Heisenberg antiferromagnet on the square lattice forS>~1

Abstract

Theoretical predictions of a semiclassical method---the pure-quantum self-consistent harmonic approximation---for the correlation length and staggered susceptibility of the two-dimensional quantum Heisenberg antiferromagnet (2DQHAF) on the square lattice agree very well with recent quantum Monte Carlo data for $S=1,$ as well as with experimental data for the $S=5/2$ compounds ${\mathrm{Rb}}_{2}{\mathrm{MnF}}_{4}$ and ${\mathrm{KFeF}}_{4}.$ The theory is parameter free and can be used to estimate the exchange coupling: for ${\mathrm{KFeF}}_{4}$ we find $J=2.33\ifmmode\pm\else\textpm\fi{}0.33$ meV, consistent with previously determined values. On this basis, the adequacy of the quantum nonlinear $\ensuremath{\sigma}$ model approach in describing the 2DQHAF when $S>~1$ is discussed.