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

• Published in: arXiv.org 2023-12
• Main Authors: Suresh, A, Soares, R D, Mondal, P, Santos Pires, J P, J M Viana Parente Lopes, Ferreira, Aires, Feiguin, A E, Plecháč, P, Nikolić, B K
• Format: Article
• Language: English
• Subjects: Angular momentum; Conduction electrons; Electron pulses; Electron spin; Entangled states; Ferromagnetism; Polarizers; Quantum entanglement; Quantum mechanics; Spin dynamics; Spin valves; Time dependence; Torque
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2210.06634

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.