Emergent magnetic state in (111)-oriented quasi-two-dimensional spinel oxides
Xiaoran Liu, B. J. Kirby, Zhicheng Zhong, Yanwei Cao, B. Pal, M. Kareev, S. Middey, J. W. Freeland, P. Shafer, E. Arenholz, J. Chakhalian
EEmergent magnetic state in (111)-orientedquasi-two-dimensional spinel oxides
Xiaoran Liu, ∗ , † B. J. Kirby, ‡ Zhicheng Zhong, ¶ Yanwei Cao, ¶ B. Pal, † M. Kareev, † S. Middey, § J. W. Freeland, (cid:107)
P. Shafer, ⊥ E. Arenholz, ⊥ and J. Chakhalian † † Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey08854, USA ‡ NIST Center for Neutron Research, National Institute of Standards and Technology,Gaithersburg, Maryland 20899, USA ¶ Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences,Ningbo, Zhejiang 315201, China § Department of Physics, Indian Institute of Science, Bengaluru 560012, India (cid:107)
Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA ⊥ Advanced Light Source, Lawrence Berkley National Laboratory, Berkeley, California94720, USA
E-mail: [email protected]
Abstract
We report on the emergent magnetic state of (111)-oriented CoCr O ultrathinfilms sandwiched by Al O in the quantum confined geometry. At the two-dimensionalcrossover, polarized neutron reflectometry reveals an anomalous enhancement of thetotal magnetization compared to the bulk value. Synchrotron x-ray magnetic circulardichroism (XMCD) demonstrates the appearance of long-range ferromagnetic orderingof spins on both Co and Cr sublattices. Brillouin function analyses further corroborates a r X i v : . [ c ond - m a t . s t r- e l ] M a y hat the observed phenomena are due to the strongly altered magnetic frustration,manifested by the onset of a Yafet-Kittel type ordering as the new ground state in theultrathin limit, which is unattainable in the bulk. Keywords spinels, ultrathin films, emergent properties, magnetismThe quest to design, discover and manipulate new quantum states of matter has fosteredtremendous research activity among condensed matter physicists. Recent progress in thefabrication of epitaxial thin films has empowered this effort with additional means and led toa plethora of interesting artificial multilayers and heterostructures grown with atomic level ofprecision.
Nowadays, to realize exotic physics linked to many-body phenomena the interesthas shifted to tailoring the magnetic states in quasi two-dimensional (2D) limit.
On onehand, according to the Mermin-Wagner theorem, in an isotropic Heisenberg spin system ofdimensionality D ≤
2, enhanced thermal fluctuations prohibit the onset of a long-range (ferro-or antiferro-) magnetic ordering at any finite temperature. On the other hand, loweringthe dimensionality brings about several new factors that can radically alter a quantumsystem including changes in band topology, ionic coordinations and covalency, crystal fields,exchange pathways, magnetic anisotropy, quantum confinement, and universality class.
As a result, in the crossover to low dimensions the magnetic ground state of a material can bedistinctly different from its three-dimensional (3D) counterpart thus opening an opportunityfor emergent or hidden materials phases.In this context, it is interesting to ask whether we can “dial-in” dimensionality of asystem from 3D to 2D in a controllable way, and what can happen to the quantum statewhen low dimensionality entwines with frustration? Here we recap that frustrated magnetsare systems where the localized spins are entangled in an incompatible way due to eithermultiple competing exchange interactions, or the underlaying lattice geometry or both.
Generally, frustration tends to suppress spin ordering and promotes a complex magnetic2hase diagram typically with a set of competing ground states. Further, a large numberof theory proposals have recently addressed another aspect showing how dimensionalityeffectively tunes the many-body function, either driving the ground state into an entirelydifferent regime on the magnetic phase diagram, or inducing unconventional phases throughquantum criticality.
