1 / 21

Spin-Orbital Entanglement and Violation of the Kanamori-Goodenough Rules

Andrzej M. Oleś Max-Planck-Institut f ü r Festk ö rperforschung, Stuttgart M. Smoluchowski Institute of Physics, Jagellonian University , Kraków Self-organized Strongly Correlated Electron Systems Seillac, 31 May 2006. Spin-Orbital Entanglement and Violation of the Kanamori-Goodenough Rules.

hieu
Download Presentation

Spin-Orbital Entanglement and Violation of the Kanamori-Goodenough Rules

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Andrzej M. Oleś Max-Planck-Institut für Festkörperforschung, Stuttgart M. Smoluchowski Institute of Physics, Jagellonian University, Kraków Self-organized Strongly Correlated Electron Systems Seillac, 31 May 2006 Spin-Orbital Entanglement and Violation of the Kanamori-Goodenough Rules • Peter Horsch, Max-Planck-Institut FKF, Stuttgart • Giniyat Khaliullin, Max-Planck-Institut FKF, Stuttgart • Louis-Felix Feiner, Philips Research Laboratories, Eindhoven • Institute of Theoretical Physics, Utrecht University oo

  2. Outline • Spin-orbital superexchange models • Goodenough-Kanamori rules in transition metal oxides • Example: magnetic and optical properties of LaMnO3 • Violation of Goodenough-Kanamori rules in t2g systems due to spin-orbital entanglement • Continuous orbital transition • Spin-orbital fluctuations in LaVO3

  3. Orbital physics in transition metal oxides Goodenough-Kanamori rules: AO order supports FM spin order FO order supports AF spin order C-AF A-AF Current status: Focus on Orbital Physics New Journal of Physics 2004-2005 http://www.njp.org LaVO3 t2g orbitals LaMnO3 eg orbitals

  4. Electron interactions and multiplet structure Two parameters: U – intraorbital Coulomb interaction, JH – Hund’s exchange Anisotropy in Hund’s exchange: [AMO and G. Stollhoff,PRB 29, 314 (1984)]

  5. Multipletstructureof transition metal ions Follows from three Racah parameters (Griffith, 1971): single parameter: η=JH /U [AMO et al., PRB 72, 214431 (2005)]

  6. Magnetic and optical properties of Mottinsulators (t<<U) Spin-orbital superexchange model for a perovskite, γ=a,b,c(J=4t2/U): contains orbital operators: By averaging over orbital operators one finds effective spin model: Here spin and orbital operators are disentangled. Superexchange determines partial optical sum rule for individual band n: [G. Khaliullin, P. Horsch, and AMO, PRB 70, 195103 (2004)]

  7. spectral weights for increasing T AF FM Exchange constants and optical spectral weights in LaMnO3 Jc and Jab for varying orbital angle  A-AF phase orbital order: exp: F. Moussa et al., PRB 54, 15149 (1996) exp: N.N. Kovaleva et al., PRL 93, 147204 (2004) S=2 spins and egorbitals are disentangled (MF can be used) [ AMO, G. Khaliullin, P. Horsch, and L.F. Feiner, PRB 72, 214431 (2005) ]

  8. Spin waves in La1-x SrxMnO3 and in bilayer manganites Isotropic spin waves inLa1-xSrxMnO3 Anisotropic spin waves in La2-2xSr1+2xMn2O7 FM phase x=0.30 x=0.35 [ T.G. Perring et al., PRL 87, 217201 (2001) ] [ T.G. Perring et al., PRB 77, 711 (1996) ] Double exchange and superexchange explain Jab and Jc [ AMO and L.F. Feiner, PRB 65, 052414 (2002); 67, 092407 (2003)]

  9. Charge transfer insulator: KCuF3 One of the best examples of a 1D AF Heisenberg model Parameters: J =33 meV, η=0.12, R=2U/( 2Δ+Up ) =1.2 Jc and Jab for varying orbital angle  spectral weights for increasing T optical properties would help to fix the parameters Valid if S=1/2 spins and egorbitals disentangle (MF can be used) [ AMO et al., PRB 72, 214431 (2005)]

