Analysis of the giant spin Hall effect in Cu(Bi) alloys

Two years after the prediction of a giant spin Hall effect for the dilute Cu(Bi) alloy [Gradhand et al., Phys. Rev. B 81, 245109 (2010)], a comparably strong effect was measured in thin films of Cu(Bi) alloys by Niimi et al. [Phys. Rev. Lett. 109, 156602 (2012)]. Both theory and experiment consider the skew-scattering mechanism to be responsible, however they obtain opposite sign for the spin Hall angle. Based on a detailed analysis of the obtained theoretical results, we propose that either the formation of extremely small clusters or the influence of interface roughness and grain boundaries decorated with Bi atoms are responsible for the observed phenomenon.

Figure 1

The spin Hall angle for the Cu(Bi) alloy with different impurity concentrations obtained from the Kubo-Středa formula using both the local-density approximation (LDA) and the generalized gradient approximation (GGA) for the exchange-correlation potential.

Figure 2

The dependence of the spin Hall angle, given by Eq. (28), on ${\delta }_s\equiv {\delta }_{{}^1/{}_2}^s$ and ${\delta }_p\equiv \frac{1}{3}({\delta }_{{}^1/{}_2}^p+2{\delta }_{{}^3/{}_2}^p)$ is shown for the relaxed geometry together with the corresponding value of $\alpha$ from Table .