Orbital Hall currents across interfaces from first-principles scattering calculations

The magnetization of a ferromagnetic (FM) -nonmagnetic metal (NM) bilayer can be controlled electrically using the relativistic spin Hall effect to generate a current of spin angular momentum. To study such a system quantitatively, spin-dependent interface parameters like the spin-mixing conductance and spin memory loss need to be known. The orbital Hall effect introduces a current of angular momentum whose origin is nonrelativistic so elements other than the heavy metals need to be considered. Virtually nothing is known about the parameters describing orbital currents. Two systems are of interest: NM|heavy metal (HM) and NM|FM bilayers. In both cases, a current of orbital angular momentum is generated in NM. This is then injected into the HM or FM where spin-orbit coupling converts it into a spin current which then exerts a torque on the local ferromagnetic moment. Computing the orbital Hall conductivity for bulk systems is relatively straightforward but studying NM|HM and NM|FM interfaces requires large supercells making them computationally very demanding. A first-principles scattering formalism that has been used to determine the parameters governing spin-dependent transport has been extended to include orbital currents allowing us to study them in detail.