Anisotropic easy axis S=1 antiferromagnetic Heisenberg model with competitive interaction on a square lattice

•The staggered magnetization as a function of the frustration is calculated for the Nèel and Collinear phases.•The phase diagrams at zero temperature are presented.•A disordered phase dependent on the values of the anisotropy parameters was found.

Using a modified spin wave theory, we study the two-dimensional spin S=1 Heisenberg antiferromagnet with both spin and spatial anisotropies and competitive next-nearest neighbor interaction J2, at zero temperature. The magnetization as a function of J2 shows the existence of three different phases namely, ordered Néel, disordered and ordered collinear phases. The existence of the disordered phase depends on the values of the anisotropy parameters. The model shows a very rich phase diagram.