Among many magnetically frustrated compounds, the family of chromate spinels MCr O (M = Mn, Fe, and Co) has attracted intense interest. These materials crystallize intothe normal spinel structure AB O , with M and Cr ions occupying the tetrahedral(A) and octahedral (B) sites, respectively. As both nearest-neighbor exchange interactions J AB and J BB are antiferromagnetic [see Fig. 1(c)], a strong competition between the ex-change interactions ( J BB /J AB > / ) causes magnetic frustration and results in a uniquethree-sublattice ferrimagnetic spiral order. In the bulk such a conical spiral order engen-ders a macroscopic spontaneous polarization which is switchable by an external magneticfield, consistent with the calculations based on the spin-current model and the inverseDzyaloshinskii-Moriya interaction model. Strikingly, when viewed along the [111] direction, the spinel crystal structure shows astacking of triangular and Kagome cation planes with intrinsically large geometrical frustra-tion (GF), embedded in the oxygen cubic close-packed frame, as illustrated in Fig. 1(a)-(b).Specifically, in this viewpoint the basic structural arrangement is “-O -B -O -A-B-A-”, con-taining four cation layers, which we denote as one quadruplet layer or QL. Therefore, wemay speculate that if the lattice can be confined along such a GF direction, the magneticfrustration will be strongly altered and lead to the formation of emergent magnetic phases.Naturally, the thin film approach can give direct access to modalities for manipulation andcontrol of these phases.Based on the above-mentioned framework, we demonstrate the power of this approachfor ground state manipulation in the prototypical case of CoCr O spinel layered along [111]direction. In bulk CoCr O , the ground state has the three-sublattice ferrimagnetic spiral3 AB < 0J BB < 0A B2B1 ABO (a) [111] [11-2] (b) (c) (d) [111] n QL … CoCr O Al O Substrate [111][11-2] [1-10]
Figure 1: (a) Crystal structure of normal spinel AB O viewed along [111] direction. Theoxygen ions stack in the cubic close-packed framework, forming both tetrahedral and oc-tahedral interstitials, which are separately occupied by A and B cations. (b) View of thestructure along the [1-10] direction. (c) Nearesst-neighbor exchange interactions in nor-mal spinels with magnetic A and B ions. Both J AB and J BB are antiferromagnetic, leadingto magnetic frustration. (d) Schematic of the ultrathin (111)-oriented CoCr O thin filmsconfined by Al O spacers.configuration with the onset of ferrimagnetism at T C ∼
93 K, and the incommensurate spin-spiral order at T S ∼
26 K.
The incommensurate to commensurate lock-in transitionfurther takes place at T L ∼
14 K. In this Letter, we report on the discovery of an emergentmagnetic state in (111)-oriented CoCr O ultrathin films confined by inert Al O layers.Spin polarized neutron reflectivity (PNR) confirm the establishment of long-range magneticordering in CoCr O slabs with thickness of few nanometers only. Importantly, analysis onthe x-ray magnetic circular dichroism (XMCD) reveals that even though the ordering ofthese quasi-2D CoCr O films is still ferrimagnetic, it is no longer of the spin-spiral type,but rather the new Yafet-Kittel type, which was theoretically proposed but never realized4n the bulk phase diagram.(111)-oriented [ n QL CoCr O /1.3nm Al O ] superlattices (1QL ≈ n = 4, 2)were fabricated by pulsed laser deposition on single crystalline (0001)-oriented Al O sub-strate, as sketched in Fig. 1(d). Al O was selected as the non-magnetic confinement spacerbecause of the good structural compatibility with CoCr O . Details of the materials syn-thesis, structural and chemical characterizations are given elsewhere.
