ABSTRACT
The dispersion relation for spin waves was obtained at first by Bloch on the microscopic model. This relation was generalized by Holstein and Primakoff. On the macroscopic, continuum model, the spin-wave dispersion law can be derived by two, quite equivalent, methods. The physical reason for introducing the supplementary boundary conditions is that the fields, acting on magnetic moments in a thin layer near the boundary, differ essentially from the fields inside the sample. In the analysis of propagating spin waves in films a difficulty arises similar to one for standing spin waves in tangentially magnetized films: partial solutions, taken separately, cannot satisfy all boundary conditions. For damped free oscillations, the numbers of magnons decrease, approaching the equilibrium (thermal) values, due to the collisions with magnons and other quasiparticles. For stationary (forced) oscillations and waves, the constancy of magnon numbers is maintained by the processes of their creation, e.g., due to the annihilation of electromagnetic-field photons.
