Dynamical theory of thermal spin fluctuations in metallic ferromagnets

Abstract

A self-consistent dynamical theory of thermal spin fluctuations is developed which describes their spatial correlation. It is based on the functional integral method and utilizes the quadratic representation for the electron free energy in a fluctuating exchange field with renormalized susceptibilities allowing for the interaction of various spin fluctuation modes. Interpolation between the single-site and homogeneous susceptibilities is used, where these susceptibilities are found self-consistently. The average over fluctuations takes account of both long-wavelength and local excitations. A closed system of equations is formed for both unknown quantities: the magnetization and the mean-square exchange field at a site. The basic characteristics of a specific magnet are the density of electron states and the atomic magnetic moment at T=0. A method is proposed for separating the relatively slow thermal-spin fluctuations from the rapid zero-spin fluctuations forming the ground state of the magnets. At T=0 we have a system of equations of mean field theory. The temperature excites thermal spin fluctuations, which are described by taking account of correlation in time and space. The magnetization, susceptibility, magnitude of the spin fluctuations and their distribution over momenta, and the degree of magnetic short-range order in iron are calculated as functions of the temperature in the ferromagnetic and paramagnetic phases, and also at the transition between them, the Curie temperature.