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Unusual Symmetries in the Kugel-Khomskii Hamiltonian

A. B. Harris·Taner Yildirim·Amnon Aharony·Ora Entin-Wohlman·I. Ya. Korenblit
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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 $|α>$ 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.

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A. B. Harris, Taner Yildirim, Amnon Aharony, Ora Entin-Wohlman, I. Ya. Korenblit. 2003-03-12. Unusual Symmetries in the Kugel-Khomskii Hamiltonian. https://doi.org/10.1103/physrevlett.91.087206

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