Topological nature of the proper spin current and the spin-Hall torque

Abstract

Spin currents are key to spin torque devices, but determining the proper spin current is non-trivial. Here we derive a general quantum-mechanical formula for the intrinsic proper spin current showing that it is topological and can be finite in the gap. For topological insulators with an out of plane magnetization and the chemical potential in the surface state gap, the net spin torque is determined by the competition between the topological spin-Hall torque due to the bulk and the topological Edelstein effect due to the surface states. We also discuss spin-3/2 hole quantum wells.

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Cited by in corpus (10)

• Quantum geometry in condensed matter
• Orbital angular momentum of Bloch electrons: equilibrium formulation, magneto-electric phenomena, and the orbital Hall effect
• Spin-Hall effect due to the bulk states of topological insulators: Extrinsic contribution to the conserved spin current
• Spin-Hall effect in topological materials: Evaluating the proper spin current in systems with arbitrary degeneracies
• Giant orbital Hall effect due to the bulk states of 3D topological insulators
• Spin-orbit torques due to topological insulator surface states: an in-plane magnetization as a probe of extrinsic spin-orbit scattering
• Wannier interpolation of spin accumulation coefficient
• Formulation of spin Nernst effect for spin-nonconserving insulating magnets
• Orbital Hall effect in spin-3/2 hole-doped semiconductors and its implications for orbitronics
• Ge as an orbitronic platform: giant in-plane orbital magneto-electric effect in a 2-dimensional hole gas