Equilibrium current vortices in simple metals doped with rare earths

Dilute alloys of rare earths have played a vital role in understanding magnetic phenomena. Here, we model the ground state of dilute $4f$ rare-earth impurities in light metals. When the $4f$ subshells are open (but not half-filled), the spin-orbit coupling imprints a rotational charge current of conduction electrons around rare-earth atoms. The sign and amplitude of the current oscillate similar to the Ruderman-Kittel-Kasuya-Yosida (RKKY) spin polarization. We compute the observable effect, namely, the \O{}rsted field generated by the current vortices and the Knight shift.