On coherent states and the Self-Consistent Harmonic Approximation

We used the Self-Consistent Harmonic Approximation (SCHA) to study the thermodynamics of the precession magnetization in a two-dimensional isotropic ferromagnet. The SCHA treats the Hamiltonian in terms of the canonically conjugate operators Sz and φ (the azimuth angle) including renormalized temperature dependent parameters to take into account higher order interactions. It is well-known that in right conditions, a dynamic magnetic field is able to provide spin pumping and drives the system to a magnon Bose-Einstein condensation. The magnon condensate is a coherent state that presents minimal uncertainty for the Sz and φ operators. Consequently, 〈Sz〉 and 〈φ〉 should constitute natural fields to describe the model, which justifies the SCHA formalism. The results obtained are consistent with other theoretical and experimental works.