Additionally, thedegree of cation distribution disorder is investigated by resonant X-ray absorption spec-troscopy (XAS). Within the experimental limit, no signs of cation distribution disorder orion valency change is observed for all samples. Specifically, the obtained absorption line-shapes as well as the absorption energy peak positions at the L , absorption edges of bothCo and Cr are practically identical to that of the bulk CoCr O reference (see Fig. S1,Supplementary). These results further confirm that the ultra-thin heterostructures are ofexpected thickness, orientation, and proper local chemical environments.First, we discuss the presence and distribution of the net magnetization in the (111)-oriented superlattices and compare it to a bulk-like CoCr O (50 QL, 24 nm) sample. Inorder to probe the rather small signals and determine the magnetic depth profiles in thesuperlattices, we performed the PNR experiments at the PBR beamline at the NIST Centerfor Neutron Scattering. The polarized neutron beam was set incident at a grazing angleand the specular reflectivity was recorded as a function of the transfer wave vector Q z alongthe surface normal. Depth profiles of the nuclear scattering length density (SLD) and themagnetization ( M ) component parallel to H were deduced by fitting the non spin-flip data toa superlattice model where the individual layer thickness and roughness were pre-determinedfrom X-ray reflectivity and fixed during the fit. Data was fitted using the NIST Refl1D software routines.Figures 2(a)-2(b) present the fitted PNR data, along with the model profiles correspond-ing to the fits. As clearly seen, a distinct magnetization per formula unit (f.u.) is observedin each ultrathin superlattice. Note, since during the measurements we applied only a mod-5 .50.30.1 M ( µ B / f . u . ) S L D ( - Å - ) M ( µ B / f . u . ) S L D ( - Å - ) M ( µ B / f . u . ) S L D ( - Å - )
50 QL (a) (b) -0.10.00.1 S p i n A s y mm e t r y -0.10.00.1
50 QL -8 -6 -4 -2 R e fl e c t i v i t y
50 QL4 QL2 QL R ++ Fit ++ R -- Fit -- T = 5 KB = 700 mT -0.10.00.1 0.060.040.02 Q (Å -1 ) Figure 2: (a) Non-spin-flip PNR data with model fitting for both CoCr O thick film (50 QL)and ultrathin [ n QL CoCr O / 1.3nm Al O ] superlattices, plotted as reflectivity and spinasymmetry, respectively. Reflectivity curves are offset in intensity for clarity of presentation.Spin asymmetry is defined as ( R ++ − R −− ) / ( R ++ + R −− ) . All data were measured at 5 Kunder 0.7 T in-plane magnetic field. (b) Depth profiles of the net magnetization ( M ) andthe nuclear scattering length density (SLD). The regions in light green denote the CoCr O slabs inside the sample, and the gray regions denote air on top of sample surface.erate magnetic field of 0.7 T, the fitted M implies the presence of a spontaneous long-rangemagnetization rather than canting of the local moment in a paramagnetic phase. First, thevalidity of the model is tested on the 50 QL film, which yields M ∼ µ B / f.u. very closeto the reported value in bulk CoCr O compounds with the spiral spin state. Contraryto expectation, in the ultrathin case the magnitude of M becomes remarkably enhanced ,reaching ∼ µ B /f.u. in 4 QL and ∼ µ B /f.u. in 2 QL samples, respectively. Toappreciate this result, we emphasize that even in the bulk the saturated magnetization fromthe collinear component of the spiral order can reach only ∼ µ B /f.u. This stronglysuggests that the nearly fourfold increase of M in 4 QL and 2 QL films cannot be attributedto mundane changes in magnetic anisotropy with thickness. Instead, these findings imply6 a)(b) (c) C r L X M C D H (T) fi tting 2 QL fi tting -1.0-0.8-0.6-0.4-0.2 C o L X M C D H (T) fi tting 4 QL fi tting -505 X M C D ( % )
50 QL 4 QL 2 QL 50 QL 4 QL 2 QL T = 15 KH = 0.1 T
Figure 3: (a) Cr and Co L , edges XMCD data of (111)-oriented CoCr O thin films ofvarious thickness. (b)-(c) Field-dependent XMCD results of n = 4 and 2 QL samples takenat Cr and Co L maximal peak positions (Cr at ∼
577 eV; Co at ∼
778 eV) with Brillouinfunction fittings.the presence of a more fundamental modification of the magnetic structure which takes placein the quasi 2D limit of the (111)-oriented ultrathin films.In order to elucidate the magnetic structure of each sublattice, we performed resonantXAS measurements with left- and right-circularly polarized beams at beamline 4.0.2 of theAdvanced Light Source at Lawrence Berkeley National Laboratory. The spectra were mea-sured at 15 K under 0.1 T magnetic field, and recorded using the luminescence detectionmode. The circularly polarized x-rays were incident with an angle of 30 ◦ relative to thesample surface. The intensities were normalized with respect to their corresponding ab-sorption spectra. The difference between these two spectra, known as the X-ray magneticcircular dichroism (XMCD), originates from the local magnetization of a specifically probedchemical element (i.e. Co or Cr). The XMCD results at Co and Cr L , edges are shownin Fig. 3(a). The dichroic signals of similar lineshpae are clearly evident for all samples7n both elements. Moreover, the sign of the XMCD spectra is opposite for Co and Cr asobserved at the strongest feature near their L edge (Cr at ∼
577 eV and Co at ∼
778 eV),signifying that the spin orientation on Cr ions is antiparallel to that of the Co ions. Toquantify the values of the orbital and spin magnetic moments on each element, we appliedthe “sum rules” analysis to the spectra.
