Theory of nuclear spin diffusion in a spatially varying magnetic field

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Abstract
Spin diffusion driven by either a magnetization gradient or a field gradient is viewed as a flow of magnetization current. An expression for this current in a nonuniform field is derived. The magnetization current is the vehicle for a cross relaxation between the nuclear dipole-dipole energy and the spin energy of interaction with the inhomogeneous part of the magnetic field. From a measurement of the decay rate of dipole energy in the presence of large field gradients, which are present in type-II superconductors or at normal-superconductor interfaces, the spin-diffusion coefficient can be determined. Coupled differential equations describing magnetization and dipole energy densities are deduced and their solution is discussed.