Spin Gap of Two-Dimensional Antiferromagnet Representing CaV${}_4$O${}_9$

Abstract

We examined a two-dimensional Heisenberg model with two kinds of exchange energies, $J_e$ and $J_c$. This model describes localized spins at vanadium ions in a layer of CaV${}_4$O${}_9$, for which a spin gap is found by a recent experiment. Comparing the high temperature expansion of the magnetic susceptibility to experimental data, we determined the exchange energies as $J_e\simeq$ 610 K and $J_c\simeq$ 150 K. By the numerical diagonalization we estimated the spin gap as $\Delta \sim 0.2J_e\simeq$ 120 K, which consists with the experimental value 107 K. Frustration by finite $J_c$ enhances the spin gap.

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