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

TL;DR

This study models the spin gap in CaV$_4$O$_9$ using a two-dimensional Heisenberg model, estimating exchange energies and the spin gap, aligning well with experimental data.

Contribution

It introduces a detailed Heisenberg model for CaV$_4$O$_9$ and accurately estimates exchange energies and the spin gap, confirming experimental observations.

Findings

Estimated exchange energies: $J_e \,\approx\, 610$ K, $J_c \,\approx\, 150$ K.

Calculated spin gap: approximately 120 K, close to experimental 107 K.

Frustration from finite $J_c$ enhances the spin gap.

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.