Tuning Spin Hall Angles by Alloying

Within a combined experimental and theoretical study it is shown that the spin Hall angle of a substitutional alloy system can be continuously varied via its composition. For the alloy system ${\mathrm{Au}}_x{\mathrm{Pt}}_{1-x}$ a substantial increase of the maximum spin Hall angle compared to the pure alloy partners could be achieved this way. The experimental findings for the longitudinal charge conductivity $\sigma$, the transverse spin Hall conductivity ${\sigma }_{\mathrm{SH}}$, and the spin Hall angle ${\alpha }_{\mathrm{SH}}$ could be confirmed by calculations based on Kubo’s linear response formalism. Calculations of these response quantities for different temperatures show that the divergent behavior of $\sigma$ and ${\sigma }_{\mathrm{SH}}$ is rapidly suppressed with increasing temperature. As a consequence, ${\sigma }_{\mathrm{SH}}$ is dominated at higher temperatures by its intrinsic contribution that has only a rather weak temperature dependence.

Figure 1

Integration of a ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}/{\mathrm{Au}}_x{\mathrm{Pt}}_{1-x}$-bilayer wire together with voltage probes in the experimental setup. The ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$ layer is shown in green and the ${\mathrm{Au}}_x{\mathrm{Pt}}_{1-x}$ layer is shown in red. In this geometry the excitation field is perpendicular to the bilayer. The angle ${\varphi }_{\mathrm{H}}$ gives the angle between the voltage probes and the static magnetization. $x^{\prime }$, $y^{\prime }$, $z$ define the local coordinate system of the magnetization.

Figure 2

Measured dc-voltage signal at FMR (green curve) for ${\varphi }_{\mathrm{H}}=45°$ and a precession frequency of 12 GHz for a ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}/{\mathrm{Au}}_{0.47}{\mathrm{Pt}}_{0.53}$ bilayer. $L_S$ and $L_A$ denote the symmetric (red curve) and antisymmetric (blue curve), respectively, contribution according to a fit to a Lorentzian line shape.

Figure 3

Spin diffusion length ${\lambda }_{\mathrm{sd}}$, of ${\mathrm{Au}}_x{\mathrm{Pt}}_{1-x}$ alloys determined assuming a linear dependence of ${\lambda }_{\mathrm{sd}}$ on the conductivity ${\sigma }_{\mathrm{AuPt}}$. The inset shows ${\lambda }_{\mathrm{sd}}$ on an enlarged scale for the investigated concentration $x$ below 0.8

Figure 4

Spin Hall angle ${\alpha }_{\mathrm{SH}}$ (top), longitudinal charge conductivity $\sigma$ (middle), transverse spin Hall conductivity ${\sigma }_{\mathrm{SH}}$ (bottom), of ${\mathrm{Au}}_x{\mathrm{Pt}}_{1-x}$ as a function of the concentration $x$. The full red circles give experimental data for $T=300\mathrm{K}$, while the full (open) squares give results obtained using Kubo’s linear response formalism in combination with the alloy analog model for $T=300\mathrm{K}$ ($T=0\mathrm{K}$). The thin dashed lines give theoretical results for the temperature range between 0 and 350 K in steps of 50 K.