Sudden collapse of magnetic order in oxygen deficient nickelate films
Jiarui Li, Robert J. Green, Zhen Zhang, Ronny Sutarto, Jerzy T. Sadowski, Zhihai Zhu, Grace Zhang, Da Zhou, Yifei Sun, Feizhou He, Shriram Ramanathan, Riccardo Comin
SSudden collapse of magnetic order in oxygen deficient nickelate films
Jiarui Li, Robert J. Green,
2, 3
Zhen Zhang, Ronny Sutarto, Jerzy T. Sadowski, Zhihai Zhu, Grace Zhang, Da Zhou, Yifei Sun, Feizhou He, Shriram Ramanathan, and Riccardo Comin ∗ Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA Department of Physics and Engineering Physics,University of Saskatchewan, Saskatoon, Saskatchewan, Canada S7N 5E2 Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z4 School of Materials Engineering, Purdue University, West Lafayette, IN 47907 Canadian Light Source, Saskatoon, SK S7N 2V3, Canada Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, NY 11973 (Dated: October 19, 2020)Oxygen vacancies play a crucial role in the control of the electronic, magnetic, ionic, and transportproperties of functional oxide perovskites. Rare earth nickelates (RENiO − x ) have emerged overthe years as a rich platform to study the interplay between the lattice, the electronic structure,and ordered magnetism. In this study, we investigate the evolution of the electronic and magneticstructure in thin films of RENiO − x , using a combination of X-ray absorption spectroscopy andimaging, resonant X-ray scattering, and extended multiplet ligand field theory modeling. We findthat oxygen vacancies modify the electronic configuration within the Ni-O orbital manifolds, leadingto a dramatic evolution of long-range electronic transport pathways despite the absence of nanoscalephase separation. Remarkably, magnetism is robust to substantial levels of carrier doping, andonly a moderate weakening of the (1 / , / , / pc antiferromagnetic order parameter is observed,whereas the magnetic transition temperature is largely unchanged. Only at a certain point long-range magnetism is abruptly erased without an accompanying structural transition. We proposethe progressive disruption of the 3D magnetic superexchange pathways upon introduction of pointdefects as the mechanism behind the sudden collapse of magnetic order in oxygen-deficient nickelates.Our work demonstrates that, unlike most other oxides, ordered magnetism in RENiO − x is mostlyinsensitive to carrier doping. The sudden collapse of ordered magnetism upon oxygen removalmay provide a new mechanism for solid-state magneto-ionic switching and new applications inantiferromagnetic spintronics. Perovskite-type 3 d transition-metal oxides (TMOs) re-alize many interesting electronic phenomena due to theirflexibility in accommodating ionic species of varying sizeand their tolerance to off-stoichiometric chemical compo-sitions. The phase diagrams of these systems host a mul-titude of broken-symmetry electronic phases, which areoften coexisting and intertwined [1–3]. In TMOs, oxy-gen vacancies, whether naturally formed or artificiallyintroduced, provide a very effective avenue to alter theelectronic properties of TMOs and in turn suppress, en-hance, or engender new emergent phases of matter [3–7].Oxygen vacancies have been shown to enhance a broadarray of functional properties, including ionic conduc-tivity [8], photoluminescence [9, 10], thermal resistance[11], electrical conductivity[5], and even superconductiv-ity [4, 12]. Although the role of oxygen vacancies differsfrom system to system, one would expect that, in a meanfield scenario, the removal of oxygen atoms changes theelectronic configuration and (potentially) band filling viacharge compensation [7, 13–16]. This uniform modifica-tion of carrier density can also alter the magnetic proper-ties [17], and long range magnetism is particularly frag-ile to carrier doping in systems with strong correlations[3, 18]. From another perspective, oxygen removal cre-ates local defects that can disrupt long range electronic ∗ [email protected] and magnetic order [19]. However, this second scenariohas not been