Spin reorientation and magnon-phonon hybridization in a ferromagnet

A model is presented for the magnetic excitations and magnon-phonon coupling in a localised moment ferromagnet in which spins can reorientate by application of a magnetic field. The model is suitable for those materials which possess a spin wave gap at zero wave vector and therefore the magnon and acoustic phonon branches can intersect. A magnon-phonon coupling linear in both spin and phonon operators is employed which has proved successful for the ferrous salts. The main effect of the applied field is to modify the spin wave gap, and to introduce a critical value for the coupling constant which enables the system to remain stable as the gap goes to zero. Furthermore the wave vector of the anticrossing point decreases as the spin wave gap increases and therefore the value of the sound velocity determined by high resolution inelastic neutron experiments is dependent on the gap.