Giant orbital Hall effect and orbital-to-spin conversion in 3d , 5d , and 4f metallic heterostructures

Abstract

The orbital Hall effect provides an alternative means to the spin Hall effect to convert a charge current into a flow of angular momentum. Recently, compelling signatures of orbital Hall effects have been identified in $3d$ transition metals. Here, we report a systematic study of the generation, transmission, and conversion of orbital currents in heterostructures comprising $3d$, $5d$, and $4f$ metals. We show that the orbital Hall conductivity of Cr reaches giant values of the order of $5\ifmmode\times\else\texttimes\fi{}{10}^{5}$ $[\frac{\ensuremath{\hbar}}{2e}]$ ${\mathrm{\ensuremath{\Omega}}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{m}}^{\ensuremath{-}1}$ and that Pt presents a strong orbital Hall effect in addition to the spin Hall effect. Measurements performed as a function of thickness of nonmagnetic Cr, Mn, and Pt layers and ferromagnetic Co and Ni layers reveal how the orbital and spin currents compete or assist each other in determining the spin-orbit torques acting on the magnetic layer. We further show how this interplay can be drastically modulated by introducing $4f$ spacers between the nonmagnetic and magnetic layers. Gd and Tb act as very efficient orbital-to-spin current converters, boosting the spin-orbit torques generated by Cr by a factor of 4 and reversing the sign of the torques generated by Pt. To interpret our results, we present a generalized drift-diffusion model that includes both spin and orbital Hall effects and describes their interconversion mediated by spin-orbit coupling.