Tuning Magnetic Coupling in Sr 2 IrO 4 Thin Films with Epitaxial Strain
A. Lupascu, J. P. Clancy, H. Gretarsson, Zixin Nie, J. Nichols, J. Terzic, G. Cao, S. S. A. Seo, Z. Islam, M. H. Upton, Jungho Kim, A. H. Said, D. Casa, T. Gog, Vamshi M. Katukuri, H. Stoll, L. Hozoi, J. van den Brink, Young-June Kim
TTuning Magnetic Coupling in Sr IrO Thin Films with Epitaxial Strain
A. Lupascu, J. P. Clancy, H. Gretarsson, Zixin Nie, J. Nichols, J. Terzic, G. Cao, S. S. A. Seo, Z. Islam, M. H. Upton, Jungho Kim, D. Casa, T. Gog, A. H. Said, Vamshi M. Katukuri, H. Stoll, L. Hozoi, J. van den Brink, and Young-June Kim ∗ Department of Physics, University of Toronto, 60 St. George St., Toronto, Ontario, M5S 1A7, Canada Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506, USA Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA Institute for Theoretical Solid State Physics, IFW Dresden, Helmholtzstrasse 20, 01069 Dresden, Germany Institute for Theoretical Chemistry, Universit¨at Stuttgart,Pfaffenwaldring 55, D-70569 Stuttgart, Germany (Dated: October 3, 2018)We report x-ray resonant magnetic scattering (XRMS) and resonant inelastic x-ray scattering(RIXS) studies of epitaxially-strained Sr IrO thin films. The films were grown on SrTiO and(LaAlO ) . (Sr AlTaO ) . substrates, under slight tensile and compressive strains, respectively.Although the films develop a magnetic structure reminiscent of bulk Sr IrO , the magnetic cor-relations are extremely anisotropic, with in-plane correlation lengths significantly longer than theout-of-plane correlation lengths. In addition, the compressive (tensile) strain serves to suppress(enhance) the magnetic ordering temperature T N , while raising (lowering) the energy of the zoneboundary magnon. Quantum chemical calculations show that the tuning of magnetic energy scalescan be understood in terms of strain-induced changes in bond lengths. PACS numbers: 75.70.Ak, 75.10.Jm, 75.30.Ds, 78.70.Ck
The physics of strong spin orbit coupling (SOC) in con-densed matter systems has been drawing increased inter-est in recent years. In particular, iridates have emergedas interesting model systems in which novel magnetismarises due to entangled spin and orbital degrees of free-dom [1, 2]. A prototypical example is the layered Sr IrO (SIO), in which Ir (5 d ) ions form a square lattice.Due to the strong SOC, the Ir orbital moment is notquenched in this compound, and the local magnetic mo-ment is described by a spin-orbit coupled j eff = 1 / IrO is that its magnetic propertiesare strikingly similar to those of the parent compoundsof cuprate superconductors [2, 7], raising the possibilitythat unconventional superconductivity could be realizedin this system by doping [8, 9]. Although superconduc-tivity has not been realized so far, doping studies haveshown that structural details, such as the Ir-O-Ir angleand the Ir-Ir distance, are important factors to considerwhen studying the magnetic properties of Sr IrO [10–16]. However, since doping may also affect the chargeconcentration in addition to the crystal structure, an al-ternative means to tune the structure is necessary to elu-cidate the structure-property relation in Sr IrO .One of the most promising approaches to the structuraltuning of oxide materials is strain engineering, accom-plished by growing thin films on substrates with varyingdegrees of lattice mismatch. This method has been suc-cessfully used to study 3d and 4d transition metal oxides.For example, it was found that strained thin film cupratesshow an increase in superconducting T c [17]. Strain can also be used to tune the properties of ferroelectrics suchas SrTiO [18] and BaTiO [19]. The study of iridate thinfilms is still in its early stages, and most studies to datehave focused on the structural and electronic propertiesof thin film Sr IrO [20–23]. Rayan Serrao et al. studiedSr IrO films with various thicknesses grown on SrTiO substrates (slight tensile strain), and reported that thin-ner samples exhibit smaller c/a ratio [21]. They alsosuggested that electronic anisotropy is reduced in thinnersamples based on their structural and x-ray spectroscopicdata. Nichols et al. grew Sr IrO films on substrates withvarying degrees of strains, ranging from highly compres-sive to highly tensile [22]. They found that the opticalabsorption peak shifts to higher energies under tensilestrain. Until recently, the magnetic properties of thesethin film samples have been largely unexplored [24].In this Letter, we report complementary x-ray res-onant magnetic scattering (XRMS) and resonant in-elastic x-ray scattering (RIXS) studies on Sr IrO thinfilm samples epitaxially grown on SrTiO (STO) and(LaAlO ) . (Sr AlTaO ) . (LSAT) substrates, whichhave been chosen to provide tensile and compressivestrain, respectively. The most surprising result is thatthe magnetic ordering temperature T N is found to be sup-pressed (enhanced) in samples with compressive (tensile)strain. This observation is somewhat counter-intuitive,since both RIXS experiments and quantum chemicalcalculations predict magnetic interaction to strengthenwhen the in-plane lattice constant shrinks. The mag-netic coupling energy scale determined from the zone-boundary magnon energy increases (decreases) undercompressive (tensile) strain, which is also well reproduced a r X i v : . [ c ond - m a t . s t r- e l ] A p r in calculated values for magnetic exchange constants. Weargue that the observed behaviour of T N could be ac-counted for by the subtle change in inter-layer magneticcoupling due to in-plane strain. Our findings illustratethat the magnetic properties of Sr IrO are highly sensi-tive to the effects of epitaxial strain.The Sr IrO thin films, 20 unit-cells thick ( ≈
50 nm),were grown using pulsed laser deposition, as describedin Ref. [22]. The films were deposited on two differentsubstrates: STO (100) (SIO-STO), with a 0.45 % nom-inal tensile strain, and LSAT (100) (SIO-LSAT), with a0.45 % nominal compressive strain. The XRMS measure-ments were conducted at the Advanced Photon Source(APS) using beamline 6-ID-B. The data were collectedat the Ir L (11 .
215 keV) absorption edge. A graphite(008) polarization analyzer was used to select outgoingphoton polarization for XRMS. Ir L -edge RIXS mea-surements were carried out using the MERIX spectrome-ter on beamline 30-ID-B at the APS. Measurements wereperformed using a spherical (2 m radius) diced Si (844)analyzer and a channel-cut Si (844) secondary monochro-mator to give an energy resolution (FWHM) of 45 meV.The RIXS data was collected in horizontal scattering ge-ometry, with a scattering angle close to 2 θ = 90 ◦ , to min-imize the background contribution from elastic scatter-ing. To maximize the signal, measurements were per-formed near glancing incidence, with an angle of inci-dence α < ◦ , for both the thin films and bulk sample. FIG. 1: L-scan profile of magnetic x-ray diffraction along(0,1,L) for SIO-LSAT (a) and SIO-STO (b). Polarizationdependence for SIO-LSAT (c) and SIO-STO (d), in the σσ channel (filled circles) and the σπ channel (empty circles).Incident energy dependence for SIO-LSAT (e) and SIO-STO(f). All data in (c)-(f) were obtained at T = 5 K at the(0 , ,
14) reflection.
The tetragonal structure of bulk Sr IrO gives riseto two distinct magnetic domains. The first domainis characterized by magnetic reflections observed at(1 , ,
4n + 2) and (0 , , , ,
4n + 2) and (1 , , , , L) and (0 , , L). Magnetic peaks have also beenobserved for odd L values when small magnetic field isapplied or when doping occurs on the Ir sites [1, 26, 27]. FIG. 2: SIO-LSAT: Scans of the (0 , ,
14) magnetic peakalong the K (a) and L-direction (b). SIO-STO: Scans of the(0 , ,
14) magnetic peak along the H (c) and L-direction (d).The baseline of the profiles in (a-d) is shifted. The solid linesthrough the data points are the results of the fit describedin the text. The solid black lines depict the H, K, and L-scans of the (1,0,18) magnetic peak for bulk Sr IrO (the peakintensity is re-scaled and the L-scan is shifted from 18 to 14). As shown in Fig. 1(a)-(b), we have observed magneticpeaks at even L positions in both thin films, which isconsistent with the magnetic structure of bulk Sr IrO at zero-field. The magnetic nature of these peaks is illus-trated in Fig. 1(c)-(d),which presents two scans obtainedin different polarization channels. The energy depen-dence of the (0 , ,
14) magnetic peaks is shown in Fig.1(e)-(f). The peaks resonate at an incident energy of11.219 keV. These observations are all very similar tothose in bulk crystals of Sr IrO .To further characterize the magnetic ordering of thefilms, we have studied the (0 , ,
14) peak as a functionof temperature. For SIO-LSAT, the K-scans (constantH and L) and L-scans (constant H and K) are shown inFig. 2 (a) and (b). Similar sets of scans are plotted inFig. 2 (c)-(d) for SIO-STO. Both in-plane scans (H and Kscans) are quite similar and only one of these are shown.Unlike the SIO-LSAT film, which shows monotonoustemperature dependence, the SIO-STO shows anomaloustemperature dependence in the 30 −
100 K range. Theseanomalies are presumably due to a variation in strainwith temperature caused by structural transitions in theSTO substrate. STO adopts several distinct structuralphases at low temperatures: with a cubic to tetragonaltransition at (T = 110 K) and several other transitions atlower temperatures [28]. The temperature dependence il-lustrates the close relation between strain and magnetismin this material. However, a further quantitative charac-terization of the SIO-STO film structure at low tempera-tures is beyond the scope of this paper, and we will onlyfocus on T >
