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GNSF: 06-81-4-100 KITP: PHY05-51164

Classical Dimers in Orbitally Degenerate Honeycomb Antiferromagnet. George Jackeli. Max-Planck Institute for Solid State Research, Stuttgart. In collaboration with: Daniel Khomskii Univ. of Cologne . Phys. Rev. Lett. 08. Krakow, 18-22 June 2008. GNSF: 06-81-4-100 KITP: PHY05-51164.

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GNSF: 06-81-4-100 KITP: PHY05-51164

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  1. Classical Dimers in Orbitally Degenerate Honeycomb Antiferromagnet George Jackeli Max-Planck Institute for Solid State Research, Stuttgart In collaboration with: Daniel Khomskii Univ. of Cologne Phys. Rev. Lett. 08 Krakow, 18-22 June 2008 GNSF: 06-81-4-100 KITP: PHY05-51164

  2. Honeycomb compound:Li2RuO3 Miura et. al., JPSJ’07

  3. Honeycomb compound:Li2RuO3 Miura et. al., JPSJ’07

  4. Honeycomb compound:Li2RuO3 directional hopping XY XZ YZ Ru4+ (d4), S=1 & 3-fold orbital

  5. FM coupling ~ AFM coupling ~ Coupled spin-orbital model Orbital degrees are static Pott’s-like! Exchange couplings:

  6. Example of an orbital and spin-coupling pattern Weak FM ~h<<1 Strong AFM ~1 Free

  7. Limit of zero Hund’s coupling Dimensionality reduction due to orbitals: Factorization in clusters of open/closed 1D AFM chains All Neel type states (SiSj+S2=0) have zero classical energy Shortest chains(=dimers) are favorable since they gain more quantum energy

  8. Spins are bound into spin-singlet on dimer bonds: Spin gaped phase = The ground state manifold Ground state manifold is spanned by hard-core dimer coverings Extensive orientational degeneracy infinitely many ways of covering

  9. By Weak Interdimer Coupling Order-out-of-disorder by Triplet Fluctuations By Magnetoelastic Coupling “dimer Jahn-Teller” mechanism Lifting the orientational degeneracy of dimers Possible Mechanisms:

  10. Interdimer coupling (~h) creates virtual triplet fluctuations (TFS) S=1 tx,y,z Different zero point energy of triplets may lift degeneracy D s S=0 hw2 hw1 2 2 Order-out-of-disorder by triplet fluctuations Fluctuations disfavor hexagonal loops, but do not fully lift the degeneracy

  11. Shortening of the strong bond =Gain of magnetic energy Different distortion pattern Costs different elastic energy Selection of ground state Degeneracy breaking by magnetoelastic coupling Elastic energy Magnetoelastic coupling

  12. Ru- displacements due to the contraction of spin-singlet bonds Li- displacements induced by contractedRu-Rubond Li Ru Unfavorable orientation of neighboring dimers destructive interference of the distortions “Dimer Jahn-Teller” mechanism

  13. Dimerized pattern and orbital order

  14. Exact realization of classical dimer problem Degeneracy lifting by “dimer Jahn-Teller” effect Formation of a peculiar VBC Summary Orbital induced dimensionality reduction Spin gap formation and spontaneous dimerization in D>1

  15. S=1/2 (d1, d5)Triangular, Kagome, Honeycomb, Pyrochlore Square (elongated octahedra) S=1 (d2, d4) Honeycomb Summary t2g-systems with dimer ground states (Theory)

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