Spin-lattice relaxation of Kramers doublets with hyperfine structure in cubic symmetry

A spin hamiltonian formalism is used to develop the theory of spin-lattice relaxation by the direct process in a system S= 1 / 2 , I= 1 / 2 with hyperfine coupling in cubic symmetry. It is shown that when J is a good quantum number the probabilities for the direct ( mod Delta m mod =1, Delta M=0) as well as the 'skew' ( mod Delta (m+M) mod =0,2) transitions can be expressed for all orientations of the magnetic field as a function of three parameters. A new experimental method is devised for measuring the 'skew' transition probabilities, effective only when high fields and low temperatures are used. The results of such measurements are presented for Tm 2+ ions in CaF 2 and SrF 2 .