Effect of $s-d$ Interaction on the Spin-Lattice Relaxation in Dilute Magnetic Alloys

The contributions of magnetic impurities to the conduction-electron-lattice and impurity-spin-lattice relaxation rates ($T_{\mathrm{sl}}^{-1\mathrm{}}$ and $T_{\mathrm{dl}}^{-1\mathrm{}}$, respectively) are theoretically investigated. The conduction-electron-impurity interaction is described by a Kondo $s-d$ exchange Hamiltonian with scattering of $d$ type. It is assumed that in the absence of $s-d$ exchange interaction there are direct lattice relaxation processes ($T_{\mathrm{sl}}^{\mathrm{}\left(0\right)-1\mathrm{}}$ and $T_{\mathrm{dl}}^{\mathrm{}\left(0\right)-1\mathrm{}}$) which are introduced in a phenomenological way, since the detailed mechanism of the $d$-electron-lattice relaxation is not known. As the $s-d$ exchange interaction is relatively strong compared to the lattice relaxation processes, the contribution of a magnetic impurity to the relaxation rates can be essentially modified by the $s-d$ interaction associated with the same impurity. The calculations are performed treating only the leading logarithmic terms in any order of the perturbation theory. This approximation limits the adequacy of the result to the regime well above the Kondo temperature and demonstrates the appearance and features of the Kondo effect in the lattice relaxation processes. However, a theory which covers the whole temperature range correctly is very likely not available at the present stage of the theory of the Kondo effect. It is found that the conduction-electron-lattice relaxation is depressed, which may be interpreted as the result of the change in the density of conduction electrons at the Fermi energy. The impurity-spin-lattice relation is found to be enhanced (depressed) for $S>\mathrm{}\frac{1}{2}$ ($S=\frac{1}{2}$). These renormalizations exhibit a strong temperature dependence in the region of the Kondo temperature which may be of importance in the interpretation of the recent transmission electron-spin-resonance experiments.