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The phase II -P-$ diagram of an easy-plane strongly anisotropic antiferromagnet is studied. It is shown that in such a system a realization of the phase with the nonmagnetic order parameter, the so-called quadruple phase, is possible. The realization of this phase is caused by several purely quantum effects, moreover the mechanism of its appearance differs in principle from that of the antiferromagnet or ferromagnet. The possibility of the disappearance of the angular phase (the so-called quadruple ferromagnetic phase) is also shown.

Elementary excitation spectra are investigated in a thin ferromagnetic film. The temperatures of stability of phase transitions “easy axis”–angular phase and “easy plane”–angular phase are obtained. It is shown that the reasons behind the formation of the angular phase is the presence of magnetoelastic interaction. The Curie temperature of the system under investigation is determined.

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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.