observed so far and is less understood.The family of rare earth nickelates (RENiO , whereRE = Nd, Sm in this paper) offers new opportunitiesto study the impact of oxygen removal on the electronicand magnetic properties in a materials system character-ized by a complex interplay between the spin, charge,and lattice degrees of freedom. RENiO manifest arich temperature-composition phase diagram which re-mains the subject of a very active line of inquiry [20–22].A pronounced metal-to-insulator transition is followedor accompanied by an antiferromagnetic (AFM) transi-tion [23]. The electronic ground state of stoichiometricRENiO is characterized as a negative charge-transfer in-sulator [24]. Here, the oxygen ligand 2 p electron is self-doped into the Ni 3 d orbital leading to a ground statewith local electronic configuration 3 d δ L δ , where L de-notes an oxygen 2 p hole [25, 26]. Upon cooling into theinsulating phase, a charge/bond disproportionation tran-sition takes place: the NiO octahedra undergo a static,long-range breathing distortion with propagation vector(1 / , / , / pc , creating two inequivalent Ni sites. As aresult, the electronic degeneracy is further split as:2 × d δ L δ → d δ + n L δ + n + 3 d δ − n L δ − n (1)where n , n represent the magnitude of the charge/bonddisproportionation, respectively. Within the bond-disproportionated phase, magnetic order sets in with a a r X i v : . [ c ond - m a t . s t r- e l ] O c t D o p i n g ( e l e c t r o n s / N i ) (c) X - r a y A s b s o r p t i o n ( a . u . )
520 530 540 550 560Energy (eV) e-dopedundoped (b) O- K edge X - r a y A s b s o r p t i o n ( a . u . ) (a) Ni- L edge Energy (eV)
FIG. 1. (a) Measured (solid) and simulated (dashed) X-ray absorption spectra across the Ni- L , edges for SmNiO − x withdifferent electron doping levels, obtained by annealing stoichiometric films in an oxygen deficient atmosphere. The doping level(number of doped electrons per Ni) is specified for each simulated spectrum. Spectra are vertically offset for clarity. (b) X-rayabsorption spectra across the O- K edges for the same SmNiO − x samples. The same color legend is used as the data series inFig. 1(a). (c) The doping levels vs. annealing time for each sample, as extracted from the comparison between experimentaland theoretical spectra. Vertical error bars reflect the uncertainty in the doping level for each sample. supercell composed of 4 lattice units along the body di-agonal direction of the pseudocubic unit cell and cor-responding propagation vector (1 / , / , / pc . Pre-vious studies have found that the spin texture in theAFM phase is either collinear ”up-up-down-down” ornon-collinear ”up-right-down-left” [27–30].Recently, reversible tuning of the oxygen stoichiome-try in thin film samples of RENiO has been achievedby means of highly-controlled post annealing procedures[31, 32]. The creation of oxygen vacancies alters theelectronic structure via charge compensation, driving thematerial into a highly insulating state. Oxygen deficiencythus offers a powerful route to tune the electronic andmagnetic ground state of RENiO − x , enabling access totheir broader electronic phase diagram [33–35]. More-over, recent work on oxygen-reduced Nd . Sr . NiO hasled to the discovery of superconductivity in the nickelatefamily [12], underscoring the importance of studying theground state properties of oxygen-deficient nickelates.In the present study, we examine the evolution of elec-tronic and magnetic ground state in RENiO − x usinga combination of extended multiplet ligand field theory,X-ray spectroscopy and resonant soft X-ray scattering.We chart out the electronic and magnetic phase diagramas a function of temperature and oxygen stoichiometry,which reveals the dual role of oxygen vacancies as (elec-tronic) dopants and (magnetic) defects. On the one hand,we find that the removal of oxygens from stoichiometricRENiO homogeneously injects electrons into the Ni 3 d and O 2 p conduction bands. On the other hand, we ob-serve an unusual evolution of (1 / , / , / pc magneticorder, which