A model of the spin Hall effect in polycrystalline nonmagnetic metals

In this paper, we theoretically investigated the effect of the polycrystalline structure of metal samples on the magnitude of the spin Hall effect. The equation for the dynamics of the averaged over the crystallite momentum of the collectivized conduction electron in the crystalline field of a homogeneous and isotropic polycrystalline metal is obtained. Averaging the obtained equation over all randomly oriented crystallites resulted in an expression for the electric field of the spin Hall effect. It significantly depends on the form of the single-electron atomic radial wave function and on the Hall coefficient. The coefficients of the spin Hall effect for some metals of 3rd-6th periods are calculated. It is shown that the results for nonmagnetic d- and f-metals within the measurement error are consistent with the experimental data. The best match is observed for Pt, alpha-W, beta-W, Pd, Nb, Ag, Mo, Cu and Al. A discrepancy of less than 20% was obtained for Au, Ti, Mn. For the considered rare-earth metals (Lu, Ho, Dy, Gd) only for paramagnetic Lu the correspondence of calculation results and experimental data is obtained. For Ho, Dy, and Gd, which exhibit ferromagnetic and antiferromagnetic states at low temperatures, the discrepancy is more than 35%. Based on the obtained results, the limitations of the developed approach are formulated.

Automated summary

In this paper, the effect of the polycrystalline structure of metal samples on the spin Hall effect was investigated theoretically. The spin Hall effect coefficients were calculated for different metals, showing good agreement for nonmagnetic metals but discrepancies for rare-earth metals. The limitations of the developed approach were discussed.