Spin-Orbit coupling in Iridium oxide compounds

Transcription

1 Spin-Orbit coupling in Iridium oxide compounds Vamshi Mohan Katukuri Fundamental Aspects of X-ray Spectroscopy Feb Utrecht In collaboration with : N. Bogdanov, L. Hozoi, J. van den Brink (IFW) V. Yushankhai, (Inst. for Nuclear Research, Dubna)

2 Sr IrO 4 : Novel J=1/ Mott insulator Ir 4+ D-layered pervoskite Ground state is an equal mixture of t g orbitals: J eff = 1, m J eff = ± 1 = 1 3 ( yz, ±σ i zx, ±σ xy, σ ) Different from atomic J = 1 state: J = 1 ( L S ), L z + S z = ± 1 3 Parallel spin and orbital moments: L eff L and L eff,z + S z = ±1 B. J. Kim, et al. Phys. Rev. Lett. 101, (008)

3 and small Coulomb interactions as compared orbitals. Metallic ground states are expected in 5d ple paths of intermediate states and thereby L S CONCLUSIONS IRIDIUM OXIDES with those of 3d TMOs. QC SrIrO4, however,is initial and final polarization of a and b,respec- Inteference between TMOs because of their characteristic wide bands known tobe amagnetic insulator (3, 4). A recent and small Coulomb interactions as compared scatters a photon with Energy X-rays from multiple study has with shown thosethat of 3d thetmos. strong SOC SrIrO4, inherent however,is to tively. The presence of initial and final polarization ofscattering a and b,respec- paths Inteference between scattering channels 5d TMOs known cantoinduce be a magnetic a Mott insulator instability (3, even 4). A recent in multiple Energy X-rays from multiple such a study weakly hascorrelated shown that the electron strong SOC system inherent (5), can to tively. give The risepresence to interferences among them, of 5d TMOs Srcan induce IrOa Mott 4 instability : RXS even in - J eff =1/ multiple scattering paths scattering channels resulting in a localized state very different from the well-known such a weakly spin S correlated =1/stateforconventional Mott insulators, proposed to be an effective electron system (5), which canisgive reflected rise toininter- ferences of the among scattered them, the resulting a localized very different fromintensity the well-known spin S =1/stateforconven-photontionallimit Mottexpressed insulators, proposed as to be an effective which is reflected in the total angular momentum Jeff = inthe intensity of the scattered strong SOC photon. total angular momentum Jeff = 1/stateinthe A 1.0 strong SOC limit expressed as jjeff ¼ ¼ T1= SrIrO4 T=10 K (1 0 ) Magnetic reflection X-ray absorption 1=,mJeff A 1.0 jjeff ¼ 1=,mJeff Magnetic Bragg diffraction ¼ T1= SrIrO4 T=10 K (1 0 ) Magnetic reflection X-ray absorption ¼ 1 L3 (p3/ 5d) L (p1/ 5d) pffiffi ðjxy, s jyz,ts ¼ p 1 þ ijzx,ts Þ ð1þ L3 (p3/ 5d) L (p1/ 5d) ffiffi ðjxy, s jyz,ts þ ijzx,ts Þ ð1þ where m is the component of J eff along the 0.6 quantization whereaxis m isand thescomponent denotes the of spin J Constructive interference eff along state. the quantization axis and s denotes theat 0.6 This state derives from the addition of S =1/to spin state. the effective This state orbital derives angular frommomentum the addition of S =1/to Leff =1, 0.4 L 3 resonance which consists the effective of triply orbital peak degenerate angular momentum t Leff =1, g states but 0.4 acts like which the atomic consists L =1statewithaminussign; of triply degenerate t g states but acts like the atomic L =1statewithaminussign; that is, L that is, L Destructive eff = L.Asaresult,J interference eff = L.Asaresult,J eff =1/hasorbital 0. eff =1/hasorbital 0. moment at L moment parallel parallel to spin to (6). spin Note (6). Note the characteristiteristic equal mixture equal mixture of xy, ofyz, xy, and yz, and zx orbitals zx orbitals the charac- with complex with complex number number i involved i involved one in one of the 0.0 of the S=1/ factorsequal and theand mixed theresonant mixed up-and-down up-and-down spin spin states states (7). (7). Photon energy (kev) This realization of a Mott insulator with J intensitiesthis at realization L of and a Mott insulator L 3 with J eff = eff = 1/ moment 1/ moment provides provides a newa new playground playground for for correlated electron phenomena, because emergent B Model correlated electron phenomena, because emergent B S=1/ Model Jeff=1/ Model physical properties that arise from it can be 1:1 L3 L only at L3 physical properties that arise from it can be 1:1 intensity ratio at edge L3 and L resonance only at L3 edge J eff =1/ system drastically different from those of the conventional Mott insulators. A prime example is when xy drastically different from those of the conventional Mott valence Jeff=1/ J eff = insulators. 1/ is realized A prime in example a honeycomb is when lattice xy valence Jeff=1/ J eff = 1/ structure is realized where electrons in a honeycomb hopping between lattice Jeff = yz,zx (5d tg) Jeff=3/ structure1/ where stateselectrons acquire complex hoppingphase; between it generates Jeff = yz,zx (5d tg) a Jeff=3/ L3 L L3 L 1/ states Berry acquire phasecomplex leading tophase; the recent it generates prediction a of Small enhancement Berry phase leadingat to the recent L prediction edge L3 L L3 L of finite t g -e g tetragonal splitting separation 1 Department of Advanced Materials, University of Tokyo, Kashiwa , Japan. and small Magnetic Materials Laboratory, Intensity (arb. units) Intensity (arb. units) L3 p3/ core p3/ 1 Department of Advanced Materials, University of Tokyo, RIKEN Advanced Science Institute, Wako , Japan. p1/ core p1/ Kashiwa , 3 RIKEN SPring-8 Japan. Center, Magnetic Sayo , Materials Japan. Laboratory, 4 Department Fig.. Resonant enhancement p1/ of the magnetic reflection (1 0 ) at the L edge. (A) p1/ Solid lines are RIKEN Advanced Science Institute, Wako , Japan. 3 of Physical Science, Hiroshima University, Higashi-Hiroshima RIKEN SPring , Center, Japan. Sayo x-ray absorption spectra indicating the presence of Ir 5 L3 (p3/) and L (p1/) edges around 11. Department , of Physics, Japan. Kwansei-Gakuin Department Uni-Figversity, Sanda , Japan. 6 Institute of Multidisciplinary and Resonant kev. The enhancement dotted red lines of the represent magnetic the reflection intensity of (1 the 0 ) magnetic at the (1 L 0 edge. ) peak (A) (Fig. Solid 3C). lines ar of Physical Science, Hiroshima University, Higashi-Hiroshima x-ray Research for Adavanced Materials, Tohoku University, Sendai Miller absorption indices are spectra definedindicating with respect thetopresence unit cell of Ir , Japan. 5 inl3 Fig. (p3/) 3A. (B) and Calculation L (p1/) of edges x-ray scattering around 11. Department of Physics, Kwansei-Gakuin University, Sanda , , Japan. Japan. 6 Institute of Multidisciplinary andmatrix 1.83elements kev. Theexpects dottedequal red lines resonant represent scattering theintensities intensity of at the L3 and magnetic L for the (1 0S ) = 1/ peak model. (Fig. 3C) Research *To for Adavanced whom correspondence Materials, Tohoku should University, be addressed. Sendai Miller For indices the Jeff = are 1/defined model, with in contrast, respectthe to resonant the unit enhancement cell in Fig. 3A. occurs (B) Calculation only for the of L3 x-ray edge, scattering and , bjkim6@gmail.com Japan. matrix zero elements enhancement expects is expected equal at resonant the L edge. scattering intensities at L3 and L for the S = 1/ model occurs only for the edge, an (B.J.K.); htakagi@k.u-tokyo.ac.jp (H.T.) *To whom correspondence should be addressed. For the Jeff = 1/ model, in contrast, the resonant enhancement bjkim6@gmail.com (B.J.K.); htakagi@k.u-tokyo.ac.jp (H.T.) zero enhancement is expected at the L edge MARCH 009 VOL 33 SCIENCE B. J. Kim, et al. Science 33, 139 (009) p3/ p3/

