Intrinsic spin Hall effect and orbital Hall effect in4dand5dtransition metals

Abstract

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 < 50µΩcm) 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 (n d = 9). On the other hand, the SHC takes a large negative value in Ta, Nb, W, and Mo where n d < 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 orbitronics device made of transition metals.

Systematic variation of spin-orbit coupling withd-orbital filling: Large inverse spin Hall effect in3dtransition metals

“…We note that V, Cr, and Ni with large θ SH sit directly above Ta, W, and Pt in the periodic table, respectively, which exhibit some of the largest θ SH . This suggests that the d-electron configuration of the transition metals plays a very important role in SHE, consistent with the prediction of Tanaka et al [27] who illuminated the role of the total number of 4d (5d) and 5s…”

Anisotropic intrinsic anomalous Hall effect in ordered3dPt alloys

“…9,10,13,14 Such a change of sign as a function of the Fermi level position within the spin subband has been also demonstrated from first-principles calculations of the spin Hall conductivity in Pt, 40 as well as from tight-binding calculations of the spin Hall conductivity in 4d and 5d transition metals. 41 Assuming that, in the latter cases, the spin-flip contribution to the spin Hall effect is negligible, 41 this results in corresponding sign changes of the σ ↓ Hall conductivity, discussed previously.…”

Study of spin pumping in Co thin film vis-à-vis seed and capping layers using ferromagnetic resonance spectroscopy

“…We cannot also rule out the effect of the phases of Co (hcp and fcc) as shown by Tokac et al [21]. Table II: The parameters evaluated from the fitting of experimental data of sample S1, S2, S3 and S4 using equation (2) [27]. However, when Pt is seed and/or capping layer the spin pumping efficiency increases e.g.…”