  The key concept in spintronics of current-driven noncollinear magnetic
textures, such as magnetic domain walls (DWs), is adiabaticity, i.e., how
closely electronic spins track classical localized magnetic moments (LMMs) of
the texture. When mistracking occurs nonadiabatic effects arise, the salient of
which is nonadiabatic spin transfer torque (STT) where spin angular momentum is
exchanged between electrons and LMMs to cause their dynamics and enable DW
motion without any current threshold. The microscopic mechanisms behind
nonadiabatic STT have been debated theoretically for nearly two decades, but
with unanimous conclusion that they should be significant only in narrow DWs.
However, this contradicts sharply experiments [O. Boulle {\em et al.}, Phys.
Rev. Lett. {\bf 101}, 216601 (2008); C. Burrowes {\em et al.}, Nat. Phys. {\bf
6}, 17 (2010)] observing nonadiabatic STT in DWs much wider than putatively
relevant $\sim 1$ nm scale, as well as largely insensitive to further
increasing the DW width $w$. Here we employ time-dependent quantum transport
for electrons to obtain both nonadiabatic and adiabatic STT from the exact
nonequilibrium density matrix and its lowest order as adiabatic density matrix
defined by assuming that LMMs are infinitely slow. This allows us to
demonstrate that our microscopically, and without any simplifications of prior
derivations like effectively static DW, extracted nonadiabatic STT: (i) does
not decay, but instead saturates at a finite value, with increasing $w$ of a
moving DW ensuring entry into the adiabatic limit, which we characterize by
showing that electronic spins do not reflect from the static DW in this limit;
and (ii) it has both out-of-DW-plane, as is the case of phenomenological
expression widely used in the LLG equation, and in-plane components, where the
former remains finite with increasing $w$.
