The magnetic properties of a quasi-two-dimensional spin 1 easy axis Heisenberg antiferromagnet with competing interactions

•The phase diagrams in zero temperature.•The critical temperature was studied as a function of frustration and D.•The sublattice magnetizations and the gap were studied.

The Neel and collinear ordered phases of the two-dimensional S=1 antiferromagnet with next and next near neighbor exchange interactions and easy axis single ion anisotropy, on the square lattice, are studied at low temperature using a Modified Spin Wave Theory. We calculate the low-temperature quantities as a function of the temperature, frustration and anisotropy. We calculate also the phase diagram at T=0. We found a disordered phase separating the Neel and collinear phases.