Theory of spin relaxation torque in metallic ferromagnets

@article{Nakabayashi2010TheoryOS,
  title={Theory of spin relaxation torque in metallic ferromagnets},
  author={Noriyuki Nakabayashi and Akihito Takeuchi and Kazuhiro Hosono and Katsuhisa Taguchi and Gen Tatara},
  journal={Physical Review B},
  year={2010},
  volume={82},
  pages={014403}
}
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 $\beta$ term in the spin transfer… 

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