Anisotropy effects on the magnetic excitations of a ferromagnetic monolayer below and above the Curie temperature

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The field-driven reorientation transition of an anisotropic ferromagnetic monolayer is studied within the context of a finite-temperature Green's function theory. The equilibrium state and the field dependence of the magnon energy gap E₀ are calculated for static magnetic field H applied in plane along an easy or a hard axis. In the latter case, the in-plane reorientation of the magnetization is shown to be continuous at T=0, in agreement with free spin wave theory, and discontinuous at finite temperature T>0, in contrast with the prediction of mean field theory. The discontinuity in the orientation angle creates a jump in the magnon energy gap, and it is the reason why, for T>0, the energy does not go to zero at the reorientation field. Above the Curie temperature TC, the magnon energy gap E₀(H) vanishes for H=0 both in the easy and in the hard case. As H is increased, the gap is found to increase almost linearly with H, but with different slopes depending on the field orientation. In particular, the slope is smaller when H is along the hard axis. Such a magnetic anisotropy of the spin-wave energies is shown to persist well above TC (T ≈ 1.2 TC).