Spin Hall effect in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>β</mml:mi></mml:math> phases of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi mathvariant="normal">T</mml:mi><mml:msub><mml:mi mathvariant="normal">a</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="normal">W</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mtext>−</mml:mtext><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> alloys

Abstract

\ensuremath{\beta}-W and \ensuremath{\beta}-Ta are well known for their large spin Hall angles (SHAs), while \ensuremath{\alpha}-W and \ensuremath{\alpha}-Ta possess small SHAs. Recent theoretical studies predicted that alloying Ta with W could enhance the SHA. In this work, a systematic study is performed on the spin Hall effect (SHE) in $\mathrm{T}{\mathrm{a}}_{x}{\mathrm{W}}_{1\text{\ensuremath{-}}x}$ alloys in the full composition range from $x=0$ to 1. We have obtained the structural phase diagram and SHAs of the \ensuremath{\alpha}- and $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{T}{\mathrm{a}}_{x}{\mathrm{W}}_{1\text{\ensuremath{-}}x}$ alloy system, based on x-ray-diffraction, transmission electron microscopy, magnetotransport measurement, and macrospin model analysis. We have observed large SHAs ranging from \ensuremath{-}0.06 to \ensuremath{-}0.23 in $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{T}{\mathrm{a}}_{x}{\mathrm{W}}_{1\text{\ensuremath{-}}x}$ and a maximum SHA of \ensuremath{-}0.59 in 5.3-nm-thick $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{T}{\mathrm{a}}_{x}{\mathrm{W}}_{1\text{\ensuremath{-}}x}$. In addition, a linear correlation between SHA and resistivity in $\mathrm{T}{\mathrm{a}}_{x}{\mathrm{W}}_{1\text{\ensuremath{-}}x}$ has been uncovered, providing evidence that the SHE in $\mathrm{T}{\mathrm{a}}_{x}{\mathrm{W}}_{1\text{\ensuremath{-}}x}$ is caused by the intrinsic mechanism and/or side-jump scattering. Furthermore, we have observed an unconventional thickness dependence of SHA in $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{T}{\mathrm{a}}_{0.25}{\mathrm{W}}_{0.75}$, which peaks at 5.3 nm. The decay of SHA upon increasing thickness is likely to be caused by the \ensuremath{\beta}- to \ensuremath{\alpha}-phase transition.

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