  We develop a time-dependent nonequilibrium Green function (NEGF) approach to
the problem of spin pumping by precessing magnetization in one of the
ferromagnetic layers within F/I/F magnetic tunnel junctions (MTJs) or F/I/N
semi-MTJs in the presence of intrinsic Rashba spin-orbit coupling (SOC) at the
F/I interface or the extrinsic SOC in the bulk of F layers of finite thickness
(F-ferromagnet; N-normal metal; I-insulating barrier). To express the
time-averaged pumped charge current, or the corresponding dc voltage signal in
open circuits that was measured in recent experiments on semi-MTJs [T. Moriyama
et al., Phys. Rev. Lett. 100, 067602 (2008)], we construct a novel solution for
the double-time-Fourier-transformed NEGFs. The two energy arguments of NEGFs in
this representation are connected by the Floquet theorem describing multiphoton
emission and absorption processes. Within this fully quantum-mechanical
treatment of the conduction electrons, we find that: (i) only in the presence
of the interfacial Rashba SOC the non-zero dc pumping voltage in F/I/N semi-MTJ
can emerge at the adiabatic level (i.e., proportional to microwave frequency);
(ii) a unique signature of this charge pumping phenomenon, which disappears if
Rashba SOC is not located with the precessing F layer, is dc pumping voltage
that changes sign as the function of the precession cone angle; (iii) unlike
standard spin pumping in the absence of SOCs, where one emitted or absorbed
microwave photon is sufficient to match the exact solution in the frame
rotating with the magnetization, the presence of the Rashba SOC requires to
take into account up to ten photons in order to reach the asymptotic value of
pumped charge current; (iv) disorder within F/I/F MTJs can enhance the dc
pumping voltage in the quasiballistic transport regime; ...
