Superexchange via cluster states: Calculations of spin-phonon coupling constants forCuGeO3

Abstract

Calculations for spin-phonon coupling constants in ${\mathrm{CuGeO}}_{3}$ are presented, applying fourth-order superexchange perturbation theory to an extended Hubbard model. In our treatment, the intermediate oxygen ligand states are described by bandlike cluster states, due to the presence of significant $\mathrm{O}(p)\ensuremath{-}\mathrm{O}(p)$ hopping. We also include the effect of the Ge ions on the O ligand states. We find a considerable q dependence of the spin-phonon coupling. For the $\ensuremath{\pi}$ modes involved in the spin-Peierls transition, our results of the coupling constants are in fair agreement with the work of Werner, Gros, and Braden. Yet some discrepancies remain, especially concerning the coupling to the vibrations, which modulate the O(2)-O(2)-Ge angle $\ensuremath{\delta}.$ Our studies of the pressure dependence of the magnetic coupling constants ${J}_{1}$ and ${J}_{2}$ suggest that relatively large nonlinear effects are present, even at small pressure values, probably due to the existence of a ``soft'' van-der-Waals--type bond direction in ${\mathrm{CuGeO}}_{3}.$