The obtained results are summarized in Table I.As seen, for all samples the magnetic moment of Co dominates over the magnetic moment ofCr and determines the overall direction of the net magnetization (i.e., M net = M Co + 2 M Cr ).In addition, M net exhibits strong enhancement from ∼ µ B /f.u. in 50 QL to ∼ µ B /f.u. in 4 QL, but reduces back to ∼ µ B /f.u. in 2 QL. The non-monotonic trend of M vs. n is similar in both XMCD and PNR characterizations. Together these observationsaffirm that even in the ultrathin limit, the ground state is indeed ferrimagnetic.Next, we turn our attention to the spin configuration of the ferrimagnetic state in (111)CoCr O ultrathin films. For this purpose we recorded the XMCD intensity of each elementas a function of applied magnetic field at the maximal absorption peak position (i.e. 577 eVfor Cr and 778 eV for Co) [see Fig. 3(b) and 3(c)]. While in the bulk it has been demonstratedthat CoCr O has a conical spiral spin configuration with the net magnetization contributedfrom three different sublattices (Co, Cr1 and Cr2), here, we find that our field-dependentXMCD data is reconciled with a new magnetic ground state described by a two-sublatticeferrimagnetic model. Specifically, unlike bulk, in the 2D limit the Cr1 and Cr2 sitescontribute equally to the net magnetization and the spins on the remaining two magneticsublattices of Co and Cr align anti-parallel to each other. Qualitatively, within the nearest-neighbor approximation, the Weiss molecular field on each site has contributions from boththe inter-sublattice ( J Co-Cr ) and the intra-sublattice ( J Co-Co and J Cr-Cr ) exchange interactions.The ratio J Co-Cr /J Cr-Cr , which is a reflection of the degree of frustration, can be extracted byfitting the field-dependent XMCD data to the modified Brillouin function of this model. According to the theory proposed by Lyons, Kaplan, Dwight, and Menyuk (LKDM), ina normal spinel compound the parameter µ = 4 J BB S B / J AB S A determines spin configuration8able 1: The magnetic moment of each element (Co and Cr ) of all samples ( n = 50,4 and 2 QL) obtained from XMCD sum rules. The net moment per CoCr O formula unit(f.u.) is calculated as M net = M Co + 2 M Cr . n (QL) M Co ( µ B /Co ) M Cr ( µ B /Cr ) M net ( µ B /f.u.)50 0.65 -0.21 0.234 0.64 -0.15 0.342 0.26 -0.05 0.16of the ground state. In particular, as shown in Fig. 4, the ground state is a two-sublatticeNéel-type collinear ferrimagnet for µ < . but turns into a three-sublattice spiral ferrimag-net for . < µ < . ; Larger values of µ indicate further enhancement of the magneticfrustration that renders the spiral ordering unstable. In our case, the Brillouin functionfitting yields the experimental values of µ ≈ In fact, in the ultrathin film geometry, the confinement along the [111] direction alsobreaks the translational symmetry along [110] and prevents the onset of the spiral long-rangeorder. In addition, we can exclude the Néel-type collinear ferrimagnetic configuration as itwould have required a net magnetization of ∼ µ B /f.u. with the overall direction followingthe Cr sublattice. This type of ordering is clearly in sharp variance with the observed XMCDresults which show a rather small net magnetization with the direction aligned along the Cosublattice.To understand what kind of new magnetic ordering emerges in the ultrathin case, we recallthat for an intermediate magnitude of frustration on a normal spinel lattice, Yafet and Kittel(YK) proposed another ground state which deviates from the Néel collinear configuration. As illustrated in Fig. 4, in this model the spins on the B site are divided in two groups, eachgroup has spins canting in an opposite way but at the same angle α YK relative to the netmagnetization direction. According to the YK theory the magnitude of the canting angle α YK is determined