Abstract
The Kugel-Khomskii Hamiltonian for cubic titanates describes spin and orbital superexchange interactions between ions having threefold degenerate orbitals. Since orbitals do not couple along “inactive” axes, perpendicular to the orbital planes, the total number of electrons in 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.
- Received 24 December 2002
DOI:https://doi.org/10.1103/PhysRevLett.91.087206
©2003 American Physical Society