Lattice instability in frustrated systems Maxim Mostovoy MPI, Stuttgart Groningen, April 22, 2004 D. Khomskii, Cologne J. Knoester, Groningen R. Moessner,

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Presentation transcript:

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

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

Geometrical frustration

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

Ordered state

Hard sphere liquid Alder & Wainwright (1957) Hoover & Ree (1968) S solid > S liquid

Kinks Kink energy Interactions between kinks in neighboring chains

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

Frustrated spins coupled to lattice Strains:

Free energy

Frustration-induced transition Free energy First order transition Ordered state Disordered state

Cr 3+ S = 3/2  CW = -390K T N = 12.5K first order ZnCr 2 O 4 S.-H. Lee et al., PRL 84, 3718 (2000) O. Tchernyshyov et al., PRL 88, (2001)

AV 2 O 4 V 3+ S = 1 first order cubic to tetragonal c < a T N (K) T st (K) Zn Mg Cd H. Mamiya et al., J. Appl. Phys. 81, 5289 (1997)

Interactions between t 2g -orbitals

Tetrahedron states

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

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

e g -orbitals

Jahn-Teller interaction

Lattice-mediated interaction

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

Orbital Casimir effect (U p,U d =  ) HolesElectrons M.M. & D. Khomskii, Phys.Rev.Lett 89, (2002), cond-mat

exchange in 2D K 2 CuF 4 1e g hole/Cu  canted antiferroorbital ferromagnetic

Frustrated orbital models xy yz zx xy yzzx triangular cubic pyrochlore 180 o -exchange 90 o -exchange LiNiO 2 ZnMn 2 O 4 xx yy zz KCuF 3

Mean field Triangular, pyrochlore ferro-obital Cubic antiferro-orbital G-type Disordered ground states arbitrary superposition

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

Strains

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

Ordered state layered canted antiferroorbital

Ordered state electrons holes LaMnO 3 KCuF 3

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