is progressively weakened upon oxygen re-moval but without a significant change in T AF M , untilit collapses at a doping level of ∼ − /Ni. The ab-sence of nanoscale spatial inhomogeneity in the electronic ground state upon doping suggests that the collapse ofmagnetic order is due to the progressive disruption of thesuperexchange interaction network caused by the randomformation of localized oxygen defect sites with removedO 2 p ligand orbitals.To understand how the electronic state in RENiO − x evolves upon doping, we performed X-ray absorptionspectroscopy (XAS) measurements on thin films ofSmNiO − x (SNO) and NdNiO − x (NNO). More detailsabout the sample and experiment can be found in thesupplementary material [36]. Figure 1 displays the SNOXAS profiles across the Ni L , and O K edges at 22 K,the lowest temperature measured in the present study.At this temperature, both undoped SNO and NNO arewell within the insulating state, as signaled by the doublepeak structure at the Ni- L resonance (853.2 and 854.8eV in Figure 1(a) and supplementary [36]), which is inclose agreement with the literature [26, 37]. A sharp andintense pre-peak at the O K edge (528.8 eV) correspondsto the transition from O 1s core level to the ligand hole Lin the 3 d δ L δ configuration (Figure 1(b)). Upon doping,we registered the following changes in the XAS spectra:(1) A clear shift of the spectral weight from the highenergy to the low energy component in the Ni- L XASprofile. The Ni- L , edge position also shifts to lowerenergy by about 0.5 eV, from the undoped sample tothe highest doping level. In this high doping limit, theXAS spectra are reminiscent of NiO where Ni has a 2+oxidation state, strongly suggesting that doped carriershave been injected into the Ni conduction band.(2) The pre-peak at the O K edge is progressively sup-pressed until it completely disappears upon doping, in-dicating that doped carriers reside on the Ni 3 d orbitalsas well as the O ligand band. The disappearance of theXAS pre-peak in the highest doping sample suggests the W a v e f u n c t i o n p r o j e c t i o n (d) f Electron filling f f Doping (electrons per Ni)
Doping (electrons per Ni) S p i n CompressedExpanded(c)
Doping (electrons per Ni) N u m b e r o f l i g a n d h o l e s (b)2×n2 O cc u p a t i o n o f N i d S h e ll Doping (electrons per Ni)(a)2×n1
Ni Ni
CompressedoctahedronExpandedoctahedron O FIG. 2. (top) Double cluster electronic model for RENiO .The alternating expanded/compressed NiO octahedra, in-equivalent Ni 3 d orbital occupation, and unbalanced O 2 p orbitals are highlighted. (a-c) Doping evolution of theSmNiO − x electronic structure from double cluster simula-tion. The evolution of different physical quantities for thetwo inequivalent sites are shown: (a) Occupation of Ni 3 d or-bitals; (b) Number of ligand holes; (c) Magnitude of Ni spinmoments. The charge/bond disproportionation magnitudesas defined in equation (1) are marked out by arrows in (a,b).(d) The configuration weights of the ground-state wave func-tion decomposed into states with different total electron filling( f , f , f ) as a function of doping. filling of the ligand band upon doping, which resemblesthe spectra of LaNiO . [38].(3) The NNO spectra manifest a similar trend as SNO.Further details are reported in the supplementary mate-rials [36].To elucidate how the doped carriers are distributed inthis correlated electronic ground state, we developed anextended multiplet ligand field theory, capable of mod-eling the ground state properties as well as the XAS ofthe doped system. Expanding on a previously successfulquantum many body double cluster model [39], we haveadded a charge reservoir term in the Hamiltonian whichcan be used to control the electron filling in the model(see supplemental materials for a complete description ofthe model [36]). The calculations were implemented us-ing the software QUANTY [40, 41]. The simulated SNO XAS spectra are overlaid onto the experimental data inFig. 1(a) for different doping levels (labeled accordingto the number of doped electrons per Ni atom). Onecan see that the simulated spectra capture all of the fea-tures and doping trends measured by XAS. By means ofa least-squares best-fit analysis of the Ni- L XAS edgeexperimental spectra vs. simulated ones, we can inferthe doping levels for each sample shown in Figure 1(a).We note that due to self absorption effects, which artifi-cially modulate the relative fluorescence yield at the L and L edges, a ∼
