating state. Therefore, we can maintainthat a new way of realizing a Mott-type insulating phaseis found in the ultrathin SrRuO sample with thicknessbeing a control parameter, which is different from thebulk sample. IV. CONCLUSION
To conclude, the good agreement between the theo-retical calculation and the experimental observation ofcharge-transfer peak splitting in the RIXS spectra sug-gests the orbital-selective QCE in ultrathin SrRuO film.We also found that the suppression of the low-energy ex-citations that arise from electron-hole continuum acrossthe metal-insulator transition. Finally, our studies pro-vide the clear experimental evidence that QCE leads toa Mott insulating phase in ultrathin SrRuO . V. ACKNOWLEDGEMENTS
We would like to acknowledge Daniel Khomskii andBumjoon Kim for helpful discussion. The work at IBSCCES is supported by Institute of Basic Science (IBS)in Korea (Grant No. IBS-R009-G1, No. IBS-R009-G2,and IBS-R009-D1). The work at PSI is supported by theSwiss National Science Foundation through the NCCRMARVEL and the Sinergia network Mott Physics Be-yond the Heisenberg Model (MPBH). We also thank Ko-rea Institute for Advanced Study for providing comput-ing resources (KIAS Center for Advanced ComputationLinux Cluster System) for this work. ∗ [email protected] † [email protected][1] K. I. Kugel, and D. I. Khomski˘ı, Soviet Physics Uspekhi , 231 (1982).[2] M. B. Salamon, and M. Jaime, Rev. Mod. Phys. , 583(2001).[3] S. Lee, J. -G. Park, D. T. Adroja, D. Khomskii, S.Streltsov, K. A. McEwen, H. Sakai, K. Yoshimura, V. I.Anisimov, D. Mori, R. Kanno, and R. Ibberson, NatureMaterials , 471 (2006).[4] L. Das, F. Forte, R. Fittipaldi, C. G. Fatuzzo, V.Granata, O. Ivashko, M. Horio, F. 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