  We propose an electrically driven spin injector into normal metals and
semiconductors, which is based on a magnetic tunnel junction (MTJ) subjected to
a microwave voltage. Efficient functioning of such an injector is provided by
electrically induced magnetization precession in the "free" layer of MTJ, which
generates the spin pumping into a metallic or semiconducting overlayer. We
theoretically describe the spin and charge dynamics in the
CoFeB/MgO/CoFeB/Au(GaAs) heterostructures. First, the magnedynamics in the free
CoFeB layer is quantified with the account of a spin-transfer torque and a
voltage-controlled magnetic anisotropy. By numerically solving the
magnetodynamics equation, we determine dependences of the precession amplitude
on the frequency $f$ and magnitude $V_\mathrm{max}$ of the ac voltage applied
to the MTJ. It is found that the frequency dependence changes drastically above
the threshold amplitude $V_\mathrm{max} \approx 200$mV, exhibiting a break at
the resonance frequency $f_\mathrm{res}$ due to nonlinear effects. The results
obtained for the magnetization dynamics are used to describe the spin injection
and pumping into the Au and GaAs overlayers. Since the generated spin current
creates additional charge current owing to the inverse spin Hall effect, we
also calculate distribution of the electric potential in the thick Au
overlayer. The calculations show that the arising transverse voltage becomes
experimentally measurable at $f = f_\mathrm{res}$. Finally, we evaluate the
spin accumulation in a long n$^+$-GaAs bar coupled to the MTJ and determine its
temporal variation and spatial distribution along the bar. It is found that the
spin accumulation under resonant excitation is large enough for experimental
detection even at micrometer distances from the MTJ. This result demonstrates
high efficiency of the described nanoscale spin injector.
