Measuring the magnetic anisotropy of the spin Hall effect and spin relaxation length in nickel and permalloy via electrical spin injection

TL;DR

Measuring the magnetic anisotropy of the spin Hall effect and spin relaxation length in Ni and Py via electrical spin injection addresses how $\theta_{\text{SHE}}$ and $\lambda_{\mathrm{s}}$ depend on magnetization orientation in ferromagnets. The authors employ two nonlocal lateral spin valve geometries with Cu channels and absorbing FMs, combined with 3D FEM simulations that include the Sharvin interface resistance, to independently extract $\lambda_{\mathrm{s}}$ and $\theta_{\text{SHE}}$. They observe large anisotropies in both quantities with opposite trends, so the product $\theta_{\text{SHE}} \lambda_{\mathrm{s}}$—and hence the spin-charge interconversion signal—remains roughly constant across orientations. Comparison with theory shows qualitative agreement but about a factor of 2 higher $\sigma_{\text{SHE}}$ than predicted, likely due to interface resistance uncertainties and related effects. The work demonstrates the necessity of measuring both $\lambda_{\mathrm{s}}$ and $\theta_{\text{SHE}}$ to accurately assess SCI in ferromagnets and informs material choices for spintronic applications.

Abstract

The spin Hall effect in ferromagnets is of great interest in the field of spintronics, and while the effect has been quantified in many materials, the dependence of the spin Hall angle on the relative orientation of spin polarization and the magnetization is less well studied. Of equal importance for the purpose of spin-charge interconversion in ferromagnets is the spin relaxation length, which is predicted to be highly anisotropic with respect to magnetization. Using a modified lateral spin valve geometry with a copper channel and permalloy spin injector, we measure the dependence of the spin Hall angle and spin relaxation length on magnetization orientation in permalloy and nickel, using two distinct device geometries. This allows us to disentangle the contributions of the spin relaxation length and spin Hall angle to the measured spin-charge interconversion voltage output. Our results indicate a large anisotropy in both the spin relaxation length and spin Hall angle in both permalloy and nickel, in agreement with theoretical calculations. The quantities change in opposite directions, with the spin relaxation length rising as the magnetization is moved parallel to the spin polarization and the spin Hall angle falling, leading to a near total cancellation of the spin-charge interconversion output.

Figures (16)

• Figure 1: Device Schematic. Two geometries were used in this work to measure the SHE. (a) H-shaped device, consisting of two Py elements (grey) along $\hat{x}$, referred to as the injector (left) and detector (right), with a third perpendicular element (absorber, centre) along $\hat{y}$ made of either Py or Ni, all connected by the Cu channel (orange). Two voltage measurements are indicated: in black is the SHE configuration (corresponding to results in Fig. 3), and in green the spin absorption configuration (corresponding to results in Fig. 2). (b) L-shaped device, again showing a Py injector (along $\hat{x}$), and a Py or Ni absorber (along $\hat{y}$) with an associated spin Hall voltage (corresponding to results in Fig. 4).
• Figure 2: Spin absorption anisotropy measurements using the H-shaped device, with a channel width of 130 nm and injector/detector distance of 500 nm (a) A reference LSV measurement, made in a device identical to that in Fig. \ref{['fig:device_schematic']}(a), but without the central FM absorber. The relative orientations of the FM injector and detector magnetizations are indicated, corresponding to two measured non-local resistances, $\pm R_{\text{NL}}$, for parallel/antiparallel magnetizations. (b, c) LSV measurements with an absorbing Py (b) and Ni (c) element placed between the injector and detector. The signal at high field is indicated as $R_{\text{NL}}^{\parallel}$ (spins polarized parallel to the absorber magnetization), and at zero field as $R_{\text{NL}}^{\perp}$ (spins polarized perpendicular to the absorber magnetization). The black dashed line represents a fit from 3D FEM simulation.
• Figure 3: SHE anisotropy measurement in (a) Py and (b) Ni, using the H-shaped device. The inset shows a false-colour SEM image of the device used, indicating the applied field $B_\mathrm{x}$, applied charge current $J_\mathrm{c}$ and the measured voltage. The orange and blue curves correspond to the two initial magnetization states of the injector, with the top right insets showing zooms at zero field. $2\Delta R_{\mathrm{ISHE}}$ at zero field and high field is annotated.
• Figure 4: SHE anisotropy measurement in (a) Py and (b) Ni using the L-shaped device. The inset shows a false-colour SEM image of the devices used, indicating the applied field $B_\mathrm{x}$, applied charge current $J_\mathrm{c}$ and the measured voltage. The orange and blue curves correspond to the two initial magnetization states of the injector, with the top right insets showing zooms at zero field. $2\Delta R_{\mathrm{ISHE}}$ at zero field and high field is annotated.
• Figure 5: Magnetic field dependence of $\lambda_\mathrm{s}$ in Py (a) and Ni (b) and $\theta_{\mathrm{SHE}}$ in Py (c) and Ni (d). The values of $\lambda_\mathrm{s}$ are obtained by fitting the data in Figs. 2b and c (H-shaped device), while $\theta_{\mathrm{SHE}}$ is extracted from fitting the data in Figs. 3a and b (H-shaped device) and Figs. 4a and b (L-shaped device), in both cases using $\lambda_\mathrm{s}$ as an input