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 Neel (collinear) state exists. When J(2)/J(1) = 1/2, both the Neel and collinear states can exist and have the same Neel temperature. The calculated free energies show that there can occur a phase transition between the two states below the Neel 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.