Spin Gap of Two-Dimensional Antiferromagnet Representing CaV4O9

We examined a two-dimensional Heisenberg model with two kinds of exchange energies, Jₑ and Jc. This model describes localized spins at vanadium ions in a layer of CaV₄O₉, 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 Jₑ 610 K and Jc 150 K. By the numerical diagonalization we estimated the spin gap as Δ ~ 0.2Jₑ 120 K, which consists with the experimental value 107 K. Frustration by finite Jc enhances the spin gap.