Electron Scattering by the Electronic Quadrupole Moment of Rare-Earth Impurities

Measurements of the magnetoresistance of gold with rare-earth impurities show that the resistivity of a rare-earth impurity is different according to whether its magnetic moment is directed parallel or perpendicular to the current. The longitudinal resistivity is larger for Tb, Dy, and Ho and smaller for Er, Tm, and Yb; the anisotropy vanishes for Gd. This indicates that the resistivity anisotropy is due to the interaction of the conduction electrons with the electric quadrupolar moment of the $f$ electrons.