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Investigating spin/orbital /lattice interplay: the case of Ca-based ruthenates

Investigating spin/orbital /lattice interplay: the case of Ca-based ruthenates. Mario Cuoco Fiona Forte Canio Noce. Dipartimento di Fisica “E.R. Caianiello” Università di Salerno Baronissi (SA)-Ital y. Laboratorio Regionale SuperMat CNR-INFM Baronissi (SA)-Ital y. Outline.

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Investigating spin/orbital /lattice interplay: the case of Ca-based ruthenates

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  1. Investigating spin/orbital /lattice interplay: the case of Ca-based ruthenates Mario Cuoco Fiona Forte Canio Noce Dipartimento di Fisica “E.R. Caianiello” Università di Salerno Baronissi (SA)-Ital y Laboratorio Regionale SuperMat CNR-INFM Baronissi (SA)-Ital y

  2. Outline • Introduction to t2g systems • Layered ruthenates: evidences for complex spin/orbital /lattice physics • Relevant microscopic ingredients • Numerical analysis on finite size clusters • Interplay of local correlation and structural distortions in magnetic phase control: elongation, flattening, rotation and tilting of octahedra • Conclusions

  3. Four t2g electrons Cubic CF splitting Tetragonal compressive CF splitting Orthorombic CF splitting ORBITAL DEGREE OF FREEDOM ACTIVE!

  4. Tc vs doping • AF insulator for [0<x<0.2]at T=0; • M–NM transition by T • Magnetic-metallic(M-M) [0.2<x<0.5] • PM metal for [0.5<x<2] • Critical FM enhancementfor x=0.5 • Superconductivity for x=2 Nakatsuji et al PRL 84, 2666 (2000); Nakatsuji et al PRB 62, 6458 (2000); Mizokawa et al PRB 69, 132410 (2004)

  5. Tc vs pressure Ca2RuO4 • Mott insulator transition induced by T or P • FM metallic (FM-M) at low T and slightly high P Nakamura et al PRB 65, 220402 (R) (2002); Snow et al PRL 89, 226401 (2002); Steffens et al PRB 72, 094104 (2005)

  6. Distorsion of the RuO6 octahedron • O(1) planar oxygen • O(2) apical oxygen • F rotation angle || c • Q tilting angle

  7. Structural parameters vs doping Insulating short Ru-O(2) bond Metallic long Ru-O(2) bond Insulating long Ru-O(1) bond Metallic short Ru-O(1) bond Friedt et al PRB 63, 174432 (2001)

  8. Sr content x Tc vs lattice distorsions Friedt et al PRB 63, 174432 (2001)

  9. Structural parameters vs pressure Steffens et al PRB 72, 094104 (2005)

  10. Spin-Orbital-Lattice interplay in Ca2RuO4 • 4 electrons or 2 holes in t2g • Orbital hole distribution not integer • AF insulator for T<113K • PM insulator 113K <T< 360K • Mott metal-insulator transition at 360K • Flattening of the octahedra at TMI • Elongated to compressed at TMI RXS at Ru K edge F-orbital order at TFO =350K RXS at Ru LII and LIII edges  AF-orbital order at TAFO =260K Jung et al PRL 91, 056403 (2003); Zegkinoglou et al PRL 95, 136401 (2005), Kubota et al PRL 95, 026401 (2005)

  11. Orbital physics in Ca2RuO4 • Orbital Order is reported to cause MIT transition • Ground state ordering in Ca2RuO4: competing ferro-orbital vs antiferro-orbital correlations • Emerging ferromagnetic correlations due to iso-electronic substitution and pressure effects: spin/orbital charge control via tuning of c-axis octahedral distortions • Crucial role of orbital degree of freedom due to strong coupling with spin, charge, and lattice via spin-orbit, and the Coulomb interactions.

