Phase diagram of the J_{1}-J_{2} frustrated anisotropic antiferromagnet with spin S=1 on the quadratic lattice.

Abstract

In the paper the phase diagram of J_{1}-J_{2} frustrated antiferromagnet with spin S=1 and single-ion anisotropy is studied on the planar quadratic lattice in the cluster approximation. The Bogolyubov inequality is adopted for the Gibbs energy calculation for the case of 2×2 and 4×4 clusters. On this basis, the ranges of existence of the antiferromagnetic, superantiferromagnetic, and paramagnetic phases are investigated for the antiferromagnetic nearest-neighbor (J_{1}<0) and next-nearest-neighbor (J_{2}<0) interactions. In particular, the occurrence of tricritical and triple points is discussed and a comparison between the results for 2×2 and 4×4 clusters is made. The results are also compared with the classical MFA method, adopted here for the model in question, as well as with selected literature results for particular choices of interaction parameters.