Phase behaviour of the antiferromagnetic plane rotator model

The phase diagram of an ultrathin film of magnetic rotors confined to the plane of the film has been determined from Monte Carlo simulations. In this square lattice system, the classical spins interact through a nearest neighbour antiferromagnetic exchange and the dipolar interactions. The phase diagram shows a dipolar antiferromagnetic phase for low values of |J|/g, and a simple antiferromagnetic phase for large values of |J|/g. The Monte Carlo data also indicate that the dipolar phase separates into two distinct phases for different values of |J|/g. In the first phase the spins are aligned along the x-or y-axis, while in the second phase the sublattice magnetization is oriented at π/4 to the x-and y-axis. The results for the plane rotator model are compared with previous results obtained for the Heisenberg model, which showed an analogous phase behaviour. This comparison clarifies the role played by out-of-plane degree of freedom and provides some further insight into this intriguing transition.