Magnetic Effects of Rare-Earth Impurities on Electron Transport in the Noble Metals

Of the dilute alloys of rare‐earth metals in the noble metals, only a few show a small resistance anomaly and a temperature‐dependent negative magnetoresistance at liquid‐helium temperatures. In a saturating magnetic field the decrease for the Gd alloys is 2%. A calculation in Born approximation shows this to be due to interference between Coulomb and spin‐dependent scattering. The absolute value of $J$ is found to be 0.04 eV when the interaction is written as $\mathrm{H\hspace{0.17em}=\hspace{0.17em}-\hspace{0.17em}J\sigma ·}\mathrm{S}{\mathrm{\delta (r-r}}_i)$ . A similar calculation for two different magnetic impurities contains cross terms in the two coupling constants. For Mn in Ag, $J$ is known to be negative from the resistance minimum (Kondo). It is concluded from the fact that, with 0.20 a.t.% Mn and 0.39 at.% Gd, only a very small magnetoresistance is observed, and that the sign of $J$ is positive. With $\text{J\hspace{0.17em}=\hspace{0.17em}0.04\hspace{0.17em}}\mathrm{eV}$ a small negative Kondo effect can be computed which is of the same order of magnitude as experimentally found. The magnetic effects in these alloys are small compared to what is reported in the literature on alloys with trivalent solvents. We have checked in a few cases that the magnetic moment agrees with the free‐ion values. The explanation of the apparently small value of $J$ probably must be found in a more careful analysis of the interference terms that may be different for different partial waves.