Large intrinsic spin Hall conductivity in orthorhombic tungsten

Abstract

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 $(\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{W})$ and the metastable phase with a cubic $Pm\overline{3}n$ structure $(\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{W})$, the latter of which shows larger SHC in $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{W}$. Through the EA search, we obtained 15 metastable structures in addition to $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{W}$ and $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{W}$ 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 (${\ensuremath{\hbar}/e)(\mathrm{\ensuremath{\Omega}}\phantom{\rule{0.16em}{0ex}}\mathrm{cm})}^{\ensuremath{-}1}$ for $Fddd$ and 1573 (${\ensuremath{\hbar}/e)(\mathrm{\ensuremath{\Omega}}\phantom{\rule{0.16em}{0ex}}\mathrm{cm})}^{\ensuremath{-}1}$ for $Cmcm$, which are almost twice as large as that of $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{W}$ and exceed 1455 (${\ensuremath{\hbar}/e)(\mathrm{\ensuremath{\Omega}}\phantom{\rule{0.16em}{0ex}}\mathrm{cm})}^{\ensuremath{-}1}$ calculated for $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{W}$.