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The key concept in spintronics of current-driven noncollinear magnetictextures, such as magnetic domain walls (DWs), is adiabaticity, i.e., howclosely electronic spins track classical localized magnetic moments (LMMs) ofthe texture. When mistracking occurs nonadiabatic effects arise, the salient ofwhich is nonadiabatic spin transfer torque (STT) where spin angular momentum isexchanged between electrons and LMMs to cause their dynamics and enable DWmotion without any current threshold. The microscopic mechanisms behindnonadiabatic STT have been debated theoretically for nearly two decades, butwith 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. {\bf6}, 17 (2010)] observing nonadiabatic STT in DWs much wider than putativelyrelevant $\sim 1$ nm scale, as well as largely insensitive to furtherincreasing the DW width $w$. Here we employ time-dependent quantum transportfor electrons to obtain both nonadiabatic and adiabatic STT from the exactnonequilibrium density matrix and its lowest order as adiabatic density matrixdefined by assuming that LMMs are infinitely slow. This allows us todemonstrate that our microscopically, and without any simplifications of priorderivations like effectively static DW, extracted nonadiabatic STT: (i) doesnot decay, but instead saturates at a finite value, with increasing $w$ of amoving DW ensuring entry into the adiabatic limit, which we characterize byshowing 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 phenomenologicalexpression widely used in the LLG equation, and in-plane components, where theformer remains finite with increasing $w$.

Wide ferromagnetic domain walls can host both adiabatic reflectionless  spin transport and finite nonadiabatic spin torque: A time-dependent quantum  transport picture