Spin-Lattice Relaxation ofS-State Ions:Mn2+in a Cubic Environment

The theory of spin-lattice relaxation is developed for $S$-state ions: in particular for ${\mathrm{Mn}}^{2+}$ in a cubic environment. The wavefunctions for ${\mathrm{Mn}}^{2+}$ are generated to first order in the spin-orbit coupling parameter, the orbit-lattice interaction is formulated in terms of spherical harmonics, and the rate equations are derived for this system. Estimates are given of the interaction coefficients based on a point-charge model, and it is shown that excellent agreement is obtained with observed spin-lattice relaxation times. However, a detailed comparison with recent experiments which give the magnitude and sign of these coefficients directly shows that though the point-charge model gives the right order of magnitude, it gives the wrong sign for the interaction coefficients.