  12. Motivation • Complex phenomenology: superconductivity, MIT, magnetic and orbital orderings, unconventional quantum liquids…. • Crucial role played by the partially filled t2g orbitals (orbital dynamics) and by the interaction among orbital , spin, charge and lattice degrees of freedom via spin–orbit, or other mechanisms • Possibility to tune from outside the quantum environment by means of some external control parameters variations (T, P, x) • High degree of difficulty due to the intrinsic quantum nature of the interactions between many degrees of freedom

  13. Issues to be investigated • What about the ground state in Ca2RuO4 • Charge fluctuations, arising from c-axis octahedral flattening vs Coulomb interactions, calculation of spin-orbital patterns • Ferromagnetism out of orbital frustration due to t2g connectivity and low dimensionality: a simple view through the spin-orbital model in the strong coupling limit • GS of Ca2RuO4 exhibits an AFO/FO due to the interplay between c-axis octahedral flattening, Coulomb interaction and spin-orbit coupling

  14. Ru site Microscopic description Coulomb interactions, c-axis octahedral distortions, and spin-orbit coupling: extracting spin/orbital patterns

  15. dxy Orbital connectivity • Only p bonds with the oxygens • Effective model: direct hopping among Ru t2gorbitals. • Due to the symmetry, hopping amplitude is non vanishing only between homologous orbitals (with no large tilting and rotation distortions).

  16. U J’ U’+ JH U’- JH Local Coulomb correlations Here we assume that: U’=U-2 JH JH=J’; U’>JH

  17. Crystal fieldvs orbital degeneracy dxy  dgz Tetragonal elongated dgz - =0 dxy Cubic symmetry Tetragonal compressed

  18. z x y Spin-orbit coupling: complex orbitals Lz  L and S are directed along z The same applies for x and y directions.

  19. dxz b) c) a) dyz dxy G-AF(1) C-AF(1/2) d) e) G-AF(0) G-AF(3/4) Possible configurations: AF-like

  20. f) g) F2(1/4) F3(1/4) h) i) F3(0) F(1/4) Possible configurations: F-like

  21. Competing charge fluctuations:crystal field vs Coulomb correlations • Flattening: AF with FO or AFO • Elongated: FM or AF with AFO or OD Cuoco et al PRB 74, 195124 (2006)

  22. Spin-orbital model in strong coupling limit For the generic bond <i,j>|| doublon occupation |a |b |c Pauli matrices Horsch et al PRL 91, 257203 (2003); PRL 86, 3879 (2001); Khaliullin et al PRL 91, 257203 (2003);

  23. |a |b |c Mean-Field: spin/orbital model Hs/o F(1/4) C-AF(1/2) F2(1/4) G-AF(1) G-AF(0) Cuoco et al PRB 74, 195124 (2006)

  24. Ferro- and antiferro-orbital patterns • Thermal activation • Spin-orbit coupling

  25. Thermal evolution of correlations Temperature drives the system towards a disordered magnetic phase with enhanced FO correlations. Forte PhD Thesis (2008); Cuoco et al in “Quantum Magnetism” (2008)

  26. doublon occupation |a |b |c Interplay between spin-orbit coupling and compresssive distorsions Spin orbit coupling effective on the AFO G-AF/FO C-AF/AFO G-AF/(AFO/FO) XAShole distribution nxy=0.5 Cuoco et al PRB 73, 094428 (2006) Mizokawa et al ,Phys. Rev. Lett.87, 077202 (2001)

  27. Summary and conclusions • Spin/orbital /charge correlations are intimately coupled: density distribution is strongly related to magnetic and orbital patterns. • Interplay between octahedron deformations, Coulomb interactions and L-Scoupling generates, even for a few sites problem, a variety of complex configurations. • We explored the competition between OO and OD patterns, correlated to AF and F configurations, in different regions of the microscopic parameters. • CF is able to separate ferro- and antiferro-type magnetic/orbital patterns, depending on the character of structural distortions. Occurrence of AF in the flat case. • L-S and CF realize an interesting interplay between the spin/orbital pattern and the character of the deformation: FO in the flatten case.

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