110 K data here.The peak profiles were fitted with a n-th powerLorentzian function: I ( q ) = I max [( q − q ) / ( ζ n κ ) +1] − n ,where ζ n = √ /n − κ the half-width at half maximum (HWHM). The parameter q iseither H, K, or L, and q is the respective peak position.The fitting procedure is detailed in the Supplemental Ma-terial [29]. The fitting results are presented in Fig. 3(a).The widths of the film magnetic peaks are approximately2-3 times broader than the (1,0,18) bulk magnetic peakalong the H and K-direction, and an order of magnitudebroader along the L-direction, as shown in Fig. 2. Themagnetic correlation length, ξ , can be estimated by in-verting κ : ξ = κ − . Both the tensile and the compressivestrain films show similar magnetic correlation lengths,with a considerable anisotropy characterized by verysmall correlation lengths along the c-axis, ξ ≈ −
20 ˚A(approximately one unit-cell) and much larger correlationlengths in the ab-plane, ξ ≈ −
400 ˚A. Such a short-range magnetic correlation along L is in stark contrast tothe magnetic ordering in bulk Sr IrO , which developsinto a full 3D long-range order [7].In Fig. 3(b) we present the temperature dependence ofthe integrated intensity for SIO-LSAT (red triangles) andSIO-STO (blue squares). The magnetic transition tem-peratures in the films are very different from that of bulk( T N = 240 K) [1, 30]. For the compressive strain (LSAT),the transition temperature is lower than the bulk, witha T N of only 210 K. The tensile strain (STO) has an in-creased T N of 270 K. This trend is illustrated in the insetof Fig. 3(b), which shows the transition temperature asa function of strain.Representative RIXS measurements performed on bulkSIO, SIO-STO, and SIO-LSAT are presented in Fig. 4.They highlight the strain effect on the magnon mode inSr IrO , which is observed at energy transfers of ∼ π ,0) zone boundary position, where the magnon en-ergy is at its maximum. The RIXS excitation spectrafor the SIO, SIO-STO and SIO-LSAT samples, includ-ing the spin-orbit exciton mode at ( π,
0) and (pi / , pi / FIG. 3: (a) The HWHM (fitting parameter κ ) is plottedas a function of temperature, along the H and L-direction forSIO-STO, and along the K and L-direction for SIO-LSAT. (b)The change in integrated intensity with temperature for the(0 , ,
14) reflection, for SIO-LSAT (red triangles) and SIO-STO (blue squares). The black arrow indicates the magnetictransition temperature of SIO bulk, and the red and blue dot-ted lines are provided as a guide to the eye. The backgroundcolouring depicts the structural transitions of the STO sub-strate. Anomalous temperature dependence below 110 K isdue to structural transitions in the STO substrate, and willnot be discussed here. The inset shows the magnetic transi-tion temperature as a function of strain. zone boundary wave-vectors, can be found in Fig. 2 ofthe Supplemental Material [29] . The strain dependenceof the zone boundary magnon energy, E ( π, , is very dif-ferent from that of T N , with compressive strain (SIO-LSAT) driving the magnon to higher energies, and tensilestrain (SIO-STO) driving it lower. Quantitative valuesfor E ( π, , extracted from multi-Gaussian data fits, areprovided in Table I.On a qualitative level, the strain-induced tuning ofmagnetic energy scales in SIO can be understood as fol-lows. The application of compressive epitaxial strain re-sults in a reduction of the in-plane lattice parameters( a and b ) and an enlargement of the out-of-plane lat-tice parameter ( c ). The magnetic exchange interactionsbetween neighbouring Ir ions are very sensitive to bondgeometry, so a decrease of Ir-O/Ir-Ir bond lengths will en-hance the interaction strength and vice-versa. Hence, weexpect compressive strain to strengthen the in-plane in- FIG. 4: Epitaxial strain effect on the low-lying magneticexcitations of Sr IrO . A comparison of Ir L -edge RIXSspectra collected at room temperature for bulk SIO, SIO-LSAT, and SIO-STO demonstrates that compressive (tensile)strain significantly raises (lowers) the energy of the ( π ,0) zoneboundary magnon. The solid lines represent Gaussian fits tothe data (described in the Supplemental Material [29]). Thedashed vertical lines represent the fitted values for the magnonenergies. teractions and weaken the out-of-plane interactions. Theenergy scale associated with the magnetic excitations isprimarily set by the strength of the in-plane