Orbital Hall effect in transition metals from first-principles scattering calculations
Max Rang, Paul J. Kelly
Abstract
We use first-principles scattering calculations based upon wave-function matching and implemented with a tight-binding muffin-tin orbital basis to evaluate the orbital Hall conductivity ${\ensuremath{\sigma}}_{\mathrm{oH}}$ for Ti, V, Cr, Cu, and Pt metals with temperature-induced lattice disorder. Only interatomic fluxes of orbital angular momentum are included in these estimates; intra-atomic fluxes, which do not contribute to the transfer of angular momentum are explicitly excluded. The resistivity and orbital Hall angle are both found to be linear in temperature so ${\ensuremath{\sigma}}_{\mathrm{oH}}$ is at most weakly temperature dependent. The value of ${\ensuremath{\sigma}}_{\mathrm{oH}}$ we obtain for bulk Cr is $\ensuremath{\approx}2\ifmmode\times\else\texttimes\fi{}{10}^{3}(\ensuremath{\hbar}/e)\phantom{\rule{0.16em}{0ex}}{(\mathrm{\ensuremath{\Omega}}\phantom{\rule{0.222222em}{0ex}}\mathrm{cm})}^{\ensuremath{-}1}$, which is substantially lower than previously obtained theoretical results (but in better agreement with values extracted from experiment). In units of ${10}^{3}(\ensuremath{\hbar}/e){(\mathrm{\ensuremath{\Omega}}\phantom{\rule{0.222222em}{0ex}}\mathrm{cm})}^{\ensuremath{-}1}$, the values obtained for Ti, V, and Pt are 5, 6, and 7, respectively.