30% discrepancy is found between thesimulated and measured data at the Ni- L edge [42].Figure 2 summarizes the effect of electron doping onthe SNO electronic structure as captured by the dopeddouble cluster simulation. Upon doping electrons into thesystem, we expect the extra carriers to redistribute in theoxygen ligand band and Ni 3 d levels. Figure 2(a,b) showsthe occupation of Ni 3 d orbitals for the two inequivalentNi sites vs. doping. The doped charges mostly occupythe oxygen ligand orbitals, whereas the Ni 3 d orbitals be-gin filling only when doping exceeds ∼ − /Ni. Thedifference in the occupation number between the two sitescorresponds to the magnitude of the charge dispropor-tionation ( n ). We note that there is a small amount ofcharge disproportionation in the undoped SNO sample.The charge disproportionation is found to be initially sta-ble but strongly reduced when doping exceeds 0.5 e − /Ni.In contrast, the strong bond disproportionation ( n ) pre-sented in the different ligand hole occupation is contin-uously suppressed to zero upon doping as shown in Fig.2(b). The doping also gradually changes the spin mo-ments at both Ni sites from low to high spin states [Fig.2(c)], consistent with previous evidence [31].The doping-induced carrier redistribution and dras-tic changes to covalency were investigated by decompos-ing the ground-state many-electron wave function | ψ (cid:105) =Σ n,i c n,i | d n + i L i (cid:105) into different Hilbert sub-spaces f n (spanned by basis vector | d n L (cid:105) , | d n +1 L (cid:105) , | d n +2 L (cid:105) ...).The doping evolution of the configuration weight Σ i c n,i averaged between compressed and expanded octahedrafor sub space f n where n = 6, 7, 8 is shown in Fig. 2(d).The undoped ground-state wave function has significantcomponents in all three sub-spaces, indicating a highlycovalent state. Upon doping, the system drastically losescovalency, and the ground-state wave function is domi-nated by single f configuration. More details about thedecomposition of the ground-state wave function into dif-ferent basis can be found in supplementary material [36].We then turned our attention to the (1/4, 1/4, 1/4) pc AFM order and its doping dependence. Fig. 3(a) showsthe rocking curve across the (1/4, 1/4, 1/4) pc magneticsuperlattice peak below (solid line) and above (dashedline) the transition temperature for different doping levelsand with the incident photon energy tuned at the Ni- L resonance (853.2 eV). In the low doping region ( n < I n t e n s i t y ( a . u . )
01 0.25 0.50 0.75Dopings (eleectrons per Ni)04020 C o rr e l a t i o n l e n g t h ( n m ) (b) 22 K300 K22 K50 55 60Theta (degree) x10x10x10 I n t e n s i t y ( a . u . ) (a) FIG. 3. (a) Rocking curves as a function of sample angletheta, across the Q AFM = (1 / , / , / pc AFM reflectionin SmNiO − x at 22 K (colored solid line) and 300 K (greydash line). The same color legend is used as the XAS dataseries in Figure 1. Curves are vertically offset for clarity. Theintensity of the last three curves was rescaled to highlight thatno scattering signal could be detected above the noise level.(b) Doping dependence of the magnetic Bragg peak intensityand correlation length measured at 22 K. The dashed line is alinear fit to the data points from samples with AFM order andextrapolates to a threshold doping n = 0 .
