Model Calculations of Spin-Lattice Relaxation for Divalent Cobalt

The spin-lattice relaxation times for divalent cobalt in the $X$ and $Y$ sites of double nitrate crystals are calculated by three schemes. The first is a dipole model of the crystal field produced by the water molecules in which the parameters are adjusted to reproduce the static wave functions, and the Debye homogeneous model is used to evaluate the motions of the water molecules. A second calculation takes into account some of the realities of the motion of the water molecules. A third calculation is made using the approximations introduced by Orbach. The results indicate that very serious errors are introduced by the inadequate description of the motion of the water molecules and that next-nearest neighbors have a large effect in the two cases treated here. The use of the dipole model with adjusted constants for evaluation of the rate of change of the crystal potential with respect to the nuclear motions may, of course, be a source of much inaccuracy.