Resonant X-Ray Diffraction Study of Strongly Spin-Orbit-Coupled Mott Insulator CaIrO3
Kenya Ohgushi, Jun-ichi Yamaura, Hiroyuki Ohsumi, Kunihisa Sugimoto, Soshi Takeshita, Akihisa Tokuda, Hidenori Takagi, Masaki Takata, Taka-hisa Arima
aa r X i v : . [ c ond - m a t . s t r- e l ] A ug Resonant X-Ray Diffraction Study of Strongly Spin-Orbit-Coupled Mott InsulatorCaIrO Kenya Ohgushi,
1, 2
Jun-ichi Yamaura, Hiroyuki Ohsumi, Kunihisa Sugimoto, SoshiTakeshita, Akihisa Tokuda, Hidenori Takagi,
2, 6, 7
Masaki Takata,
3, 4 and Taka-hisa Arima
2, 3, 8 Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan JST, TRIP, Chiyoda, Tokyo 102-0075, Japan RIKEN SPring-8 Center, Sayo, Hyogo 679-8148, Japan Japan Synchrotron Radiation Research Institute, SPring-8, Sayo, Hyogo 679-5198, Japan Department of Physics, Kwansei Gakuin University, Sanda, Hyogo 669-1337, Japan Department of Advanced Materials Science, University of Tokyo, Kashiwa, Chiba 277-8561, Japan Advanced Science Institute, RIKEN, Wako, Saitama 351-0198, Japan Institute of Multidisciplinary Research for Advanced Materials,Tohoku University, Sendai, Miyagi 980-8577, Japan (Dated: September 26, 2018)We performed resonant x-ray diffraction experiments at the L absorption edges for the post-perovskite-type compound CaIrO with ( t g ) electronic configuration. By observing the magneticsignals, we could clearly see that the magnetic structure was a striped order with an antiferro-magnetic moment along the c -axis and that the wavefunction of a t g hole is strongly spin-orbitentangled, the J eff = 1 / J eff = 1 / PACS numbers: 75.25.-j, 75.25.Dk, 78.70.Ck, 75.50.Ee
There is a new trend toward exploring Mott physicsin a system with a strong spin-orbit interaction [1–5].Theoretical calculations on the Hubbard model revealedthat the spin-orbit interaction drives a transition from acorrelated metal to an insulator [3–5]. This novel Mottinsulating state is actually realized in a layered perovskiteSr IrO , including Ir ions with a ( t g ) electronic con-figuration [1, 2]. In this compound, one hole among t g manifolds takes a complex wavefunction with the spinand orbital magnetic moments of 1 / / µ B , re-spectively. This so-called J eff = 1 / d transition element.The superexchange interaction between two Ir ionsin the J eff = 1 / J S i · S j ( S j being the spin at the j -th Irsite) is dominant in a corner-shared IrO bond (the Ir–O–Ir bond angle being 180 ◦ ), it completely vanishes inthe edge-shared IrO bond (the Ir–O–Ir bond angle be-ing 90 ◦ ) owing to an interference effect. Instead, themagnetic interaction of the edge-shared bonds becomesa highly anisotropic and ferromagnetic one, − J S zi S zj ,where the z direction is perpendicular to the plane ex-panded by the two Ir atoms and two O atoms responsiblefor the edge-shared bond [Fig. 1(a)]. This interaction,which is called the quantum compass model, is uniquein the sense that the spin anisotropy is produced by theperturbation effect of the Hund’s coupling (not the spin-orbit interaction). To test the validity of this theory, it is necessary to elucidate the magnetic structure of an Iroxide with an edge-sharing network.CaIrO forms the post-perovskite structure shown inFig. 1 (a). It is composed of edge-shared (corner-shared)IrO octahedra along the a -( c -)axis, where each octahe-dron is compressed along the corner-shared O direction(the z direction) with a bond length ratio of 0.97 [7].This structure is in stark contrast to Sr IrO , where elon-gated IrO octahedra with the bond length ratio 1.04 areconnected solely by sharing corners. Hence, CaIrO isan ideal platform for investigating the universal role ofspin-orbit coupling in Ir oxides. The compound showsa Mott insulating behavior characterized by the chargegap ∼ T N ) [8]. Adeviation from the Curie-Weiss law above T N as well aslarge coercive fields below T N suggest an emergence ofthe spin-orbit interaction.In this Letter, we investigated the magnetic and or-bital structure of CaIrO by using the resonant x-raydiffraction [9] at the L absorption edges. This techniqueis particularly powerful in compounds with 5 d transi-tion metals because the wavelength of the x-ray