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We study spin accumulation and spin transfer torque in a domain wall bysolving the Boltzmann equation with a diffusion approximation. We obtained theanalytical expressions of spin accumulation and spin transfer torque. Both theadiabatic and the non-adiabatic components of the spin transfer torqueoscillate with the thickness of the domain wall. We show that the oscillationplays a dominant role in the non-adiabatic torque when the domain wallthickness is less than the spin-flip length, which is defined by the product ofthe Fermi velocity and the spin-flip scattering time.

Theory of spin accumulation and spin transfer torque in a magnetic domain wall