The Phase Transition of Square Lattice Antiferromagnets at Finite Temperature

Abstract

The magnetic properties of the two-dimensional $J_1-J_2$ 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 Néel (collinear) state exists. When $J_2/J_1=1/2$, both the Néel and collinear states can exist and have the same Néel temperature. The calculated free energies show that there can occur a phase transition between the two states below the Néel 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.