exchangeinteractions. Thus, we expect compressive strain to in-crease the value of E ( π, . In contrast, the energy scaleassociated with magnetic ordering is set by the strengthof the interactions between neighbouring Ir-O layers, sowe expect compressive strain to reduce the size of T N . Asimilar, but opposite, trend can be expected when tensilestrain is applied: stretching the a and b -axes will reducethe in-plane interactions and lower E ( π, , while shrink-ing the c -axis will enhance the out-of-plane interactionsand increase T N . TABLE I: Effective singlet-triplet splittings ∆ E ST inSIO bulk and SIO films for two adjacent Ir ions (meV).MRCI+SOC results, see text. Experimental RIXS values forthe zone boundary magnon energy (proportional to J ) arealso provided. Strain-induced relative changes in the energyscales are listed in parentheses.Sample RIXS: E ( π, Model I: ∆ E ST Model II: ∆ E ST SIO-STO 172 ± ± ± This argument is supported by ab initio multirefer-ence configuration-interaction (MRCI) calculations [46]on embedded clusters of two nearest-neighbour IrO oc-tahedra. The ab initio wave function approach has beenshown to yield results in good agreement with experi-ments measuring the magnetic interactions in 3 d [47, 48]and 5 d [49] oxides, as well as determining the dependence of the effective coupling constants on strain in cuprates[50] and on additional distortions in a few other d -metalcompounds [49, 51, 52]. Singlet-triplet splittings for clus-ter models of bulk SIO and strained films of SIO are listedin Table I. The results were obtained by MRCI calcula-tions including SOC’s (MRCI+SOC) [53]. Two differentstructural models were employed for the SIO films. Sincethe precise structural details are experimentally difficultto access in the films, we assumed in a first set of calcu-lations that the Ir-O-Ir bond angles are the same as inbulk [3] and only the interatomic distances change withstrain (Model I). At the other extreme, we considered astructural model for which the in-plane Ir-O bond lengthsare fixed to the values measured in bulk [3] and for re-producing the strain induced variation of the lattice pa-rameters [22] we modified the Ir-O-Ir angles (Model II).For Model I, the variations of the average energy of thetriplet terms with respect to the singlet state, denotedin Table I as ∆ E ST , are large, 3.5 to 7 meV. Since thestructure of the triplet components is always the same,with two of them nearly degenerate and the splitting be-tween the lowest and highest triplet terms taking valuesin a narrow interval between 0.9 to 1.2 meV (see theSupplemental Material [29]), we can safely conclude thatfor Model I the most important changes with strain con-cern the variation of the isotropic Heisenberg exchange J . The overall trend observed in the RIXS spectra for J is in this case nicely reproduced. In contrast, for ModelII, the variations of ∆ E ST are much smaller and do notfollow the trend observed for J by RIXS. This suggeststhat the most significant structural change that occursin the epitaxial thin films is the tuning of the Ir-Ir andIr-O bond lengths. Further detailed investigations of thelocal structure by local probes such as EXAFS would beextremely useful.In conclusion, we have explored the magnetic proper-ties of Sr IrO thin films, with tensile (STO) and com-pressive (LSAT) epitaxial strain, using x-ray resonantmagnetic scattering and resonant inelastic x-ray scatter-ing. The films show a quasi-two-dimensional magneticorder for both substrates, with magnetic ordering vectorsreminiscent of the bulk magnetic structure. Comparedto bulk Sr IrO , the film magnetic correlation lengthsshow a large anisotropy, with in-plane correlation lengthsof 300 −
400 ˚A and very small (10 −
20 ˚A) correlationlengths along the c-axis. We have observed that the mag-netic ordering temperature T N is suppressed for the com-pressive strain (LSAT) and enhanced for the tensile strain(STO). In contrast, the RIXS experiments show thatthe magnetic exchange interactions, determined from thezone-boundary magnon energy, increases (decreases) un-der compressive (tensile) strain. These results are sup-ported by quantum chemistry calculations, which suggestthat the most significant structural change taking placein the films is a tuning of the Ir-O bond length. Other ap-plied perturbations in Sr IrO seem to change the mag-netic structure of Sr IrO at fairly moderate levels (i.e.,relatively low applied fields and dopant concentrations).In comparison, a significant epitaxial-strain has no effecton the magnetic ordering wave-vector, while it is alter-ing the energy scales associated with T N and J. 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