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

We studied the spin accumulation and spin-transfer torque in a magnetic domain wall by solving the Boltzmann equation for spin accumulation with the diffusion approximation. We obtained analytical expressions of spin accumulation and spin-transfer torque. Both the adiabatic and the nonadiabatic components of the spin-transfer torque oscillate with the thickness of the domain wall. We showed that the oscillating component plays a dominant role in the nonadiabatic torque when the domain wall is thinner than the spin-flip length. We also showed that the magnitude of the nonadiabatic torque is inversely proportional to the thickness of the domain wall.