Anisotropic k-ƒ interactions from spin-orbit coupled 5d intermediate states

The anisotropy of the conduction electron-4? local moment interaction ($\text{k-?}$) gives rise to anisotropic transport effects. The contribution from the orbital character of the 4? moment has been well documented by magnetotransport studies on noble metals containing non-S state rare-earth ions. To determine whether there is an additional contribution to the anisotropy from the spin-orbit coupled 5d electron states we have studied the magnetoresistivity of Ag: Gd alloys. We have not found any significant anisotropy of the magnetoresistivity. By comparing this result and previous Hall effect and magnetoresistivity data on noble metal-rare earth alloys with our model calculation, we come to the conclusion that the spin-orbit splitting of the 5d virtual bound state is relatively small. We discuss the details of the resulting anisotropy of the $\text{k-?}$ interaction.