Effect of tunneling on the evolution of nuclear magnetization

Abstract

The semiclassical perturbation calculation of the nuclear-spin relaxation has been extended to lower temperatures by taking into account the tunneling splittings of the lowest-energy states of N${\mathrm{H}}_{4}$ tetrahedron embedded in a crystal lattice. The effect of the lattice is represented by classical correlation functions. The proton-spin relaxation has been calculated for large and arbitrary tunneling splittings in a tetrahedral crystal field, for the case of tunneling around a single ${C}_{3}$ axis and around ${C}_{2}$ axes only. The cases of large tunneling splitting in an asymmetric crystal field and in a crystal field with trigonal distortion are also discussed. The effect of tunneling in a tetrahedral crystal field with a small distortion is examined in detail. It is shown that in a special case the tunneling-assisted relaxation may be responsible for the establishment of equilibrium in a spin-polarization-torsional spectroscopy experiment. The presented model calculation is valid at temperatures from \ensuremath{\sim} 100 to \ensuremath{\sim} 10 K, when the correlation-function approximation breaks down.