Spin relaxation torque in metallic ferromagnets

Spin relaxation torque ${\cal T}$ in uniform metallic ferromagnets with the spin-orbit interaction arising from random impurities is calculated microscopically. ${\cal T}$ is shown to be written by spatial derivatives of the electric field, but is not always given as a divergence of a torque dipole density. The result is due to the fast dissipation of the orbital angular momentum, and thus a conserving spin current cannot be defined. It is discussed that the $β$ term in the spin transfer torque can also be asymmetric.

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