Giant Spin Hall Effect Induced by Skew Scattering from Bismuth Impurities inside Thin Film CuBi Alloys

We demonstrate that a giant spin Hall effect (SHE) can be induced by introducing a small amount of Bi impurities in Cu. Our analysis, based on a new three-dimensional finite element treatment of spin transport, shows that the sign of the SHE induced by the Bi impurities is negative and its spin Hall (SH) angle amounts to $-0.24$. Such a negative large SH angle in CuBi alloys can be explained by applying the resonant scattering model proposed by Fert and Levy [Phys. Rev. Lett. 106, 157208 (2011)] to $6p$ impurities.

Figure 1

(a) Schematic of the ISHE measurement. The ISHE in CuBi deflects spin-up and down electrons $|e|$ ($e$ is the charge of the electron) denoted by spheres with arrows to the same side. Other arrows indicate the electron motion direction. (b) Electrochemical potential distributions for spin-up and down electrons in Cu. Spin-up and down electrons diffuse in opposite directions, which characterizes a pure spin current (no charge current). (c) Scanning electron microscopy image of our spin Hall device. The one-sided yellow arrow in (c) represents the positive direction of the magnetic field in the case of the ISHE measurement.

Figure 2

(a) DSHE and (b) ISHE signals of ${\mathrm{Cu}}_{99.5}{\mathrm{Bi}}_{0.5}$ measured at $T=10\mathrm{K}$. For comparison, the ISHE resistances of a 20 nm thick pure Cu ($\rho =6.3\mu \Omega ·\mathrm{cm}$), Pt ($10\mu \Omega ·\mathrm{cm}$), and ${\mathrm{Cu}}_{97}{\mathrm{Ir}}_3$ ($14\mu \Omega ·\mathrm{cm}$) are also added in (b). (c) A typical AMR signal of Py1 showing the saturation of the magnetization above 2000 Oe for $H_{\perp }$ along the $y$ direction [see Fig. 1a].

Figure 3

(a) NLSV signals measured at $T=10\mathrm{K}$ with a ${\mathrm{Cu}}_{99.5}{\mathrm{Bi}}_{0.5}$ middle wire (open symbols) and without a CuBi wire (closed symbols). The arrows represent the magnetization directions of Py1 (left) and Py2 (right). Note that, for the NLSV measurement, the magnetic field is aligned along the easy axis ($x$ direction) of the Py wires. (b) Spin diffusion length ${\lambda }_{\mathsf{M}}$ of CuBi alloys at 10 K as a function of ${\rho }_{\mathrm{imp}}$ (see definition in the text). The closed and open symbols correspond, respectively, to the 3D and 1D analyses.

Figure 4

(a) SH resistivity of CuBi alloys as a function of ${\rho }_{\mathrm{imp}}$. The closed and open symbols correspond, respectively, to the 3D and 1D analyses. The SH angles ${\alpha }_{\mathsf{H}}^{3\mathrm{D}}$ and ${\alpha }_{\mathsf{H}}^{1\mathrm{D}}$ correspond to the slopes of solid and broken lines, respectively. The inset shows the resistivity induced by Bi impurities ${\rho }_{\mathrm{imp}}$ as a function of Bi concentration. (b) For comparison, the SH resistivity of CuIr alloys is plotted as in (a), but the experimental data are derived from Fig. 3 in Ref. 18. The linear variation of the SH resistivity with ${\rho }_{\mathrm{imp}}$ is not limited by the solubility of Ir up to concentrations as large as $12\%$. (c),(d) 3D mappings of the spin accumulation voltage for the (c) ${\mathrm{Cu}}_{99.5}{\mathrm{Bi}}_{0.5}$ and (d) ${\mathrm{Cu}}_{97}\mathrm{I}{\mathrm{r}}_3$ SH devices calculated with SpinFlow 3D [16].