The Phase Transition of Square Lattice Antiferromagnets at Finite Temperature

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 N\'{e}el (collinear) state exists. When $J_{2}/J_{1}=1/2$, both the N\'{e}el and collinear states can exist and have the same N\'{e}el temperature. The calculated free energies show that there can occur a phase transition between the two states below the N\'{e}el 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.