2007/11/30 by T. Tanaka, H. Kontani, M. Naito +4 · 2 citations
Physics and Astronomy · #cond-mat.str-el #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevb.77.165117
published as PRB 77, 165117 (2008) · 17 pages, 12 figures, 3 tables, resubmitted to Physical Review B
arxiv created 2008/02/26 · arxiv updated 2009/12/01
We study the intrinsic spin Hall conductivity (SHC) in various 5d-transition metals (Ta, W, Re, Os, Ir, Pt, and Au) and 4d-transition metals (Nb, Mo, Tc, Ru, Rh, Pd, and Ag) based on the Naval Research Laboratory tight-binding model, which enables us to perform quantitatively reliable analysis. In each metal, the obtained intrinsic SHC is independent of resistivity in the low resistive regime (ρ< 50 μΩcm) whereas it decreases in proportion to ρ-2 in the high resistive regime. In the low resistive regime, the SHC takes a large positive value in Pt and Pd, both of which have approximately nine d-electrons per ion (nd=9). On the other hand, the SHC takes a large negative value in Ta, Nb, W, and Mo where nd<5. In transition metals, a conduction electron acquires the trajectory-dependent phase factor that originates from the atomic wavefunction. This phase factor, which is reminiscent of the Aharonov-Bohm phase, is the origin of the SHC in paramagnetic metals and that of the anomalous Hall conductivity in ferromagnetic metals. Furthermore, each transition metal shows huge and positive d-orbital Hall conductivity (OHC), independently of the strength of the spin-orbit interaction (SOI). Since the OHC is much larger than the SHC, it will be possible to realize a \it orbitronics device made of transition metals.