Phase transition of square-lattice antiferromagnets at finite temperature

Abstract

The magnetic properties of the two-dimensional ${J}_{1}\ensuremath{-}{J}_{2}$ model with both exchanges ${J}_{1}$ and ${J}_{2}$ being antiferromagnetic and a single-ion anisotropy at nonzero temperature are investigated. As ${J}_{2}/{J}_{1}<1/2$ ($>1/2$), only the N\'eel (collinear) state exists. When ${J}_{2}/{J}_{1}=1/2$, both the N\'eel and collinear states can exist and have the same N\'eel temperature. The calculated free energies show that there can occur a phase transition between the two states below the N\'eel point when the single-ion anisotropy is strong enough. It is a first-order transition at nonzero temperature. It is possible that the doping in real materials can modify the ratio of ${J}_{2}/{J}_{1}$ to reach $1/2$ so as to implement the phase transition.