Influence of a One-Ion Anisotropy on Stabilization of the Long-Range Magnetic Order in Two-Dimensional Ferromagnet

In the paper the possibility of stabilization of the long-range magnetic order in a two-dimensional ferromagnetic with one-ion easy-plane anisotropy is explored. It is shown that at the presence of a small anisotropy in a two-dimensional ferromagnetic the long-range magnetic order is stabilized by magnetoelastic interaction. If one-ion anisotropy is comparable or even exceeds the exchange interaction in the system there exists a long-range non-vectorial quadrupolar tensorial magnetic order.