Spin-Spin Interactions and Two-Dimensional Ferromagnetism

Abstract

It is widely known that a two dimensional lattice of spins coupled by Heisenberg (positive) exchange interactions has no long-range ferromagnetic order [1]. >From the point of view of the excitations, the quadratic dependence of the spin-wave frequency on the wave vector results in a divergence of the number of excited spin waves at any finite temperature T, thus precluding any long-range magnetization. Because the divergence is only logarithmic in the spin wave energy, it has been possible and customary to obtain a finite magnetization by introducing various cut-offs such as an anisotropy field or a finite sample size. The role of the spin-spin interactions, which are present in every magnetic material, does not seem to have been investigated even though they are anisotropic and might, as a consequence, remove the divergence of the spin deviation at finite T.