Critical Sound Propagation in Magnetic Metals and Bottleneck Phenomena

Abstract

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.PACS numbers: 05.70.Jk, 62.65.+kThere are many different regimes in the critical sound attenuation in magnets, depending on sound frequency, reduced temperature and some relevant relaxation frequencies [1,2]. In this paper we study an Ising-like, local spin system coupled to the longitudinal sound mode and three kinds of energy densities. In analysis of metal systems, we should take into consideration the relaxation between the three components of the system -the localised spins, conduction electrons, and the lattice. As we shall see, in some circumstances a ratio of the relaxation rates may be such as to modify the phonon self-energy and a kind of bottleneck effect can appear.We consider a one-component spin (order parameter) S(x) coupled to the local strain e αβ(x) and three energy densities: the spin energy eS(x), lattice energy eL(x) and the spin energy of the conduction electrons ec(x). The interactions are described by the functional where the first three terms in this Hamiltonian compose the Ginzburg-Landau functional for the order parameter. The energy field eL(x) is related to all vibrations of lattice atoms excluding sound. Elastic degrees of freedom are already accounted (fourth and fifth term of (1)) and for isotropic media C44 = 2 (C11 -C12), where Cαβ are the bare elastic constants. The next three terms form the lowest-order expansion of the functional with respect to energy fields (909)