  Using the nascent concept of quantum spin-transfer torque [A. Zholud et al.,
Phys. Rev. Lett. {\bf 119}, 257201 (2017); M. D. Petrovi\'{c} {\em et al.},
Phys. Rev. X {\bf 11}, 021062 (2021)], we demonstrate that a current pulse can
be harnessed to entangle quantum localized spins of two spatially separated
ferromagnets (FMs) which are initially unentangled. The envisaged setup
comprises a spin-polarizer (FM$_p$) and a spin-analyzer (FM$_a$) FM layers
separated by normal metal (NM) spacer. The injection of a current pulse into
the device leads to a time-dependent superposition of many-body states
characterized by a high degree of entanglement between the spin degrees of
freedom of the two distant FM layers. The non-equilibrium dynamics are due to
the transfer of spin angular momentum from itinerant electrons to the localized
spins via a quantum spin-torque mechanism that remains active even for {\em
collinear but antiparallel} arrangements of the FM$_p$ and FM$_a$
magnetizations (a situation in which the conventional spin-torque is absent).
We quantify the mixed-state entanglement generated between the FM layers by
tracking the time-evolution of the full density matrix and analyzing the
build-up of the mutual logarithmic negativity over time. The effect of
decoherence and dissipation in the FM layers due to coupling to bosonic baths
at finite temperature, the use of multi-electron current pulses and the
dependence on the number of spins are also considered in an effort to ascertain
the robustness of our predictions under realistic conditions. Finally, we
propose a ``current-pump/X-ray-probe'' scheme, utilizing ultrafast X-ray
spectroscopy, that can witness nonequilibrium and transient entanglement of the
FM layers by extracting its time-dependent quantum Fisher information.
