Orbital Hall effect in transition metals from first-principles scattering calculations

We use first-principles scattering calculations based upon wave-function matching and implemented with a tight-binding MTO basis to evaluate the orbital Hall conductivity \(\sigma_{\rm oH}\) 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; intraatomic 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 \(\sigma_{\rm oH}\) is at most weakly temperature dependent. The value of \(\sigma_{\rm oH}\) we obtain for bulk Cr is \( \approx 2 \times 10^3 (\hbar/e) \, (\Omega \, {\rm cm})^{-1}\) which is substantially lower than previously obtained theoretical results but agrees well with experiment. In units of \(10^3 (\hbar/e) (\Omega \, {\rm cm})^{-1}\), the values obtained for Ti, V and Pt are \(5\), \(6\) and \(7\), respectively.