by the strength of frustration. The Néel-type collinear configuration is9 afet-Kittel μ Néel Spiral μ = 0.89 Figure 4: The relation between inverse thickness /n , parameter µ and long-range magneticordering in CoCr O . Note, bulk can be regarded as n → ∞ . The magenta solid dot standsfor the possible tricritical point.the special case of α YK = 0.In the following, we speculate on a possible mechanism for the stabilization of the YKspin configuration in (111)-oriented CoCr O ultrathin films. First, we note that in generalthe YK configuration can be triggered due to structural ‘imperfection’ of a spinel compound,i.e., the existence of tetragonal distortion, cation distribution disorder, or inclusion ofhigher order exchange interactions. For our samples tetragonal distortion can be ruledout as the films are grown along the three-fold symmetry axis. Moreover, the existence offinite cation distribution disorder is excluded by our XAS results. Therefore, we suggestthat the YK state is likely stabilized due to the activated additional exchange interactions.Indeed, recent LSDA+U calculations revel that J AA , which was neglected in the conventionalLKDM theory, can reach ∼
10% of J AB . Also the strength of the second nearest-neighborB-B interaction, J BBB , is estimated ∼
3% of J BB . Thus, by confining the films to a fewQLs, the overall effect of quantum confinement is likely to enhance the relative strength of J AA and J BBB , which shifts the magnetic energy balance towards the YK state.Based on the above discussion, we propose an extended magnetic phase diagram whichnow includes the YK spin configuration for (111) normal spinel films as a function of µ and10nverse thickness /n (dimensionality) to reflect the propensity towards 2D. As illustratedin Fig. 4, the magnetism of both bulk compounds and thick films follows the conventionalLKDM theory with the magnetic ground state of either Néel or the spiral type, separatedby the critical value of µ = 0 . . As the thickness is further reduced towards the ultrathinlimit, the YK state emerges at the intermediate regime. It is interesting to point out thatpotentially there might exist a tri-critical point separating these three magnetic phases asmarked by the magenta dot on Fig. 4.In summary, we report on the discovery of a new magnetic state in quasi 2D (111)-orientedCoCr O ultrathin films. Upon the dimensionality reduction along the [111] direction, thesubtle interplay among multiple exchange interactions is markedly altered and the systemshifts into the intermediate region of the extended magnetic phase diagram. As a consequenceof quantum confinement and the activated higher order exchange interactions, a hiddenYafet-Kittel spin configuration takes over the spiral one as the ground state. Our findingshighlight the utility of dimensionally control and designed lattice topology towards novelmagnetic states inaccessible in the bulk. Acknowledgement
The authors thank D. Khomskii, G. Fiete, X. Hu, D. D. Sarma and P. Mahadevan fornumerous insightful discussions. X.L. and J.C. were supported by the Gordon and BettyMoore Foundation’s EPiQS Initiative through Grant GBMF4534, and by the Departmentof Energy under grant de-sc0012375. This research used resources of the Advanced LightSource, which is a Department of Energy Office of Science User Facility under ContractNo. DE-AC0205CH11231. This research used resources of the Advanced Photon Source, aU.S. Department of Energy Office of Science User Facility operated by Argonne NationalLaboratory under Contract No. DE-AC02-06CH11357.11 upporting Information Available
The following files are available free of charge.Additional information regarding XAS analysis and PNR fittings. These materials areavailable free of charge.
References (1) Schlom, D.; Chen, L.; Eom, C.; Rabe, K.; Streiffer, S.; Triscone, J.
