Current-induced spin transfer torque in a Neeel domain wall in the

Current-induced spin transfer torque in a Neeel domain wall in the linear response theory
P. Baláž1, V. K. Dugaev2,3, J. Barnaś1,4
1
Department of Physics, Adam Mickiewicz University, ul. Umultowska 85, 61-614 Poznań, Poland
Department of Physics, Rzeszów University of Technology, Al. Powstańców Warszawy 6, 35-959 Rzeszów, Poland,
3
CFIF, Instituto Superior Tecnico, TU Lisbon, av. Rovisco Pais, 1049-001 Lisbon, Portugal
4
Institute of Molecular Physics, Polish Academy of Sciences, ul. M. Smoluchowskiego 17, 60-179 Poznań, Poland
2
Spin polarized current flowing through a material with a nonuniform magnetic texture transfers the spin
angular momentum to the local magnetic moments and creates spin accumulation around the magnetic
domain walls. As a result, the spin transfer torque is exerted on the localized magnetic moments and
induces domain wall dynamics. We have considered the problem of current-induced spin-torque in a
thick Neel magnetic domain wall in a ferromagnetic material. Making use of the adiabatic
approximation and the linear response theory we calculated the spin accumulation in the domain wall
and consequently we derived the expression for the adiabatic and non-adiabatic spin torque
components. Both components depend on both the exchange coupling of conduction electrons to the
magnetization and the current polarization. In addition, we derived the domain wall nonadiabaticity,
which is shown to be enhanced in the case of weak coupling of the conduction electrons to the
localized magnetic moments.