While the metastable $\beta$ (A15) phase of tungsten has one of the largest spin Hall angles measured, the origin of this high spin Hall conductivity is still unclear. Since large concentrations of oxygen and nitrogen are often used to stabilize $\beta$ tungsten, it is not obvious whether the high spin Hall conductivity is due to an intrinsic or extrinsic effect. In this work, we have examined the influence of O and N dopants on the spin Hall conductivity and spin Hall angle of $\beta$-W. Using multiple first-principles approaches, we examine both the intrinsic and extrinsic (skew-scattering) contributions to spin Hall conductivity. We find that intrinsic spin Hall conductivity calculations for pristine $\beta$-W are in excellent agreement with experiment. However, when the effect of high concentrations (11 at.%) of O or N interstitials on the electronic structures is taken into account, the predicted intrinsic spin Hall conductivity is significantly reduced. Skew-scattering calculations for O and N interstitials in $\beta$-W indicate that extrinsic contributions have a limited impact on the total spin Hall conductivity. However, we find that the spin-flip scattering at O and N impurities can well explain the experimentally found spin-diffusion length within the range of 1–5 nm. To explain these findings, we propose that dopants (O and N) help to stabilize $\beta$-W grains during film deposition and afterwards segregate to the grain boundaries. This process leads to films of relatively pristine small $\beta$-W grains and grain boundaries with high concentrations of O or N scattering sites. This combination provides high spin Hall conductivity and large electrical resistance, leading to high spin Hall angles. This work shows that engineering grain-boundary properties in other high spin Hall conductivity materials could provide an effective way to boost the spin Hall angle.

中文翻译：

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杂质对β-W中自旋霍尔电导率的影响

而亚稳态 $\beta$钨的（A15）相具有最大的自旋霍尔角之一，这种高自旋霍尔电导率的起源仍不清楚。由于通常使用高浓度的氧气和氮气来稳定$\beta$对于钨，自旋霍尔电导率高是由于固有效应还是非固有效应，这一点并不明显。在这项工作中，我们研究了O和N掺杂对自旋霍尔电导率和自旋霍尔角的影响。$\beta$-W。使用多种第一性原理方法，我们检查了自旋霍尔电导率的内在和外在（偏斜散射）贡献。我们发现原始的自旋霍尔电导率计算$\beta$-W与实验非常吻合。但是，当考虑到高浓度（11 at。％）的O或N间隙对电子结构的影响时，预测的固有自旋霍尔电导率将大大降低。O和N插页式广告中的歪斜散射计算$\beta$-W表示外在影响对总自旋霍尔电导率的影响有限。但是，我们发现在O和N杂质处的自旋翻转散射可以很好地解释实验发现的自旋扩散长度在1-5 nm范围内。为了解释这些发现，我们建议掺杂剂（O和N）有助于稳定$\beta$-W晶粒在膜沉积过程中，然后偏析到晶粒边界。这个过程导致电影相对原始的小$\beta$-W晶粒和晶界具有高浓度的O或N散射位点。这种组合提供了高自旋霍尔电导率和大电阻，从而导致了高自旋霍尔角。这项工作表明，在其他高自旋霍尔电导率材料中工程化晶界特性可以提供提高自旋霍尔角的有效方法。