Spin Hall Effect Induced by Resonant Scattering on Impurities in Metals

The spin Hall effect is a promising way for transforming charge currents into spin currents in spintronic devices. Large values of the spin Hall angle, the characteristic parameter of the yield of this transformation, have been recently found in noble metals doped with nonmagnetic impurities. We show that this can be explained by resonant scattering off impurity states split by the spin-orbit interaction. By using as an example copper doped with $5d$ impurities we describe the general conditions and provide a guide for experimentalists for obtaining the largest effects.

Figure 1

Skew scattering (squares) and side-jump (triangles) contributions to the spin Hall angle calculated from Eqs. (11, 13) as a function of the number of $d$ electrons, $Z_d$, for $5d$ impurities in Cu. $Z_d$ increases from about 1 for Lu to about 9 for Pt (the calculations in the text for Ir have been done with $Z_d=8$, see text and Ref. 23). All other parameters are indicated in the text. The side-jump contribution is calculated for an impurity concentration of 2%. Inset: Density of states (DOS) of a $5d$ virtual bound state with $S\mathrm{\text{−}}O$ splitting between $j=3/2$ and $j=5/2$ states.