Onsager Reaction Field Theory for Two-Dimensional Spatially Anisotropic Heisenberg Ferromagnet with the x-Axis Long-Range Interaction

The competition between the x-axis long-range interaction (which decays as J/r (p )tion is studied for the two-dimensional spatially anisotropic Heisenberg ferromagnet within the frame of Onsager reaction field theory. For alpha=J/J>0, there exists the phase transition at finite temperatures in the region 1<p<3; No finite-temperature transitions exist for p >= 3. It is found that the interplay between spatially anisotropic interactions has an influence on the thermodynamic quantities (such as spin susceptibility, correlation functions and correlation length) of the system. The crossover from effective one- to two-dimensional behavior is found at alpha=alpha(c)(p), where alpha(c)(p)is a decreasing function of the long-range parameter P. For alpha=0.2 and p=1.655, and taking j=57.7K, the critical temperature and susceptibility obtained by Onsager reaction field theory are in agreement with the results from the experimental studies of the perovskites Pr0.5Sr0.5MnO3.