beam iscomparable to the lattice parameters [2, 10–12] and thescattering amplitude is enhanced due to a dipole-allowednature. We also note that neutron scattering measure-ments are not applicable to the present system with astrong neutron-absorbing element Ir. We clarify that themagnetic structure of CaIrO is a striped-type one andthat the J eff = 1 / FIG. 1: (Color online) (a) Crystal structure of the post-perovskite CaIrO . The solid lines indicate the conventionalunit cell, which is twice as large as the primitive unit cell.The magnetic interaction, as well as the magnetic structuredetermined in this study, are also shown. (b) Temperature( T ) dependence of the magnetization ( M ) at the magneticfield ( H ) of 0.1 T [13] (upper), and the intensity ( I ) of the 00 5 reflection at ψ = 0 (lower). pressed octahedral coordination. We then compare theseresults with theoretical predictions.Single crystalline CaIrO was grown by the fluxmethod. CaCO , IrO , and CaCl with a molar ratio of1:1:16 was slowly cooled from 1200 ◦ C to 1000 ◦ C for 240h. Resonant x-ray diffraction measurements were per-formed at the beamline BL19LXU at SPring-8 [13, 14].An incident beam was monochromated by a pair of Si(1 1 1) crystals and irradiated on the (0 0 1) surface ofthe sample, which was mounted in a He closed-cycle re-frigerator installed on a four-circle diffractometer witha vertical scattering plane geometry. The intensities ofincident and scattered beams were detected by an ioniza-tion chamber and a Si PIN photodiode, respectively. Thepolarization of the incident beam was perpendicular tothe scattering plane ( σ ) and that of the scattered beamwas analyzed by using the 0 0 8 reflection of pyrolyticgraphite. The azimuthal angle ψ is defiled as ψ = 0 ◦ when σ || a . We also performed similar experiments atthe beamline BL02B1 at SPring-8, where we use an imag-ing plate as a detector [15].Figure 2 displays the absorption spectra obtained byfluorescence measurements at room temperature ( T ) aswell as the energy dependence of the scattered intensityof the 0 0 5 reflection at T = 10 K. At ψ = 0 ◦ [Fig. 2(b)],we can observe a strong resonance peak at the L edge ∼ .
015 % of the funda-mental 0 0 4 reflection. There are fine structures denotedby A and B with an integrated intensity ratio of 1:0.20,which origin will be addressed below. The space groupof CaIrO is Cmcm orthorhombic symmetry, where 0 0 2 n +1 reflections are forbidden according to the c -glide re-flection. The polarization analysis indicates the π ′ char-acter of the scattered beam I σ - σ ′ /I σ - π ′ = 3 % [inset ofFig. 2(b)], which also rules out the Thomson scatteringas the origin. The T variation of the integrated inten-sity well follows that of the weak ferromagnetic moment[Fig. 1(b)]. Considering also that the anisotropic tensorof susceptibility (ATS) scattering is prohibited in this ge-ometry as discussed later, we conclude that the observedreflection originates from a commensurate antiferromag-netic order. Importantly, the 0 0 5 reflection cannot bedetected within an experimental accuracy at the L edge ∼ I L /I L < . L edge, we alsoobserved magnetic reflections at 0 0 l with l = 1 , , , and9. The observed magnetic reflections at 0 0 2 n + 1 arewell accounted for by considering an antiparallel arrange-ment of two Ir spins [labeled 1 and 2 in Fig. 1(a)] in aprimitive unit cell. In principle, one can also determinethe spin direction experimentally by the ψ dependenceof the magnetic signal: I mag ∝ sin ψ , cos ψ , and 1 forthe spin direction along the a, b, and c axes, respectively[16]. However, the needle-like crystal morphology alongthe a axis prevents us from performing such an analysis.We therefore employed the representation analysis, theresults of which are summarized in Table I. We note thatthe crystallographic space group for the magnetic phasebelow T N has been revealed to be Cmcm by oscillationphotographs obtained at BL02B1. Considering the para-sitic ferromagnetism along the b -axis [Fig. 1(b)] togetherwith the second order nature of the magnetic transition,we conclude that the Γ g representation with the antifer-romagnetic moments along the c -axis is