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Lattice instability in frustrated systems

Lattice instability in frustrated systems . Maxim Mostovoy MPI, Stuttgart. D. Khomskii, Cologne. N . V. Prokof´ev , Amherst. J. Knoester , Groningen. R. Moessner , Paris. Groningen , April 22 , 2004. Outline. Geometrical f rustration Magnetoelastic transitions in

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Lattice instability in frustrated systems

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  1. Lattice instability in frustrated systems Maxim Mostovoy MPI, Stuttgart D. Khomskii, Cologne N.V. Prokof´ev, Amherst J. Knoester, Groningen R. Moessner, Paris Groningen, April22, 2004

  2. Outline • Geometrical frustration • Magnetoelastic transitions in frustrated spin systems • Orbital interactions • Frustration of orbital ordering and its lifting

  3. Geometrical frustration

  4. AFM Ising on triangular lattice Ground state entropy (Wannier, Houtappel, 1950) Spin correlations at T=0 (Stephenson, 1970)

  5. Ordered state

  6. Hard sphere liquid Alder & Wainwright (1957) Hoover & Ree (1968) Ssolid > Sliquid

  7. Kinks Kink energy Interactions between kinks in neighboring chains

  8. Kink crystal 1 kink / 3 sites M.M., N.Prokof’ev, D.Khomskii & J.Knoester, PRL 90 (2003)

  9. Frustrated spins coupled to lattice Strains:

  10. Free energy

  11. First order transition Free energy Frustration-induced transition Orderedstate Disorderedstate

  12. S = 3/2 Cr3+ ZnCr2O4 CW = -390K first order TN = 12.5K O. Tchernyshyov et al., PRL 88, 067203 (2001) S.-H. Lee et al., PRL 84, 3718 (2000)

  13. V3+ S = 1 Zn Mg Cd TN(K)40 45 35 Tst(K)50 65 97 AV2O4 H. Mamiya et al., J. Appl. Phys. 81, 5289 (1997) first order cubic to tetragonal c < a

  14. Interactions between t2g-orbitals

  15. Tetrahedron states

  16. Frustration and its lifting Jahn-Teller S.-H. Lee et al., cond-mat/0312558

  17. Orbital interactions • Jahn-Teller interaction • Coupled orbital & spin exchange (Kugel-Khomskii) • `Orbital Casimir´ effect • Peierls-like interaction

  18. eg-orbitals

  19. Jahn-Teller interaction

  20. Lattice-mediated interaction

  21. Kugel-Khomskii model (a) (b) (c) (d) (a): (b)+(c):

  22. M.M. & D. Khomskii, Phys.Rev.Lett 89, 227203 (2002), cond-mat 0304494 Orbital Casimir effect (Up,Ud = ) Holes Electrons

  23. 1800-exchange in 2D K2CuF41eg hole/Cu q q canted antiferroorbital ferromagnetic

  24. zx yz xy yz zz xy zx yy xx Frustrated orbital models 90o-exchange 180o-exchange triangular pyrochlore cubic LiNiO2 KCuF3 ZnMn2O4

  25. Mean field Cubic antiferro-orbital G-type Triangular, pyrochlore ferro-obital arbitrarysuperposition Disordered ground states

  26. Order from disorder Quantum orbital fluctuations chose six unform states: G.Khaliullin, PR B 64, 212405 (2001) M.M. & D.Khomskii,PRL 89, 227203 (2002)

  27. Strains

  28. Orbital-strain interaction Jahn-Teller coupling electron Peierls coupling Strain energy hole

  29. Ordered state layered canted antiferroorbital

  30. Ordered state KCuF3 holes electrons LaMnO3

  31. Conclusions • Frustration of spin and orbital ordering makes the crystal lattice instable • JT distortion occurs together with lattice distortion lifting the frustration of orbital ordering

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