Phase Transitions in a Uniaxial Ferromagnet

The phase transitions occurring in a uniaxial ferromagnet are studied for all temperatures up to the Curie temperature. The stability limits are obtained in the molecular-field approximation, and the critical dynamic behavior is discussed for a simple model taking spin-lattice relaxation effects into account. For fields applied in the easy direction and temperatures below some characteristic temperature $T_1<T_C$, and for fields applied in the hard direction and all temperatures $T<\mathrm{}{T}_C$, the instability occurs with respect to angular deviations of the magnetization from its equilibrium direction, the associated soft mode is a ferromagnetic resonance (or perpendicular relaxation) mode, and one obtains critical fluctuations of magnetization direction. The same holds approximately true for fields applied at an arbitrary angle and temperatures $T<\mathrm{}{T}_1$. For fields applied in the easy direction and temperatures in the interval $T_1<T<\mathrm{}{T}_C$, the instability occurs with respect to deviations of magnetization magnitude, the associated soft mode is a parallel relaxation mode, and one obtains critical fluctuations of magnetization magnitude. The type of singularity of the static susceptibility and the behavior of the soft-mode frequencies at the stability limits are given for the different cases.