  Current-induced spin-transfer torques (STTs) have been studied in Fe, Co and
Ni domain walls (DWs) by the method based on the first-principles noncollinear
calculations of scattering wave functions expanded in the tight-binding
linearized muffin-tin orbital (TB-LMTO) basis. The results show that the
out-of-plane component of nonadiabatic STT in Fe DW has localized form, which
is in contrast to the typical nonlocal oscillating nonadiabatic torques
obtained in Co and Ni DWs. Meanwhile, the degree of nonadiabaticity in STT is
also much greater for Fe DW. Further, our results demonstrate that compared to
the well-known first-order nonadiabatic STT, the torque in the third-order
spatial derivative of local spin can better describe the distribution of
localized nonadiabatic STT in Fe DW. The dynamics of local spin driven by this
third-order torques in Fe DW have been investigated by the
Landau-Lifshitz-Gilbert (LLG) equation. The calculated results show that with
the same amplitude of STTs the DW velocity induced by this third-order term is
about half of the wall speed for the case of the first-order nonadiabatic STT.
