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 with the distance r ) and the y -axis nearest-neighbor interaction J̃ is studied for the two-dimensional spatially anisotropic Heisenberg ferromagnet within the frame of Onsager reaction field theory. For α = J̃/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 α = α_c(p) , where α_c(p) is a decreasing function of the long-range parameter p . For α = 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 Pr_0.5S_r0.5MnO_3 .