  10. Spin-orbital models with entanglement • d1 model – titanates (LaTiO3, YTiO3), S=1/2, t2gorbitals; • d2 model – vanadates (LaVO3, YVO3), S=1, t2g orbitals, (xy)1(yz/zx)1 configuration; • d9 model – KCuF3, S=1/2, eg orbitals. Spin-orbital models were derived in: d1 model [G. Khaliullin and S. Maekawa, PRL 85, 3950 (2000)] d2 model [G. Khaliullin, P. Horsch, and AMO, PRL 86, 3879 (2001)] d9model [L.F. Feiner, AMO, and J. Zaanen, PRL 78, 2799 (1997)]

  11. eg orbitals t2g orbitals Orbital degrees of freedom In t2g systems (d1,d2) two flavors are active, e.g. yz and zx along c axis – described by pseudospin operators: At finite η the orbital operators contain: GdFeO3-type distortions induce orbital interactions leading to FO order: Pseudospin operators for eg systems (d9) with 3z2-r2and x2-y2: Jahn-Teller ligand distortions favor AO order:

  12. Spin-orbital superexchange at JH=0 => chain along c axis => 2D model in ab planes

  13. Intersite spin, orbital and spin-orbital correlations Spin correlations: Orbital and spin-orbital correlations for t2g (d1 and d2)systems: Orbital and spin-orbital correlations for eg (d9) model: • Definitions follow from the structure of the spin-orbital SE at JH0; • Method: exact diagonalization of four-site systems.

  14. Intersite correlations for increasing Hund’s exchange η V=0 V=J d1 Sij – spin correlations Tij –orbital correlations Cij– spin-orbital correlations d2 • all correlations identical in d1at η=0: Sij =Tij =Cij =  0.25 [SU(4)]; • regions of Sij<0 and Tij<0 both at V=0 and V=J in d1(2) models; • Cij<0 in low-spin (S=0) states; • different signs of Sijand Tij in d9 d9 GK rules violated in d1, d2 [AMO, P. Horsch, L.F. Feiner, G. Khaliullin, PRL 96, 147205 (2006)]

  15. Spin exchange constants Jij for increasing Hund’s exchangeη V=0 V=J d1 In the shadded areas Jij is negative FM Sij is negative AF for d1 and d2t2gmodels => GK rules are violated d2 In d9eg model spin correlations Sij follow the sign of Jij => GK rules are obeyed d9 [AMO, P. Horsch, L.F. Feiner, G. Khaliullin, PRL 96, 147205 (2006)]

  16. Dynamical exchange constants due to entanglement Fluctuations of Jijare measured by Fluctuations dominate the behavior of t2g systems at η=0, V=0: for a bond <ij> fluctuations: ( S=0 / T=1 )  ( S=1 / T=0 ) d1 model: [ SU(4) symmetry ] d2 model: Fluctuations large but do not dominate for eg system at η=0, V=0: d9 model: ,i.e.,

  17. Quantum corrections in spin-orbital models Large corrections beyond MF due to spin-orbital entanglement [AMO, P. Horsch, L.F. Feiner, G. Khaliullin, PRL 96, 147205 (2006)]

  18. when only Ising term: sharp transition S=0 S=4 Continuous orbital phase transition in d2 model with full t2gorbital dynamics: V=J continuous transition quantum numbers T and Tznonconserved orbital transitions are continuous T and Tz conserved

  19. Optical spectral weights for the C-AF phase of LaVO3 mean-field approach orbital and spin-orbital dynamics orbital disorder unlike in LaMnO3 Data: S. Miyasaka et al., [ JPSJ 71, 2086 (2002) ] spin-orbital fluctuations important at T>0! [G. Khaliullin, P. Horsch, and AMO, PRB 70, 195103 (2004)]

  20. spin triplet orbital singlet spin singlet orbital triplet [AMO, P. Horsch, L.F. Feiner, and G. Khaliullin, PRL 96, 147205 (2006)] 4.Joint spin-orbital fluctuations in LaVO3 magnetic and optical properties [G. Khaliullin, P. Horsch, and AMO, PRL 86, 3879 (2001); PRB 70, 195103 (2004)] Conclusions • Spins and orbitals disentangle in eg systems ( LaMnO3 ) • [AMO, G. Khaliullin, P.Horsch, and L.F. Feiner, PRB 72, 214431 (2005)] • 2. In systems with t2gdegrees of freedom • 3. Dynamic spin and orbital fluctuations in t2g systems: spins and orbitals are entangled static Goodenough-Kanamori rules are violated Any other experimental manifestations of entanglement?

  21. Thank you for your attention!

More Related