Annu. Rev. Mater.Res. , , 589–626.(2) Hwang, H. Y.; Iwasa, Y.; Kawasaki, M.; Keimer, B.; Nagaosa, N.; Tokura, Y. Nat.Mater. , , 103–113.(3) Stemmer, S.; Allen, S. Annu. Rev. Mater. Res. , , 151–171.(4) Bhattacharya, A.; May, S. J. Annu. Rev. Mater. Res. , , 65–90.(5) Coey, J. A.; Pickett, W. MRS Bulletin , , 1040–1047.(6) Hellman, F. et al. Rev. Mod. Phys. , , 025006.(7) Mermin, N. D.; Wagner, H. Phys. Rev. Lett. , , 1133–1136.(8) Bansil, A.; Lin, H.; Das, T. Rev. Mod. Phys. , , 021004.(9) Chakhalian, J.; Freeland, J. W.; Millis, A. J.; Panagopoulos, C.; Rondinelli, J. M. Rev.Mod. Phys. , , 1189.(10) Liu, X.; Middey, S.; Cao, Y.; Kareev, M.; Chakhalian, J. MRS communications , , 133–144.(11) Song, C.; You, Y.; Chen, X.; Zhou, X.; Wang, Y.; Pan, F. Nanotechnology , ,112001. 1212) Ramirez, A. P. Annu. Rev. Mater. Sci. , , 453–480.(13) Greedan, J. E. J. Mater. Chem. , , 37–53.(14) Bramwell, S. T.; Gingras, M. J. P. Science , , 1495–1501.(15) Balents, L. Nature , , 199–208.(16) Wosnitza, J.; Zvyagin, S. A.; Zherlitsyn, S. Rep. Prog. Phys. , , 074504.(17) Vojta, M. Rep. Prog. Phys. , , 064501.(18) Starykh, O. A. Rep. Prog. Phys. , , 052502.(19) Schmidt, B.; Thalmeier, P. Phys. Rep. , , 1.(20) Lee, S. H.; Takagi, H.; Louca, D.; Matsuda, M.; Ji, S.; Ueda, H.; Ueda, Y.; Katsufuji, T.;Chung, J.; Park, S.; Cheong, S.; Broholm, C. J. Phys. Soc. Jpn. , , 011004.(21) Tokura, Y.; Seki, S. Adv. Mater. , , 1554.(22) Ganguly, S.; Chimata, R.; Sanyal, B. Phys. Rev. B , , 224417.(23) Windsor, Y. W.; Piamonteze, C.; Ramakrishnan, M.; Scaramucci, A.; Rettig, L.;Huever, J. A.; Bothschafter, E. M.; Bingham, N. S.; Alberca, A.; Avula, S. R. V.;Noheda, B.; Staub, U. Phys. Rev. B , , 224413.(24) Heuver, J. A.; Scaramucci, A.; Blickenstorfer, Y.; Matzen, S.; Spaldin, N. A.; Ederer, C.;Noheda, B. Phys. Rev. B , , 214429.(25) Aqeel, A.; Vlietstra, N.; Heuver, J. A.; Bauer, G. E. W.; Noheda, B.; van Wees, B. J.;Palstra, T. T. M. Phys. Rev. B , , 224410.(26) Kim, I.; Oh, Y.; Liu, Y.; Chun, S.; Lee, J.; Ko, K.; Park, J.; Chung, J.; Kim, K. Appl.Phys. Lett. , , 042505. 1327) Zhang, H. G.; Wang, Z.; Liu, E. K.; Wang, W. H.; Yue, M.; Wu, G. H. Appl. Phys.Lett. , , 17B735.(28) Yang, S.; Bao, H. X.; Xue, D. Z.; Zhou, C.; Gao, J. H.; Wang, Y.; Wang, J. Q.;Song, X. P.; Sun, Z. B.; Ren, X. B.; Otsuka, K. J. Phys. D: Appl. Phys. , ,265001.(29) Guzman, R.; Heuver, J.; Matzen, S.; Magén, C.; Noheda, B. Phys. Rev. B , ,104105.(30) Chen, X.; Yang, Z.; Xie, Y.; Huang, Z.; Ling, L.; Zhang, S.; Pi, L.; Sun, Y.; Zhang, Y. J. Appl. Phys. , , 17E129.