Influence of cubic anisotropy on the ground state and thermodynamic properties of Heisenberg magnets

The quantum description of Heisenberg cubic ferromagnets with single-ion anisotropy is considered. The spin operators are represented in terms of the Hubbard operators, and this makes it possible to take into account exactly the effects of single-ion anisotropy of arbitrary symmetry, and also an arbitrary orientation of the external magnetic field. In conjunction with solution of the single-ion problem, this makes it possible to investigate the influence of anisotropy on the magnetization of a cubic ferromagnet in the ground state and the spectrum of single-ion energies. It is shown that for a cubic ferromagnet with $S=2$ there is a change in the kind of phase transition, from the second to the first, at $K/I_0=1.912$, and for $K>4I_0$ the ferromagnetic ordering disappears. The Curie temperature of cubic ferromagnets with $S=2,\ 5/2,\ 3,\ 7/2$ is studied as a function of the anisotropy.