Nuclear spin relaxation in paramagnetic solutions. Effects of large zero-field splitting in the electron spin Hamiltonian

Abstract

Expressions are derived describing nuclear spin relaxation in paramagnetic salt solutions under conditions where the electron spin Hamiltonian is dominated by a uniaxial quadratic zero-field splitting (zfs) interaction. In this situation, the electron spin vector is quantized along molecular axes rather than along the external magnetic field. By expressing the time dependence of the electron spin operators, written in the molecular coordinate frame, in the Heisenberg representation and then transforming these expressions to the laboratory coordinate system, simple closed form expressions for the paramagnetic nuclear relaxation increment have been derived. Electron–nuclear dipole–dipole and scalar relaxation mechanisms are considered. The resulting expressions parallel those of Solomon–Bloembergen–Morgan theory, but are valid in the zfs limit rather than the Zeeman limit. Nuclear relaxation rates in the zfs and Zeeman limits exhibit characteristic qualitative differences, some of which have been noted in earlier studies. Of particular note is the fact that the scalar contribution to T−11p is much larger in the zfs than in the Zeeman limit. In most circumstances, T−11p=T−12p in the zfs limit, while in the Zeeman limit, scalar relaxation usually contributes significantly only to T−12p. A vector model of this phenomenon is suggested. The results are valid for arbitrary values of the electron spin quantum number but they assume that electron spin relaxation is in the Redfield limit, i.e., that the correlation times of the coupling between electron spin and the lattice be short on the time scale of electron spin relaxation. This condition is probably satisfied widely when the static zfs is large.