(31) Pronin, A. V.; Uhlarz, M.; Beyer, R.; Fischer, T.; Wosnitz, J.; Gorshunov, B. P.;Komandin, G. A.; Prokhorov, A. S.; Dressel, M.; Bush, A. A.; Torgashev, V. I. Phys.Rev. B , , 012101.(32) Kocsis, V.; Bordács, S.; Varjas, D.; Penc, K.; Abouelsayed, A.; Kuntscher, C. A.;Ohgushi, K.; Tokura, Y.; Kézsmárki, I. Phys. Rev. B , , 064416.(33) Kamenskyi, D.; Engelkamp, H.; Fischer, T.; Uhlarz, M.; Wosnitza, J.; Gorshunov, B. P.;Komandin, G. A.; Prokhorov, A. S.; Dressel, M.; Bush, A. A.; Torgashev, V. I.;Pronin, A. V. Phys. Rev. B , , 134423.(34) Efthimiopoulos, I.; Liu, Z. T. Y.; Khare, S. V.; Sarin, P.; Lochbiler, T.; Tsurkan, V.;Loidl, A.; Popov, D.; Wang, Y. Phys. Rev. B , , 064108.(35) Tsurkan, V.; Zherlitsyn, S.; Yasin, S.; Felea, V.; Skourski, Y.; Deisenhofer, J.; vonNidda, H.-A. K.; Wosnitza, J.; Loidl, A. Phys. Rev. Lett. , , 115502.(36) Kaplan, T. A.; K., D.; Lyons, D.; Menyuk, N. J. Appl. Phys. , , S13.(37) Lyons, D. H.; Kaplan, T. A.; Dwight, K.; Menyuk, N. Phys. Rev. , , 540.1438) Yamasaki, Y.; Miyasaka, S.; Kaneko, Y.; He, J.-P.; Arima, T.; Tokura, Y. Phys. Rev.Lett. , , 207204.(39) Choi, Y. J.; Okamoto, J.; Huang, D. J.; Chao, K. S.; Lin, H. J.; Chen, C. T.; vanVeenendaal, M.; Kaplan, T. A.; Cheong, S.-W. Phys. Rev. Lett. , , 067601.(40) Dey, K.; Majumdar, S.; Giri, S. Phys. Rev. B , , 184424.(41) Katsura, H.; Nagaosa, N.; Balatsky, A. V. Phys. Rev. Lett. , , 057205.(42) Sergienko, I. A.; Dagoto, E. Phys. Rev. B , , 094434.(43) Tomiyasu, K.; Fukunaga, J.; Suzuki, K. Phys. Rev. B , , 214434.(44) Chang, L. J.; Huang, D. J.; Li, W.-H.; Cheong, S.-W.; Ratcliff, W.; Lynn, J. W. J.Phys.: Condens. Matter , , 456008.(45) Yafet, Y. Phys. Rev. , , 290.(46) Liu, X.; Choudhury, D.; Cao, Y.; Middey, S.; Kareev, M.; Meyers, D.; Kim, J.-W.;Ryan, P.; Chakhalian, J. Appl. Phys. Lett. , , 071603.(47) Liu, X.; Kareev, M.; Cao, Y.; Liu, J.; Middey, S.; Meyers, D.; Freeland, J. W.;Chakhalian, J. Appl. Phys. Lett. , , 042401.(48) Kirby, B. J.; Kuienzle, P. A.; Maranvill, B. B.; Berk, N. F.; Krycka, J.; Heinrich, F.;Majkrzak, C. F. Curr. Opin. Colloid Interface Sci. , , 44.(49) Thole, B. T.; Carra, P.; Sette, F.; van der Laan, G. Phys. Rev. Lett. , , 1943.(50) Carra, P.; Thole, B. T.; Altarelli, M.; Wang, X. Phys. Rev. Lett. , , 694.(51) Chen, C. T.; Idzerda, Y. U.; Lin, H. J.; Smith, N. V.; Meigs, G.; Chaban, E.; Ho, G. H.;Pellegrin, E.; Sette, F. Phys. Rev. B , , 152.(52) Goodenough, J. B. Magnetism and the Chemical Bond ; Interscience: New York, 1974.1553) Vonsovskii, S. V.