Orientational dependence of intrinsic orbital and spin Hall effects in hcp structure materials

We investigate the orientation dependence of the intrinsic orbital Hall effect (OHE) and spin Hall effect (SHE) in hexagonal close-packed (hcp) structure materials. The symmetry constraints of the hcp structure restrict the orbital (spin) current to the orbital (spin) Hall current. It also shows that there exist three symmetry-wise independent orientations in the hcp structure. We calculate the orbital Hall conductivity (OHC) and the spin Hall conductivity (SHC) of three hcp materials (Sc, Y, and Zr). We find that all these materials have sizable OHC, while the SHC is orders of magnitude smaller. Especially, the OHCs of Sc and Zr have significant orientation dependence, which may be employed to experimentally probe the OHE.