Quantum effects of magnetization of an easy-axis ferromagnet with $S=1$

We analyze the influence of quantum effects on magnetic properties of a strongly anisotropic easy-axis ferromagnet with single-ion anisotropy comparable to the exchange interaction of spins with $S=1$. We show that in this case, despite the quantum approach, we can apply a description inspired by the Landau theory of phase transitions. We consider two magnetization cases: by a longitudinal and by a transverse external magnetic field. We determine the critical values of the fields and find quantum corrections manifested in the so-called “shortening” of the mean spin modulus. We find that for a sufficiently large single-ion anisotropy, the angular dependence of the critical field differs from the Stoner–Wohlfarth astroid.