Fluctuation spectra in weakly coupled Van Vleck paramagnets: Some theoretical and experimental aspects

The ESR relaxation of impurities in rare-earth Van Vleck paramagnets with weak coupling is investigated both theoretically and experimentally. It is shown that the impurity relaxation is appreciably dependent on the fluctuation spectra of the host rare-earth ions. The line shapes of the fluctuation spectra are calculated using the method of moments for cases of interest. The role of the host exchange interaction and that of the rare-earth crystalline-field splitting in the relaxation process are demonstrated. The theory is applied to interpret the ESR linewidth behavior of Gd in the metallic Van Vleck paramagnets Pr${\mathrm{In}}_3$ (reported for the first time) as well as the linewidth behavior of Gd in the Van Vleck pnictides $\mathrm{Pr}X$ ($X=\mathrm{P},\mathrm{As},\mathrm{Sb},\mathrm{Bi}$) (reported previously and in the present work). The host exchange interaction in the pnictides was extracted by fitting the theory to the experimental ESR thermal broadening. These exchange parameters are compared with those estimated by means of other techniques. The rapid relaxation phenomenon in Pr${\mathrm{In}}_3$:Gd is partially attributed to a relatively low-lying ${\Gamma }_5$ crystalline-field-splitting level in this system. The conduction-electron contribution to the relaxation rate is shown to be significant in Pr${\mathrm{In}}_3$:Gd and La${\mathrm{In}}_3$Gd. The exchange interaction between the Gd and conduction electrons was extracted in both systems.