Giant enhancement of the intrinsic spin Hall conductivity in β-tungsten via substitutional doping

A key challenge in manipulating the magnetization in\nheavy-metal/ferromagnetic bilayers via the spin-orbit torque is to identify\nmaterials that exhibit an efficient charge-to-spin current conversion. Ab\ninitio electronic structure calculations reveal that the intrinsic spin Hall\nconductivity (SHC) for pristine $\\beta$-W is about sixty percent larger than\nthat of $\\alpha$-W. More importantly, we demonstrate that the SHC of $\\beta$-W\ncan be enhanced via Ta alloying. This is corroborated by spin Berry curvature\ncalculations of W$_{1-x}$Ta$_x$ ($x$ $\\sim$ 12.5%) alloys which show a giant\nenhancement of spin Hall angle of up to $\\approx$ $-0.5$. The underlying\nmechanism is the synergistic behavior of the SHC and longitudinal conductivity\nwith Fermi level position. These findings, not only pave the way for enhancing\nthe intrinsic spin Hall effect in $\\beta$-W, but also provide new guidelines to\nexploit substitutional alloying to tailor the spin Hall effect in various\nmaterials.\n