Statistical Theory of Spin Relaxation and Diffusion in Solids

Abstract

A comprehensive theoretical description is given for the spin relaxation and diffusion in solids. The formulation is made in a general statistical-mechanical way. The method of the nonequilibrium statistical operator (NSO) developed by Zubarev is employed to analyze a relaxation dynamics of a spin subsystem. Perturbation of this subsystem in solids may produce a nonequilibrium state which is then relaxed to an equilibrium state due to the interaction between the particles or with a thermal bath (lattice). The generalized kinetic equations were derived previously for a system weakly coupled to a thermal bath to elucidate the nature of transport and relaxation processes. In this paper, these results are used to describe the relaxation and diffusion of nuclear spins in solids. The aim is to formulate a successive and coherent microscopic description of the nuclear magnetic relaxation and diffusion in solids. The nuclear spin-lattice relaxation is considered and the Gorter relation is derived. As an example, a theory of spin diffusion of the nuclear magnetic moment in dilute alloys (like Cu-Mn) is developed.It is shown that due to the dipolar interaction between host nuclear spins and impurity spins, a nonuniform distribution in the host nuclear spin system will occur and consequently the macroscopic relaxation time will be strongly determined by the spin diffusion. The explicit expressions for the relaxation time in certain physically relevant cases are given.

Nonequilibrium statistical operator method and generalized kinetic equations

“…Следует отметить, что полученные обобщенные кинетические уравнения служат полезным инструментом исследования квантовой динамики в конденсированных средах [15], [16], [18], [49]. Одним из методов исследования квантовой динамики является метод редуцированной (приведенной) матрицы плотности.…”

“…В этом подходе приведенная матрица плотности получается посредством усреднения ρ 1 = Tr 2 ρ полной матрицы по нерелевантным степеням свободы термостата. Известным примером такого подхода являются уравнения Редфилда для спиновой матрицы плотности, которые также были получены (в обобщенной форме) с помощью метода НСО [15], [16], [49]. Уравнения типа Редфилда для ⟨P αβ ⟩ в общем виде записываются как…”

“…в случае отсутствия внешнего поля (случай с переменным внешним полем рассмотрен в [15], [16], [49]). Здесь ρ αα ′ есть матричный αα ′ -элемент спиновой матрицы плотности, [15], [16], [50], поведение малой динамической подсистемы с гамильтонианом H 1 , которая взаимодействует с термостатом с гамильтонианом H 2 .…”

Electronic Transport in Metallic Systems and Generalized Kinetic Equations

“…To describe properly the lattice subsystem let us remind that the normal coordinate Q q,λ is defined by the relation 52, 86 48) where N is the number of unit cells per unit volume and e ν ( q) is the polarization vector of the phonon. The Hamiltonian of the phonon subsystem in terms of normal coordinates is written as 52,86…”

“…We should mention here that some aspects of the spin transport in solids were discussed by us in Refs. 45,48 In the present study a qualitative theory for conductivity in metallic systems is developed and applied to systems like transition metals and their disordered alloys. The nature of transition metals is discussed in details and the tight-binding approximation and method of model Hamiltonians are described.…”