Unusual Symmetries in the Kugel-Khomskii Hamiltonian

Abstract

The Kugel-Khomskii Hamiltonian for cubic titanates describes spin and orbital superexchange interactions between $d^1$ ions having three-fold degenerate $t_{2g}$ orbitals. Since orbitals do not couple along "inactive" axes, perpendicular to the orbital planes, the total number of electrons in $|\alpha >$ orbitals in any such plane and the corresponding total spin are both conserved. A Mermin-Wagner construction shows that there is no long-range spin ordering at nonzero temperatures. Inclusion of spin-orbit coupling allows such ordering, but even then the excitation spectrum is gapless due to a continuous symmetry. Thus, the observed order and gap require more symmetry breaking terms.

4 pages (two column format with 2 figures), to appear in Phys. Rev. Lett. (submitted on Dec. 2002)

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• Orbital liquid in three dimensional Mott insulator: $LaTi{O}_3$
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• Anisotropic Spin Hamiltonians due to Spin-Orbit and Coulomb Exchange Interactions
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