realized. The ob-tained magnetic structure is schematically drawn in Fig.1(a). It is a stripe-type order with a parallel alignmentalong the a -axis and an antiparallel alignment along the c -axis. This markedly contrasts with the checkerboardspin arrangement on the IrO plane in Sr IrO [2].We move to the wavefunction of a t g hole. When thetetragonal crystal field ∆ ( > ζ are present, thesixfold degenerated t g orbitals are split into three dou- TABLE I: The magnetic structures of the irreducible repre-sentations (Γ i ) for the Cmcm space group. M denotes themagnetic point group, where 1 stands for the time-reversaloperation. a, b, and c represent the spin directions. AF and Fdenote the antiferromagnetic and ferromagnetic arrangementof spins at two Ir sites in a unit cell.Γ i M generators a b c Γ g mmm 2 x , 2 y , 1 AF · · Γ g mmm 2 x , 2 y , 1 F · · Γ g mmm 2 x , 2 y , 1 · F AFΓ g mmm 2 x , 2 y , 1 · AF F I ( a r b . un i t s ) I ( a r b . un i t s ) I ( a r b . un i t s ) I ( a r b . un i t s ) ψ ~ 0º (σ || a ) ψ ~ 90º (σ || b ) × 10 A B C D A B B' C' L L (a) (b) (c) I ( a r b . un i t s ) -1.0 -0.5 0.0 0.5 1.0 ∆θ A (º) π ' σ ' I ( a r b . un i t s ) -1.0 -0.5 0.0 0.5 1.0 ∆θ A (º) σ ' π ' FIG. 2: (Color online) (a) X-ray absorption spectra near theIr L edge for CaIrO . (b) The energy dependence of themagnetic scattering intensity ( I ) of the 0 0 5 reflection at T =10 K and ψ = 0 ◦ . The inset shows the polarization analysisof the scattered light at the L edge, where ∆ θ A representsthe analyzer angle. (c) Same data as (b) except for ψ = 90 ◦ .The ATS scattering is dominant in this geometry. Note thatthe data at the L edge is magnified by 10 for clarity. bly degenerated bands. At the ground state, one holeoccupies one of the highest energy orbitals | ϕ, ± > = √ A +2 ( A | xy, ± > ±| yz, ∓ > + i | zx, ∓ > ), where A = − ζ − √ √ ζ +4 ζ ∆+12∆ ζ quantifies the role of thetetragonal crystal field: A = 0 when ∆ /ζ = ∞ and A = 1when ∆ /ζ = 0; the latter corresponds to the J eff = 1 / [13].When one electron is virtually excited from the 2 p orbitals in a resonant process, the t g bands are fullyoccupied; this simplicity enables us to calculate theatomic scattering tensor straightforwardly. By combin-ing contributions of two Ir sites in a striped-orderedstate, we obtain the tensor structure amplitude ˆ F forthe 0 0 2 n + 1 reflection. Nonzero components in ˆ F are F ab = − F ba ≡ iF mag and F bc = F cb ≡ F ATS [17].The F mag term changes its sign by applying the time-reversal operation, and represents the magnetic scatter-ing. The F ATS term corresponds to the ATS scatter-ing. The local principal axes towards the corner-sharedO, z , of two Ir sites in a primitive unit cell are alter-nately titled by an angle ± α ( ∼ ◦ ) from the c -axis [Fig.1(a)]. This difference in the local anisotropy revives 0 02 n + 1 reflections, which are pronounced in a resonant condition. The scattering intensity shows the polariza-tion and azimuthal dependence as follows: I σ - σ ′ = 0and I σ - π ′ = | cos θ sin ψF ATS + i sin θF mag | , where θ isthe Bragg angle. The scattering intensity also shows alarge difference between at the L and L edges. We canquantitatively estimate this by referring to calculated re-sults: F mag = ± (cos α/ f ( A − A − / ( A + 2) and F ATS = − (sin 2 α/ f ( A + A − / ( A + 2) for the L edge; and F mag = ∓ (cos α/ f ( A − / ( A + 2) and F ATS = − (sin 2 α/ f ( A − / ( A + 2) for the L edge.The intensity ratio of the L to L edges are plottedin Fig. 3. One can see that both the magnetic and ATSscattering intensity ratio steeply decrease with approach-ing to the J eff = 1 / A = 1) and that particularlythe ATS scattering ratio with a larger value is more use-ful to determine the orbital character in a large A regionthan the magnetic scattering ratio.We now focus on the spectra at ψ = 90 ◦ [Fig. 2(c)],where the ATS scattering becomes largest. The ψ -independent magnetic scattering is overlapping; however,we can conclude that the ATS scattering is dominant at ψ = 90 ◦ , I ATS /I mag ∼
30 at the L edge, by comparingthe intensity at ψ = 0 and 90 ◦ . We confirmed a π ′ char-acter of the scattered beam I σ - σ ′ /I σ - π ′ = 3 .
