Mixed Ising ferrimagnets with next-nearest-neighbour couplings on square lattices

We study Ising ferrimagnets on square lattices with antiferromagnetic exchange couplings between spins of values S = 1/2 and 1 on neighbouring sites, couplings between S = 1 spins at next-nearest-neighbour sites of the lattice and a single-site anisotropy term for the S = 1 spins. Using mainly ground state considerations and extensive Monte Carlo simulations, we investigate various aspects of the phase diagram, including compensation points, critical properties and temperature-dependent anomalies. In contrast to previous belief, the next-nearest-neighbour couplings, when being of antiferromagnetic type, may lead to compensation points.