The two-dimensional Heisenberg ferromagnet with various types of interactions: temperature dependence of magnetic parameters

The temperature dependences of the anisotropy constant, spin-wave stiffness and spontaneous magnetizations for the two-dimensional (2D) Heisenberg model with various types of anisotropy and interactions have been calculated with the use of the low-temperature perturbation (spin-wave) theory. The authors argue that this theory is effective within a large portion (if not the main part) of the ferromagnetic phase. On the contrary, the Polyakov renormalization procedure is found to be inapplicable for the ferromagnetic phase at any anisotropy. They consider both the easy-axis and the easy-plane cases, taking into account one-site and exchange anisotropy as well as the higher-order magnetic anisotropy and the dipole-dipole interaction. For realistic models the latter is found not to change essentially the temperature dependence of the magnetic parameters. In particular, they did not find the reorientation (easy-axis to easy-plane) phase transition due to dipole-dipole interaction predicted by Pescia and Pokrovsky (1990). However, in general, the temperature dependence of the anisotropy constant proves to be much more sensitive to the type of the anisotropy and interactions than that of the spin stiffness and the spontaneous magnetization. In the easy-plane case the difference between the spin-wave stiffness for the in-plane and the normal polarizations is found to be extremely strongly temperature-dependent. At temperatures comparable with T C this difference may be of the order of magnitude of the stiffness itself, while at T=0 it is of relativistic origin. For the case of a very small anisotropy the authors also propose a renormalization procedure to perform a partial summation of the perturbation series.