21 for the suddencollapse of magnetic order. disappears upon warming above the transition temper-ature. The integrated AFM superlattice peak intensitydecreases linearly in the low doping region [Fig. 3(b)],in contrast to the increase of Ni spin moments obtainedfrom the simulation [Fig. 2(c)]. Despite the suppressionof the total scattering intensity, no significant changes inthe peak width or shape are observed, suggesting thatthe suppression of AFM order is not due to the creationof topological defects. The introduction of oxygen vacan-cies does not alter the thermodynamic properties of theAFM order, as the normalized temperature dependenceof the integrated peak intensity are highly overlapped forthe first five doping levels [Figure 4(a)]. No magneticscattering intensity was observed above the noise levelfor higher doping levels (n > pc AFMorder does not preclude the emergence of magnetic orderwith different ordering vectors as previously found in theoxygen reduced nickelates [7, 43, 44].The temperature-doping phase diagram is sketched outin Figure 4(b). The (1/4, 1/4, 1/4) pc magnetic order issuppressed upon doping and collapses beyond a dopinglevel of ∼ Doping T e m p e r a t u r e ( K ) I n t e n s i t y T AFM N o r m a l i z e d I n t e n s i t y Temperature (K)
FIG. 4. (a) Temperature dependence of the AFM orderingpeak integrated intensity in SmNiO − x . The intensity for themagnetic ordered samples are normalized to the lowest tem-perature. The same color legend is used as the XAS dataseries in Figure 1. (b) Temperature-doping plot of the mag-netic phase diagram in SmNiO − x . The magnetic scatteringintensity is color coded in the background. The AFM transi-tion temperature for each sample is marked out. The stripedarea highlights the temperature range that cannot be accessedin our study. ordering of oxygen defects [16, 47]. However, a reductionof the magnetic order parameter with no significant vari-ation in the ordering temperature is unreported. Severalscenarios are examined to explain the simultaneous in-crease of the Ni spin moment and decrease of the AFMorder parameter, while T AF M remains unchanged. First,a microscopic phase separation picture may be invokedto explain the experimental results: the inhomogeneousdistribution of oxygen vacancies creates two phases, withundoped AFM regions coexisting alongside doped non-magnetic ones. Upon doping, the AFM scattering in-tensity decreases linearly as the coverage of undoped re-gions is reduced, while the T AF M remains unchanged. Toassess this possibility, we have performed a spectromi-croscopy study using X-ray photoemission electron mi-croscopy (XPEEM). No systematic electronic inhomo-geneity was observed at either the O- K edge or Ni- L edge, down to the length scale of our spatial resolutionlimit ( ∼
10 nm), indicating an homogeneous electronicstate with spatially uniform carrier doping. Details of theXPEEM data are described in the supplementary mate-rials [36].With a phase segregation scenario ruled out, we fo-cused on an atomistic picture to explain the phase di-agram. In this picture, the superexchange interactionbetween neighboring Ni spins is mediated by oxygen lig-ands. Each Ni atom is linked to its six nearest-neighborNi sites via six octahedrally coordinated oxygen atoms.The removal of oxygen not only alters the local Ni chargesand spin moments via an effective doping mechanism,but it also destroys the superexchange interaction path-ways that mediate the magnetic interaction across Ni mo-ments. When the density of oxygen vacancies is low,long-range AFM order can still be sustained. Whenthe atomic-scale disruption of the 3D magnetic superex-change network reaches a given threshold, long rangemagnetic order can no longer be supported. In our study,AFM order disappears at a doping level of around 0.21electrons/Ni, corresponding to SmNiO . .In summary, we have systematically studied the elec-tronic and magnetic structure of RENiO − x (Re = Sm,Nd). The introduction of oxygen vacancies is shown to bean effective approach to continuously tune the 3 d δ L δ electronic ground state. By a combination of X-ray spec-troscopy and model simulations, we established a proto-col to quantitatively determine the doping level of eachsample. The doped electrons are shown to redistributeinto the Ni 3 d level and O