The standard theoretical picture of magnetization dynamics driven by the conventional Slonczewski-Berger spin transfer torque (STT) or spin-orbit torque is based on quantum transport theory of noninteracting electrons. This allows us to computing the torque, which is then fed into the Landau-Lifshitz-Gilbert equation for time evolution of magnetization viewed as a classical vector of fixed length. However, this approach cannot explain recently discovered quantum STT [1] in spin valves at ultralow temperature. The conventional STT occurs only when spin-polarization of injected electrons and localized spins within a ferromagnet are noncollinear. Conversely, quantum STT occurs when these vectors are collinear but antiparallel, thereby requiring a fully quantum treatment of both electrons and localized spins. We have recently introduced [2] time-dependent density matrix renormalization group (tDMRG) as a fully quantum framework for STT, and applied it to understand how quantum STT can lead to magnetization reversal. This talk will overview pedagogically standard description of torque in spin valves [3], van der Waals heterostructures [4] of two-dimensional magnetic materials and magnetic domain walls [5], and then proceed to show how tDMRG simulates time evolution of a many-body quantum state of electrons and localized spins. The quantum STT can reverse the direction of localized spins, but without rotatation from the initial state. Such nonclassical reversal is always highly inhomogeneous across the ferromagnet and accompanied by reduction of the magnetization associated with localized spins, even to zero at specific locations. This is because quantum STT driven nonequilibrium dynamics generates highly entangled nonequilibrium many-body state of all flowing and localized spins, despite starting from initially separable quantum state of a mundane ferromagnet, thereby leading to true decoherence of each localized spin subsystem. The global entanglement growth differentiates between quantum and conventional STT since in the former case it nearly reaches the maximum possible value. 

[1] A. Zholud, R. Freeman, R. Cao, A. Srivastava, and S. Urazhdin, Spin transfer due to quantum magnetization fluctuations, Phys. Rev. Lett. 119, 257201 (2017).
[2] M. D. Petrović, A. E. Feiguin, P. Plecháč, and B. K. Nikolić, Spintronics meets time-dependent density matrix renormalization group: Nonclassical magnetization reversal and global entanglement growth due to current-pulse-driven quantum spin torque, https://arxiv.org/abs/2002.04655.
[3] B. K. Nikolić, K. Dolui, M. Petrović, P. Plecháč, T. Markussen, and K. Stokbro, First-principles quantum transport modeling of spin-transfer and spin-orbit torques in magnetic multilayers, Chapter of Handbook of Materials Modeling, Volume 2 Applications: Current and Emerging Materials (Springer, Cham, 2018); https://arxiv.org/abs/1801.05793.
[4] K. Dolui, M. D. Petrović, K. Zollner, P. Plecháč, J. Fabian and B. K. Nikolić, Proximity spin-orbit torque on a two-dimensional magnet within van der Waals heterostructure: Current-driven antiferromagnet-to-ferromagnet reversible nonequilibrium phase transition in bilayer CrI3, Nano Lett. 20, 2288 (2020).
[5] M. D. Petrović, P. Plecháč, and B. K. Nikolić, Annihilation of topological solitons in magnetism: How domain walls collide and vanish to burst spin waves and pump electronic spin current of broadband frequencies, https://arxiv.org/abs/1908.03194.