College Park, Maryland June 6 - 10 , 2004
T1-C1 (8:30 AM): Unusual Symmetry of the Kugel-Khomskii Hamiltonian for Orbitons (Invited)
A. B. Harris (University of Pennsylvania / Philadelphia PA 19104)
The Kugel-Khomskii Hamiltonian, HKK, has been used for about three decades to describe spin and orbital dynamics of cubic transition metal (TM) ions having a single electron in the three-fold degenerate t2g crystal field levels (α=X, Y, Z). (An X orbital is a dyz wavefunction, Y=dxz, etc.) In this idealized model the electron hopping matrix element t(αi,αj) between nearest neighboring TM ions on a simple cubic lattice is nonzero only for αi=αj and only if αi=αj is not the same as the axis separating the two ions. KK showed that their model gives rise to a Heisenberg-like spin Hamiltonian with exchange integrals of order t2/U, where U is the on-site Coulomb energy. Because electrons in, say, an X orbital cannot hop along the X axis, it is clear that the total number of electrons in X orbitals in any given plane perpendicular to the X axis is a good quantum number. We (ABH, T. Yildirim, A. Aharony, O. Entin-Wohlman, and I. Korenblit) have shown in Phys. Rev. B69, 035107 (2004) that HKK is invariant with respect to a global rotation of the spin of electrons in, say, X orbitals when summed over all ions in a single plane perpendicular to the X axis. We will give a qualitative discussion of this and other symmetries and show how they appear within numerical and mean field calculations.
The most striking consequence of these symmetries is that the spin correlations are two dimensional and long range spin order can not occur at any nonzero temperature. Since this result is in obvious disagreement with experimental results on systems such as lanthanum titanate, we conclude that the KK Hamiltonian can not be a 'minimum' model to describe such real systems. Stated differently, the KK Hamiltonian, unlike the Heisenberg Hamiltonian for conventional magnetic materials, does not give a zeroth order description of real materials.
Accordingly, it is essential, from the outset, to include the relevant perturbations that destroy these unusual symmetries, if one is to understand real materials. Alternatively, although it is probably impossible to find a real material with these exact symmetries, it may be possible to construct systems which are nearly ideal and whose anomalous properties would be a consequence of closely approximating the unusual symmetries described here.
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