4 Branching Ratio and L S (0:05 B =Ir) []. Note that XMC (ordered) FM moment which differs ment (canted AFM). In the strong however, m l =m s ¼ hl z i=hs z i is a p Aim BR = I L 3 I L = n h + L S gs n h L S gs Sr IrO 4 L S gs =.1 (Haskel, et al. PRL 109, 01) For j = 1/, L S gs = 1.0 A pure j = 1/ ground state? Ab initio calculation of L S gs Determine multiconfigurational character of spin-orbit ground state. D. Haskel, et al. PRL 109, 0704 (01);

5 Quantum chemistry cluster approach Complete active space self-consistent field All possible occupations, both orbitals and expansion coefficients are variationally optimized Doubly occupied, orbitals are optimized together with active Frozen after Hartree-Fock Virtual orbitals Ir 6s, O 3s,... Active orbitals Ir 5d Semi-active orbitals O p Frozen orbitals Ir 1s,sp,... O 1s, all orbitals centered on NN octahedra Multireference configuration interaction Single and double excitations on top of CASSCF WF's O p Ir 5d correlations polarization effects

6 I RIDIUM OXIDES QC C ONCLUSIONS hl Si Energy d Hypothetical cubic pervoskite structure eg 5d 10Dq= tg.9 ev J=1/ J=3/ Active orb. tg only tg +eg 0.68 ev! 3 / = ev In 1st order perturbation, hl Si~ due the presence of eg s, Hole char. 33.3% (xy+xz+yz) 90%tg + 10% eg hl Si λ0 10Dq+λ/ *only 1 singlets, 6 quartets and 1 sextet are considered (< 5 ev)

7 MOTIVATION QC RE Tetragonal distortion 3.8% 5d t g =0.15 ev e g t g L S : Sr IrO 4 10Dq=3.7 ev J=1/ J=3/ 0.11 ev 0.66 ev Energy diagram rough estimate: with δ = t g λ, l s = 1 4 [1 + 9 δ 9+δ δ ] l s tg = 0.98 Ψ j= 1 l s Ψ j= 1 = 1 Ψ j= 3 l s Ψ j= 3 = 1 Active orb. t g only t g +e g Pert. Mod. Exp. L S Hole char. 37% (yz+xz)+6% xy 9% t g + 8% e g - -

8 Iridium oxides: L S gs λ =0.456 ev; λ = 0.6 ev Compound tg 10Dq L S gs Exp. Calc. Model Cubic (Hypothetical) Na IrO 3 (Honey comb) Ba IrO 4 (D layered) Sr IrO 4 (D layered) ;.1 BaIrO 3 (3 dim) Y Ir O 7 (Pyrochlore) Sr 3 IrCuO 6 (Chain) J. P.Clancy et al. arxiv (01); D. Haskel, et al. PRL 109, 0704 (01)

9 Conclusions J=1/ state is very sensitve to the octahedral distortions None of the iridium oxides have a pure J=1/ ground state The electronic structure parameters ( tg, 10Dq, λ, λ ) are important in deriving the relevant spin hamiltonian for magnetic interactions in these materials