Abstract
The spin Hall angle (SHA) is a measure of the efficiency with which a transverse spin current is generated from a charge current by the spin-orbit coupling and disorder in the spin Hall effect (SHE). In a study of the SHE for a Pt|Py (Py=Ni_{80}Fe_{20}) bilayer using a first-principles scattering approach, we find a SHA that increases monotonically with temperature and is proportional to the resistivity for bulk Pt. By decomposing the room temperature SHE and inverse SHE currents into bulk and interface terms, we discover a giant interface SHA that dominates the total inverse SHE current with potentially major consequences for applications.
Highlights
The spin Hall effect (SHE) refers to the generation of a transverse spin current by an electrical current flowing in a conductor [1,2,3]
The spin Hall angle (SHA) is a measure of the efficiency with which a transverse spin current is generated from a charge current by the spin-orbit coupling and disorder in the spin Hall effect (SHE)
By decomposing the room temperature SHE and inverse SHE currents into bulk and interface terms, we discover a giant interface SHA that dominates the total inverse SHE current with potentially major consequences for applications
Summary
We develop a first-principles computational scheme to calculate local longitudinal and transverse currents in a scattering geometry and apply it to the study of the SHE in pure “bulk” Pt and in a PyjPt bilayer (Py 1⁄4 Ni80Fe20). From the PyjPt bilayer calculations we extract a value of the SHA for bulk Pt that is consistent with the pure, bulk value, while the interface makes a significant contribution to both the SHE and ISHE that should be taken into account in interpreting experiments. To study the SHE, we calculate the local longitudinal and transverse charge and spin current densities in the scattering region so that both intrinsic and extrinsic contributions are naturally included. Electron and spin current densities are obtained as expectation values of the velocity operator v 1⁄4 1⁄2R ; H =ðiħÞ [35,36] and evaluated using the Hamiltonian matrix H RR0 for real-space TB LMTOs and the position operator R RR0 1⁄4 RδRR0 where R
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