The magnetic susceptibility of virtual bound state alloys

Abstract

The static and dynamical longitudinal and transverse magnetic impurity spin susceptibilities of the nondegenerate virtual bound state model are calculated as functions of temperature, magnetic field, virtual level width and for arbitrary separation of the quasibound level from the Fermi surface of an infinite structureless conduction electron band. Within this exactly solvable quantum-mechanical model problem the static spin susceptibilities remain finite at zero temperature and follow power law behaviour for low temperatures; at higher temperatures a Curie-Weiss law is obeyed. The dynamical susceptibilities are shown to exhibit interesting temperature, magnetic field and frequency dependent variation; in particular a continuous transition between quantum-mechanical and classical domains is analytically tractable. The longitudinal resonance lineshape is found to deviate from the Lorentzian Bloch equation form but reduces to such in the classical high-temperature regime. For the transverse absorption spectrum this rate equation description may also be obtained by freezing the fluctuating pseudospin with a strong external magnetic field. The impurity spin relaxation rates are finite and approach a constant at high temperatures.