Spin transport driven by an external electric field in uniform metallic ferromagnets with the spin-orbit interaction arising from random impurities is studied microscopically. Spin relaxation torque T is shown to be written by spatial derivatives of the electric field, but with anisotropy arising from the magnetization. The field-driven contribution of the spin current is also anisotropic. The diffusive spin current is shown to be written as a gradient of the spin chemical potential, and the linear-response expression for the spin chemical potential is derived. It is discussed that the β term in the spin-transfer torque can also be anisotropic.
Physical Review B
- Pub Date:
- July 2010
- General formulation of transport theory;
- Spin relaxation and scattering;
- Condensed Matter - Mesoscale and Nanoscale Physics
- Phys. Rev. B 82, 014403 (2010)