Interpretation of low-temperature Mössbauer spectra in the presence of Kondo deviations. I. General considerations

In this paper, we first derive the general expression for the Mössbauer line shape of a powder source when cascade effects come into play. Then we consider the case of a paramagnetic impurity—in a metal—which exhibits an incipient Kondo effect, and we examine the problems which arise when the relaxation of this impurity by the conduction electrons is studied by Mössbauer spectroscopy, i.e., in the presence of hyperfine coupling. We extend conventional relaxation theory up to third order in ${\mathcal{H}}_1=-2\mathrm{}{J}_{\mathrm{sf}}\alpha \overrightarrow{\mathrm{S}}·\overrightarrow{\mathrm{s}}$ and investigate under what conditions the third-order damping terms can be expressed as products of first- and second-order transition amplitudes. We find that this occurs when either "extreme narrowing" or "secular" approximations are valid; in these two cases, the Kondo correction to the relaxation matrix reduces to the standard computation of the second-order transition amplitude. In the following paper, these results are applied to the study of relaxation effects of the hyperfine populations at low temperatures, in the Mössbauer cascade of an Au ${}_{}{}^{170}{}_{}{}^{}\mathrm{Yb}$ source.