Abstract
We introduce time-dependent density matrix renormalization group (tDMRG) as a solution to long standing problem in spintronics -- how to describe spin-transfer torque (STT) between flowing spins of conduction electrons and localized spins within a magnetic material by treating the dynamics of both spin species fully quantum-mechanically. In contrast to conventional Slonczewski-Berger STT, where the localized spins are viewed as classical vectors obeying the Landau-Lifshitz-Gilbert equation and where their STT-driven dynamics is initiated only when the spin-polarization of flowing electrons and localized spins are noncollinear, quantum STT can occur when these vectors are collinear but antiparallel. Using tDMRG, we simulate the time evolution of a many-body quantum state of electrons and localized spins, where the former are injected as a spin-polarized current pulse while the latter comprise a quantum Heisenberg ferromagnetic metallic (FM) spin-$\frac{1}{2}$ XXZ chain initially in the ground state with spin-polarization antiparallel to that of injected electrons. The quantum STT reverses the direction of localized spins, but without rotation from the initial orientation, when the number of injected electrons exceeds the number of localized spins. Such nonclassical reversal, which is absent from LLG dynamics, is strikingly inhomogeneous across the FM chain and it can be accompanied by reduction of the magnetization associated with localized spins, even to zero at specific locations. This is because quantum STT generates a highly entangled nonequilibrium many-body state of all flowing and localized spins, despite starting from the initially unentangled ground state of a mundane FM. Furthermore, the mutual information between localized spins at the FM edges remains nonzero even at infinite separation as the signature of dynamical buildup of long-range entanglement.
Highlights
The conventional spin-transfer torque (STT) has been at the forefront of basic [1] and applied [2] research in spintronics since the seminal theoretical predictions of Slonczewski [3] and Berger [4] and its experimental confirmations, initially in spin valves [5,6,7] and later in magnetic tunnel junctions [8,9,10]
We introduce the time-dependent density matrix renormalization group as a solution to a longstanding problem in spintronics—how to describe spin-transfer torque (STT) between flowing spins of conduction electrons and localized spins within a magnetic material by treating the dynamics of both spin species fully quantum mechanically
Using time-dependent density matrix renormalization group (tDMRG), we simulate the time evolution of a many-body quantum state of electrons and localized spins, where the former are injected as a spin-polarized current pulse while the latter comprise a quantum Heisenberg ferromagnetic metallic (FM) spin-12 XXZ chain initially in the ground state with spin polarization antiparallel to that of injected electrons
Summary
The conventional spin-transfer torque (STT) has been at the forefront of basic [1] and applied [2] research in spintronics since the seminal theoretical predictions of Slonczewski [3] and Berger [4] and its experimental confirmations, initially in spin valves [5,6,7] and later in magnetic tunnel junctions [8,9,10]. We introduce the adaptive time-dependent density matrix renormalization group (tDMRG) [44,45,46,47,48] as a numerical framework capable of describing quantum and conventional STT on the same footing Since this simulation method works directly with the original quantummechanical operators of the localized spins, it can capture reversal of localized spins due to STT which is highly sought in spintronic applications [1,2,22,24]. By removing the confining potential for times t ≥ 0, electrons spread into the region of the localized FM moments, as illustrated, simulated, and animated in the tDMRGcomputed movie in Supplemental Material [18] This protocol mimics injection of a spin-polarized current pulse often employed in STT-operated spintronic devices [1,2,22,24].
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