Electron-mediated entanglement of two distant macroscopic ferromagnets within a nonequilibrium spintronic device*

Using the nascent concept of quantum spin-transfer torque, we predict that a charge current pulse can be harnessed to entangle two spatially separated ferromagnets (FMs) within a spin-valve. The injection of a current pulse endows the spin-valve system with rich nonequilibrium dynamics, where a quantum superposition of many-body states places the spatially separated FM layers into a mixed entangled state. This is due to a transfer of spin angular momentum from conduction electrons to the localized spins via quantum spin-transfer torque that remains active even for collinear but antiparallel arrangements of the two FMs. The dynamical build-up of mixed-state entanglement between the FM layers is quantified by calculating the mutual logarithmic negativity, entanglement entropy, and mutual information over time via fully quantum many-body approaches. The effect of decoherence on our scheme, the use of multi-electron pulses, and the scaling with system size are also analyzed to ascertain the robustness of our predictions under realistic experimental conditions. Finally, we propose a "current-pump/X-ray-probe" scheme, utilizing ultrafast X-ray spectroscopy, which can witness nonequilibrium entanglement of the FM layers by extracting their time-dependent quantum Fisher information.