Critical sound propagation in magnetic metals and bottleneck phenomena

A semiphenomenological model of sound propagation in a critical magnetic system is proposed, which takes into account a relaxation of energy between the system of localised spins and the conduction electron spins as well as the coupling of the longitudinal phonon to bilinear combination of spin fluctuations and to the energy densities. A general expression for the acoustic self-energy is obtained within the one-loop approximation. The effect of "bottlenecking" and its influence on the critical singularities in the sound characteristics is discussed.