Dilute anisotropic Heisenberg ferromagnet with biquadratic exchange interactions and single-ion anisotropy

Abstract

The effects of site dilution on the spin-1 anisotropic XXZ Heisenberg ferromagnet with bilinear- and biquadratic- exchange interactions, J and J′, and single-ion anisotropy, D, have been studied with the use of an improved two-site cluster effective field theory. The dependence of the critical temperature, T c, on the strength of J′, and/or D, has been calculated for some two- and three- dimensional dilute lattices. With variation of the exchange anisotropy ratio, γ, cross-over from anisotropic Ising to isotropic Heisenberg character is found in the behaviour of the T c versus α (=J′/J) curve. It is suggested that in the vicinity of the critical concentration, c 0, the value of γ required for the occurrence of this cross-over converges to a unified value, independent of the lattice structure. A spurious reentrant phenomenon appearing in the concentration dependence of T c is discussed in relation to the decoupling approximation adopted in the calculation.