Spin Hall effect in the high-resistivity high-entropy alloy AlCrMoW

TL;DR

This work addresses how to achieve large spin Hall effects in high-resistivity materials by studying Al$_x$(CrMoW)$_{1-x}$ high-entropy alloy thin films. The authors synthesize, pattern, and extensively characterize these films on Ta seeds, using harmonic Hall measurements and broadband FMR, complemented by SPR-KKR density functional theory calculations to extract and compare the spin Hall conductivity $\sigma_\mathrm{SH}$ and spin Hall angle $\theta_\mathrm{SH}$ across compositions. They find a maximum $\theta_\mathrm{SH} = -0.12 \pm 0.01$ at $x \approx 0.25$ with $\sigma_\mathrm{SH} \approx -72{,}000\ \hbar/(2e)\ \mathrm{S/m}$, and a resistivity peak near $x = 0.5$ of about $180\ \mu\Omega\mathrm{cm}$; experiments align well with intrinsic SHC predictions, with vertex corrections playing a minor role. The results show that HEAs containing a main-group element can form simple crystal structures while delivering high resistivity and sizeable SHE, offering a scalable route for spin Hall device engineering.

Abstract

We study thin films of the high-entropy alloy system Al$_{x}$(CrMoW)$_{1-x}$, grown on Ta seed layers by magnetron co-sputtering. Between $x=0.2$ and $x=0.6$, a resistivity larger than 100$μΩ$cm is achieved, with a peak of 180$μΩ$cm at $x=0.5$. Around the stoichiometric composition AlCrMoW, the alloy forms a bcc solid solution. The harmonic Hall method was used to characterize the spin Hall angle of the alloy series, where a maximum spin Hall angle of $θ= -0.12 \pm 0.01$ is observed for $x=0.25$. The implied spin Hall conductivity is $σ_\mathrm{SH} \approx -72\,000 \, \hbar/(2e)$\,S/m. The experimental results show excellent agreement with density functional theory calculations, which show similar trends and values. The results demonstrate that high-entropy alloys with a main-group element component can form a simple crystal structure and show high resistivity. This suggests that a whole new class of materials for spin Hall device engineering is available with simple methods.

Figures (3)

• Figure 1: a) X-ray diffraction measurements of selected samples with Cu K$_\alpha$ radiation. b) X-ray reflectivity measurements on the same samples. The measurements are multiplied by 10 with respect to one another for clarity. c) Fourier transform spectra of the XRR measurements.
• Figure 2: Effective magnetisation and Gilbert damping parameter $\alpha$ as a function of the Al concentration. The Lande-factor was held constant at $g=2.1$.
• Figure 3: Comparison of measured and calculated data. a) spin Hall conductivity, b) spin Hall angle, and c) resistivity. Red squares represent calculations, blue triangles are harmonic Hall results. In c), green filled squares represent four-point measurements. The Nordheim fit represents a parabolic fit with fixed endpoints to the SPR-KKR calculation results.