ligand hole bands and quicklysuppress the charge disproportionation while leaving thebond disproportionation and local moments remarkablystable. We also show that electron doping has onlymarginal effect on (1/4, 1/4, 1/4) pc AFM order exceptfor a suppression of the ordering strength. The magneticorder collapses around a doping threshold of n ∼ . − x . On the one hand, the oxygen vacancies act aselectron donors and homogeneously doped electrons intothe valence band orbital manifold. On the other hand,the oxygen vacancies suppress magnetic order as theycreate local defects in the magnetic superexchange fab-ric. Our study reveals a surprising insensitivity of AFMordering upon carrier doping, that singles out doped rareearth nickelates from the established phenomenology ofother TMOs. Further, the sharp erasure of magneticorder realizes the possibility of reversible magneto-ionicswitching of magnetism and use of oxygen-deficient nick-elates for antiferromagnetic spintronics, low-power logicdevices, and nonvolatile memory cells [48].We wish to thank George A. Sawatzky, BernhardKeimer, Eva Benckiser, Matthias Hepting, Alex Fra˜no,Alex McLeod, William Zheng, and John Mitchell for in-sightful discussions. This material is based upon worksupported by the National Science Foundation underGrant No. 1751739. This work was supported by theAir Force Office of Scientific Research Young Investi-gator Program under grant FA9550-19-1-0063. RJGwas supported by the Natural Sciences and Engineer-ing Research Council of Canada (NSERC). Part of theresearch described in this paper was performed at theCanadian Light Source, a national research facility ofthe University of Saskatchewan, which is supported bythe Canada Foundation for Innovation (CFI), NSERC,the National Research Council (NRC), the Canadian In-stitutes of Health Research (CIHR), the Governmentof Saskatchewan, and the University of Saskatchewan. This research used resources of the Center for FunctionalNanomaterials and National Synchrotron Light SourceII, which are US Department of Energy Office of ScienceFacilities at Brookhaven National Laboratory under Con-tract DE-SC0012704. S.R. acknowledges AFOSR grantFA9550-19-1-0351 for support. [1] E. Fradkin, S. A. Kivelson, and J. M. Tranquada, Rev.Mod. Phys. , 457 (2015).[2] E. Dagotto, Science , 257 (2005).[3] B. Keimer, S. A. Kivelson, M. R. Norman, S. Uchida,and J. Zaanen, Nature , 179 (2015).[4] J. L. Tallon, in Frontiers in Superconducting Materials (Springer-Verlag, Berlin/Heidelberg) pp. 295–330.[5] G. Herranz, M. Basleti´c, M. Bibes, C. Carr´et´ero,E. Tafra, E. Jacquet, K. Bouzehouane, C. Deranlot,A. Hamzi´c, J.-M. Broto, A. Barth´el´emy, and A. Fert,Phys. Rev. Lett. , 216803 (2007).[6] Z. Zeng, M. Greenblatt, and M. Croft, Phys. Rev. B ,8784 (1999).[7] R. D. S´anchez, M. T. Causa, A. Caneiro, A. Butera,M. Vallet-Reg´ı, M. J. Sayagu´es, J. Gonz´alez-Calbet,F. Garc´ıa-Sanz, and J. Rivas, Phys. Rev. B , 16574(1996).[8] G. Gouget, M. Duttine, U. C. Chung, S. Fourcade,F. Mauvy, M. D. Braida, T. Le Mercier, and A. De-mourgues, Chemistry of Materials , 2828 (2019).[9] D. Kan, T. Terashima, R. Kanda, A. Masuno, K. Tanaka,S. Chu, H. Kan, A. Ishizumi, Y. Kanemitsu, Y. Shi-makawa, and M. Takano, Nature Materials , 816 (2005).[10] S. Mochizuki, F. Fujishiro, and S. Minami, Journal ofPhysics Condensed Matter , 923 (2005).[11] L. Chen, Y. Zhang, X. Wang, B. Jalan, S. Chen, andY. Hou, The Journal of Physical Chemistry C , 11482(2018).[12] D. Li, K. Lee, B. Y. Wang, M. Osada, S. Crossley, H. R.Lee, Y. Cui, Y. Hikita, and H. Y. Hwang, Nature ,624 (2019).[13] M. Hoffmann, V. S. Borisov, S. Ostanin, I. Mertig,W. Hergert, and A. Ernst, Phys. Rev. B , 094427(2015).[14] W. Li, R. Zhao, L. Wang, R. Tang, Y. Zhu, J. H. Lee,H. Cao, T. Cai, H. Guo, C. Wang, L. Ling, L. Pi, K. Jin,Y. Zhang, H. Wang, Y. Wang, S. Ju, and H. Yang,Scientific Reports , 2618 (2013).[15] M. M. Seikh, C. Simon, V. Caignaert, V. Pralong, M. B.Lepetit, S. Boudin, and B. Raveau, Chemistry of Mate-rials , 231 (2008).