Unusual Symmetries in the Kugel-Khomskii Hamiltonian

Details Unusual Symmetries in the Kugel-Khomskii Hamiltonian Unusual Symmetries in the Kugel-Khomskii Hamiltonian

2003-03-12

arxiv.org/abs/cond-mat/0303219v1

Physics

Condensed Matter

Strongly Correlated Electrons

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

Scientific paper

10.1103/PhysRevLett.91.087206

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.

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