Relaxation of nuclear and electronic magnetic moments in heavy-electron compounds

Estimates are presented of nuclear-spin-lattice relaxation rates in the normal state of heavy-electron metals due to dipolar coupling of nuclear moments and 4f or 5f spin fluctuations. The 4f or 5f sites are modeled as point ions in the LS limit with dynamics of the $N_{\mathrm{grd}}$-fold degenerate Anderson model. Dipolar coupling alone is sufficiently large to account for the relaxation of ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$ in ${\mathrm{CeBe}}_{13}$ and ${\mathrm{UBe}}_{13}$, as has been found for other light nuclei in heavy-electron and local moment systems. However, for heavy nuclei with large intrinsic relaxation rates due to stronger on-site coupling to conduction electrons, the dipolar contribution underestimates the observed relaxation by orders of magnitude. I suggest that nuclear resonance is a more effective probe than electron-spin resonance of the heavy-fermion state primarily because the probe nuclei sit closer to the heavy-electron sites so that the strong range dependence of both dipolar and transferred exchange (Ruderman-Kittel-Kasuya-Yosida) interactions favors nuclear relaxation. I show for the Anderson lattice, using both mean field formalism and Green’s function formalism (the latter explicitly including dynamic many-body effects and assuming a dispersionless interaction contribution to the f-electron self-energy) that many-body cancellation effects are relevant in magnetic relaxation in heavy-electron compounds only when coupling of probe moments to distant heavy-electron sites is vanishingly small. I show that since the maximal f-electron enhancement of impurity electronic moment relaxation follows the square of the ratio of the paramagnetic transition temperature ($T_P$) to the effective degeneracy temperature or ‘‘Kondo’’ energy scale ($T_0$) that those heavy-fermion systems close to magnetic instabilities are more suitable for study with electron spin resonance. Detailed studies of the relaxation in that instance are beyond the scope of this paper.