Density-Matrix Derivation of the Spin-Diffusion Equation

Abstract

A diffusion equation is derived for the spatial motion of spin magnetization that has an inhomogeneous distribution. The particles of the system are assumed to be fixed in space and have a spin of ½. Only those terms in the interaction Hamiltonian are used that commute with the Zeeman Hamiltonian. A density-matrix calculational technique is used, and an assumption is made that the interaction Hamiltonian is small enough that the density matrix is diagonal to first order. The first-order results are similar to Bloembergen's, but have a different multiplying coefficient. An average diffusion constant is evaluated explicitly for a simple cubic lattice for cases of the applied magnetic field along the [100], [110], and [111] directions.