9% [inset ofFig. 2(c)].At the L edge, we can discern four fine structurescentered at 11.214, 11.221, 11.237, and 11.249 keV withan integrated intensity ratio of 1:0.95:0.06:0.04. The firstand second peaks, the energies of which coincide withinflection points of the absorption spectrum, are also ob-served at ψ = 0 ◦ and are ascribed to the virtual exci-tation from the 2 p J = 3 / t g and e g orbitals, respectively (inset of Fig. 3). The energy differ-ence of these two peaks corresponds to the crystal fieldsplitting due to the octahedral crystal field, which is esti-mated to be 10 Dq = 7 eV. This value is much larger thantypical values in the 3 d and 4 d transition metal oxides,e.g. 10 Dq = 4 eV in Ca RuO [18]. This can be inter-preted as the strong covalency effect in a 5 d transitionmetal enlarging the band splitting. The higher energystructures denoted by C and D are likely related to the6 s and 6 p bands.At the L edge, as in the case of ψ = 0 ◦ , we could notobserve any signal at the energy related to t g orbitals asan intermediate state. We note that a peak structure cen-tered at 12.832 keV corresponds to an inflection point ofthe absorption spectrum at the higher energy side; hence,the intermediate state is e g orbitals. The intensity ratioat the t g related energy is I L /I L < . A > .
87. On the other hands,the finite ATS signal at the L edge indicates A < t g hole has a slightly modi-fied J eff = 1 / I ( L ) / I ( L ) ( % ) A ATSmagnetic
FIG. 3: (Color online) The calculated intensity ratio in themagnetic and ATS scattering of the L to L edges as a func-tion of the A coefficient. The A = 1 corresponds to the J eff = 1 / metallic iridates with no magnetic order [8, 19, 20], wherevarious exotic quantum states are anticipated [4, 21].Our result that the J eff = 1 / enables us to argue the magnetic structure in theframework of the theory by Jackeli and Khaliullin unam-biguously [6]. We recall that the theory predicts an an-tiferromagnetic (ferromagnetic) interaction through thecorner-(edge-)shared bonds, being consistent with ourspin arrangements. Moreover, the weak ferromagnetismalong the b -axis can be successfully explained by the the-ory. There are two mechanisms which induce the spincanting. One is that the anisotropic axis z in the quan-tum compass model is distinguishable between the Ir(1)–Ir(1’) and Ir(2)–Ir(2’) bonds [Fig. 1(a)]. Another is theDzyaloshinskii–Moriya (D–M) interaction at the Ir(1)–Ir(2) bond with the D–M vector D , = ( D, ,
0) (thesite symmetry at the midpoint of the bond being m m ).A mean field treatment of the Hamiltonian including J -and J -terms, and the D–M interaction gives the moststable spin arrangement to be the experimentally ob-served stripe-type order with the spin canted angle of α .On the other hands, when we assume the antiferromag-netic magnetic moment of 1 µ B /Ir, which is the expectedvalue for the completely localized J eff = 1 / µ B /Ir indicatesthe canted angle ∼ ◦ . This is much smaller than α ∼ ◦ .The reason for this discrepancy between the theory andexperiment is likely related to a reduced spin momentdue to quantum fluctuations, a slight deviation from the J eff = 1 / post-perovskite by the resonant x- ray diffraction. The orbital of a t g hole is the J eff = 1 / [1] B. J. Kim, Hosub Jin, S. J. Moon, J.-Y. Kim, B.-G. Park,C. S. Leem, Jaejun Yu, T. W. Noh, C. Kim, S.-J. Oh, J.-H. Park, V. Durairaj, G. Cao, and E. Rotenberg, Phys.Rev. Lett. , 076402 (2008).[2] B. J. Kim, H. Ohsumi, T. Komesu, S. Sakai, T. Morita,H. Takagi, and T. Arima, Science , 1329 (2009).[3] D. Pesin and L. Balents, Nat. Phys. , 376 (2010).[4] B.-J. Yang and Y. B. Kim, Phys. Rev. B , 085111(2010).[5] H. Watanabe, T. Shirakawa, and S. Yunoki, Phys. Rev.Lett. , 216410 (2010).[6] G. Jackeli and G. Khaliullin, Phys. Rev. Lett. ,017205 (2009)[7] S. Hirai, M. D. Welch, F. Aguado, S. A. T. Redfern, Z.Kristallogr.
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