Finite-temperature ordering in two-dimensional magnets

Abstract

We study the two-dimensional quantum Heisenberg antiferromagnet on the square lattice with easy-axis exchange anisotropy. By the semiclassical method called pure-quantum self-consistent harmonic approximation we analyze several thermodynamic quantities and investigate the existence of a finite temperature transition, possibly describing the low-temperature critical behavior experimentally observed in many layered real compounds. We find that an Ising-like transition characterizes the model even when the anisotropy is of the order of ${10}^{\ensuremath{-}2}J$ $(J$ being the intralayer exchange integral), as in most experimental situations. On the other hand, typical features of the isotropic Heisenberg model are observed for both values of anisotropy considered, one in the quasi-isotropic limit and the other in a more markedly easy-axis region. The good agreement found between our theoretical results and the experimental data relative to the real compound ${\mathrm{Rb}}_{2}{\mathrm{MnF}}_{4}$ shows that the insertion of the easy-axis exchange anisotropy, with quantum effects properly taken into account, provides a quantitative description and explanation of the experimental data, thus allowing us to recognize in such anisotropy the main agent for the observed onset of finite temperature long-range order.