Spectrum and damping of spin waves in a Heisenberg ferromagnet with single-ion anisotropy

The Vaks–Larkin–Pikin diagrammatic technique for spin operators is generalized to the case of a Heisenberg ferrodielectric with single-ion anisotropy. The energy spectrum of the crystalis analyzed qualitatively. Conditions are found under which the energy of certain collective excitations vanishes, and the damping becomes anomalously large. This singularity is due to an intersection of the energy sublevels of an isolated spin. It is shown that already in the first approximation the selfconsistent field method reveals new processes of inelastic interaction of magnons that are characteristic of anisotropic crystals alone.