Nuclear spin relaxation in paramagnetic systems ( S = 1) in the slow-motion regime for the electron spin. II. The dipolar T2 and the role of scalar interaction

Abstract

The previously presented theory ( Mol. Phys. 48, 329 (1983)) for the dipolar contribution to the spin-lattice relaxation in paramagnetic systems is extended. The theory, which allows the electron spin relaxation to be in the slow motion regime, is generalized to cover both the longitudinal and the transverse relaxation and to include both the dipole-dipole (DD) and the scalar interaction in the Hamiltonian coupling the nuclear spin to the lattice. The lattice is described in terms of the electron Zeeman interaction, a zero-field splitting (ZFS) of cylindrical symmetry and the isotropic rotational diffusion. It is shown that the spectral densities at the nuclear Larmor frequency and at zero frequency consist of three terms. Besides the usual DD and scalar components, a cross-term is shown to contribute to nuclear spin relaxation rates for certain parameter ranges. In the absence of exchange, the numerical calculations for S = 1 show that the DD and cross term spectral densities at zero frequency are independent of the magnetic field and the ZFS parameter. This is traced to the cross correlation between the DD and ZFS interactions. A formal way to include chemical exchange in the model is sketched. The effect of including exchange is that the DD-ZFS cross correlation is reduced.