[16] F. Ramezanipour, J. E. Greedan, J. Siewenie, R. L. Don-aberger, S. Turner, and G. A. Botton, Inorganic Chem-istry , 2638 (2012).[17] S. Balamurugan, K. Yamaura, A. B. Karki, D. P. Young,M. Arai, and E. Takayama-Muromachi, Phys. Rev. B , 172406 (2006).[18] D. N. Basov and A. V. Chubukov, Nature Physics , 272(2011).[19] S. Stølen, E. Bakken, and C. E. Mohn, Physical Chem-istry Chemical Physics , 429 (2006).[20] G. Catalan, Phase Transitions , 729 (2008).[21] S. Middey, J. Chakhalian, P. Mahadevan, J. Freeland,A. Millis, and D. Sarma, Annual Review of Materials Research , 305 (2016).[22] S. Catalano, M. Gibert, J. Fowlie, J. ´I˜niguez, J.-M.Triscone, and J. Kreisel, Reports on Progress in Physics , 046501 (2018).[23] J. B. Torrance, P. Lacorre, A. I. Nazzal, E. J. Ansaldo,and C. Niedermayer, Phys. Rev. B , 8209 (1992).[24] J. Zaanen, G. A. Sawatzky, and J. W. Allen, Phys. Rev.Lett. , 418 (1985).[25] T. Mizokawa, D. I. Khomskii, and G. A. Sawatzky, Phys.Rev. B , 11263 (2000).[26] V. Bisogni, S. Catalano, R. J. Green, M. Gibert,R. Scherwitzl, Y. Huang, V. N. Strocov, P. Zubko, S. Ba-landeh, J.-M. Triscone, G. Sawatzky, and T. Schmitt,Nature Communications , 13017 (2016).[27] J. L. Garc´ıa-Mu˜noz, J. Rodr´ıguez-Carvajal, and P. La-corre, Europhysics Letters (EPL) , 241 (1992).[28] V. Scagnoli, U. Staub, A. M. Mulders, M. Janousch, G. I.Meijer, G. Hammerl, J. M. Tonnerre, and N. Stojic,Phys. Rev. B , 100409 (2006).[29] A. Frano, E. Schierle, M. W. Haverkort, Y. Lu, M. Wu,S. Blanco-Canosa, U. Nwankwo, A. V. Boris, P. Wochner,G. Cristiani, H. U. Habermeier, G. Logvenov, V. Hinkov,E. Benckiser, E. Weschke, and B. Keimer, Phys. Rev.Lett. , 106804 (2013).[30] M. Hepting, R. J. Green, Z. Zhong, M. Bluschke, Y. E.Suyolcu, S. Macke, A. Frano, S. Catalano, M. Gibert,R. Sutarto, F. He, G. Cristiani, G. Logvenov, Y. Wang,P. A. van Aken, P. Hansmann, M. Le Tacon, J.-M.Triscone, G. A. Sawatzky, B. Keimer, and E. Benckiser,Nature Physics , 1097 (2018).[31] L. Wang, S. Dash, L. Chang, L. You, Y. Feng, X. He,K. J. Jin, Y. Zhou, H. G. Ong, P. Ren, S. Wang, L. Chen,and J. Wang, ACS Applied Materials and Interfaces ,9769 (2016).[32] M. Kotiuga, Z. Zhang, J. Li, F. Rodolakis, H. Zhou,R. Sutarto, F. He, Q. Wang, Y. Sun, Y. Wang, N. A.Aghamiri, S. B. Hancock, L. P. Rokhinson, D. P. Landau,Y. Abate, J. W. Freeland, R. Comin, S. Ramanathan,and K. M. Rabe, Proceedings of the National Academy of Sciences , 21992 (2019).[33] I. V. Nikulin, M. A. Novojilov, A. R. Kaul, S. N. Mu-dretsova, and S. V. Kondrashov, Materials Research Bul-letin , 775 (2004).[34] A. Tiwari and K. Rajeev, Solid State Communications , 119 (1998).[35] J. L. Garc´ıa-Mu˜noz, M. Suaaidi, M. J. Mart´ınez-Lope,and J. A. Alonso, Phys. Rev. B , 13563 (1995).[36] See Supplemental Material for additional details.[37] F. Y. Bruno, S. Valencia, R. Abrudan, Y. Dumont,C. Carr´et´ero, M. Bibes, and A. Barth´el´emy, AppliedPhysics Letters , 021920 (2014).[38] M. Abbate, G. Zampieri, F. Prado, A. Caneiro, J. M.Gonzalez-Calbet, and M. Vallet-Regi, Phys. Rev. B ,1 (2002).[39] R. J. Green, M. W. Haverkort, and G. A. Sawatzky,Phys. Rev. B , 195127 (2016).[40] M. W. Haverkort, M. Zwierzycki, and O. K. Andersen,Phys. Rev. B , 165113 (2012).[41] M. W. Haverkort, Journal of Physics: Conference Series , 012001 (2016).[42] S. Eisebitt, T. B¨oske, J.-E. Rubensson, and W. Eber-hardt, Phys. Rev. B , 14103 (1993).[43] T. Moriga, O. Usaka, I. Nakabayashi, Y. Hirashima,T. Kohno, S. Kikkawa, and F. Kanamaru, Solid StateIonics , 211 (1994).[44] J. A. Alonso, M. J. Mart´ınez-Lope, J. L. Garc´ıa-Mu˜noz,and M. T. Fern´andez-D´ıaz, Journal of Physics CondensedMatter , 6417 (1997).[45] S. V. Trukhanov, I. O. Troyanchuk, N. V. Pushkarev,and H. Szymczak, Journal of Experimental and Theoret-ical Physics , 308 (2002).[46] W. Zhong, H. Y. Jiang, X. L. Wu, N. J. Tang, W. Chen,and Y. W. Du, Chinese Physics Letters , 742 (2003).[47] B.-X. Wang, S. Rosenkranz, X. Rui, J. Zhang, F. Ye,H. Zheng, R. F. Klie, J. F. Mitchell, and D. Phelan,Phys. Rev. Materials , 064404 (2018).[48] T. Jungwirth, X. Marti, P. Wadley, and J. Wunderlich,Nature Nanotechnology11