Theory of spin relaxation torque in metallic ferromagnets Noriyuki Nakabayashi, Akihito Takeuchi, Kazuhiro Hosono, Katsuhisa Taguchi, Gen Tatara Department of Physics, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397, Japan (Dated: November 1, 2018) 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. PACS numbers: 72.10.Bg 72.25.Rb 1 arXiv:1002.0207v2 [cond-mat.mes-hall] 28 Apr 2010 Abstract