Impact of Structure on Magnetic Coupling in CaV4O9

Abstract

The strong corrugation of the ${\mathrm{V}}_4$ ${\mathrm{O}}_5$ layer in the spin gap system Ca${\mathrm{V}}_4$ ${\mathrm{O}}_9$ is examined for its impact on the exchange coupling constants between the spin- $\frac{1}{2}$ V ions. Local spin density calculations show that the V spin occupies a $d_{x^2{-y}^2}$ orbital ( $\hat{x}$ and $\hat{y}$ are the V-V directions) that would have vanishing second order exchange coupling if the ${\mathrm{V}}_4$ ${\mathrm{O}}_5$ layer were flat. The Kanamori-Goodenough superexchange rules, and the small calculated energy difference of ferromagnetic and antiferromagnetic alignments of spins for the real structure, indicate that second neighbor couplings dominate over nearest neighbor. This suggests two coupled $S=\frac{1}{2}$ metaplaquette systems, each tending toward singlet formation.