Large intrinsic spin Hall conductivity in orthorhombic tungsten

In this paper, we explored metastable phases showing large intrinsic spin Hall conductivity (SHC) in bulk tungsten (W) using a crystal structure search scheme based on an evolutionary algorithm (EA) and first-principles calculations. W has been known to have the most stable phase with the body-centered-cubic (bcc) structure (alpha-W) and the metastable phase with a cubic Pm (3) over barn structure (beta-W), the latter of which shows larger SHC in beta-W. Through the EA search, we obtained 15 metastable structures in addition to alpha-W and beta-W and found that orthorhombic Fddd and Cmcm structures show larger SHC at the Fermi level. The Fddd structure is formed by adding a fourfold helical distortion along the [110] direction to bcc and the Cmcm structure is obtained by further distortion of Fddd. Although the energies are higher by about 300 meV/atom than that of bcc, the SHC values at the Fermi level are 1710 ((h) over bar /e)( Omega cm)(-1) for Fddd and 1573 ((h) over bar /e)( Omega cm)(-1) for Cmcm, which are almost twice as large as that of a-W and exceed 1455 ( (h) over bar /e)( Omega cm)(-1) calculated for beta-W.