Phase diagram of uniaxial antiferromagnetic particles: Field perpendicular to the easy axis

We consider a spherical uniaxial antiferromagnetic particle in the presence of an external magnetic field perpendicular to its easy axis. The model is described by a classical Heisenberg Hamiltonian including a single-ion uniaxial anisotropy, where the magnetic moments of the particle are represented by continuous spin vectors. We employ mean-field calculations and Monte Carlo simulations to determine the phase diagram of the system. The phase diagram in the plane field versus temperature is obtained for particles with radii ranging from three up to twelve spacing lattice units. We have seen that a particle with more than nine shells behaves as a true thermodynamic system. We find the explicit dependence of the zero temperature critical field and the Néel temperature on the diameter of the particle. At low temperatures, we have also shown that, for particles with three or more shells, the critical field follows a T² law, which is in agreement with the predictions of the spin-wave theory, when the field is perpendicular to the easy axis.