Self-consistent determination of spin Hall angles in selected $5d$ metals by thermal spin injection

We demonstrate a self-consistent and versatile method to determine the relative spin Hall angle ${\theta }_{\text{SH}}$ and spin diffusion length ${\lambda }_{\text{SF}}$ of selected $5d$ metals (Pt, Au, Ta, and W) by thermal spin injection from a common ferromagnetic insulator, yttrium iron garnet, into thin metal films of various thicknesses. The values of ${\theta }_{\text{SH}}$ for Pt and Au are opposite in sign to those of Ta and W. The inverse spin Hall effect voltage depends on spin Hall resistivity, which is the product of ${\theta }_{\text{SH}}$ and electrical resistivity. We also show evidence of magnetic proximity effects including magnetoresistance and the anomalous Hall effect in these $5d$ metals, except for Au.

Figure 1

Schematics of spin current injection using (a) a nonlocal lateral structure, (b) spin pumping, and (c) a thermal spin injection structure. Red arrows indicate the spin current direction. (d) Patterned metal Hall bar on YIG. Thickness-dependent resistivity of (e) Ta and (f) W thin films on YIG. The solid red lines are best fit using the Fuchs-Sondheimer formalism.

Figure 2

(a) Field-dependent thermal voltage of Pt(10 nm)/YIG, Au(10 nm)/YIG, Ta(10 nm)/YIG, and W(10 nm)/YIG under a vertical temperature difference of 20 K/mm. Thickness dependence of (b) thermal voltages and (c) thermal voltages divided by the resistivity of Pt (blue), Au (pink), Ta (black), and W (red) on YIG. The solid lines in (c) are best fit using Eq. (2).

Figure 3

(a) Magnetoresistance (MR) measurement of Ta(3 nm)/YIG and W(3 nm)/YIG as a function of magnetic field $H$ at α = 0° (ρ_∥) and 90° (ρ${}_T$). (b) MR angular dependence of Ta(3 nm)/YIG and W(3 nm)/YIG at 300 K under a 15 kOe magnetic field in $xy$ (in film plane, black), $xz$ (red), and $yz$ (blue) plane field scans with the angles α, φ, θ relative to the $x,x,z$ axes, respectively. (c) MR ratio as a function of Ta and W thickness $t$ on YIG under 800 Oe. The dashed lines are a guide to the eye.

Figure 4

(a) Field dependence of Hall resistance $R_H$ at different temperatures of (a) Ta(10 nm)/${\text{SiO}}_2$ and W(10 nm)/${\text{SiO}}_2$ showing only the ordinary Hall effect and (b) Ta(6 nm)/YIG and W(6 nm)/YIG showing the anomalous Hall effect. (c) Temperature dependence of anomalous Hall resistance $R_{\mathrm{AHE}}$ for Ta(6 nm)/YIG, W(6 nm)/YIG, and Pt(15 nm)/YIG. The dashed lines are a guide to the eye.