Spin dynamics in multilevel magnetic systems

Abstract

The correlated-effective-field theory of many-body magnetism, introduced by the author in an earlier paper to describe the equilibrium properties of magnetic ions with complicated level structure, is extended to discuss spin dynamics in a similar context. The method goes beyond the random-phase approximation by incorporating a measure of spontaneous fluctuations in a manner which ensures self-consistency with respect to the fluctuation-dissipation theorem. After a formal derivation of equations defining mode frequency dispersion and scattering strength, the method is used to discuss the problem of singlet-ground-state ferromagnetism. The singlet-triplet model is discussed in the paramagnetic phase and the soft mode on approach to the Curie temperature is shown to be a zone-center zero-frequency electronic mode. A more realistic model involving a singlet-ground-state ion in a cubic-crystal-field environment is also investigated to explore the manner in which excitations between excited crystal-field levels interact with excitations out of the singlet ground state as the temperature is raised. Numerical calculations of frequency dispersion and mode strength are performed as functions of temperature, and quantitative results for the correlated-effective-field and random-phase approximations are compared for both the singlet-triplet and cubic-crystal-field problems.