Abstract
We introduce the time-dependent density matrix renormalization group (tDMRG) as a solution to a 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- 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 Landau-Lifshitz-Gilbert 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 feature arises 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. The growth in time of entanglement entropy differentiates between the quantum and conventional (i.e., noncollinear) setups for STT, reaching a much larger asymptotic value in the former case.
- Received 26 June 2020
- Revised 15 April 2021
- Accepted 28 April 2021
DOI:https://doi.org/10.1103/PhysRevX.11.021062
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
A typical electric current carries an equal number of electrons whose intrinsic angular momentum is either “spin-up” or “spin-down.” But in a spin-polarized current, one is more prevalent than the other. Passing a spin-polarized current through a thin magnet can flip the orientation of its magnetism. This spin-transfer torque effect is at the heart of much research in contemporary spintronics, which aims to use spins to transfer and store information much more efficiently than conventional electronics. And yet, a fully quantum-mechanical framework for describing spin-transfer torque has been lacking since its inception in the 1990s, relying instead on a quantum-classical “standard model.” Here, we introduce a numerical framework, adapted from strongly electron-correlated physics, which describes spin transfer between flowing electrons and local magnetization as a nonequilibrium quantum many-body effect.
The need for such a fully quantum theory of spin-transfer torque has been prompted by recent experiments at ultralow temperatures, where spins of flowing electrons and the local magnetization remain collinear, and the standard quantum-classical description predicts no net effect. Our time-dependent density-matrix-renormalization-group calculations unveil highly nonclassical magnetization reversal, accompanied by the dynamical transformation of a relatively trivial magnetic material into a long-range entangled quantum system, which is, therefore, also of great interest to quantum information science.
The same fully quantum-mechanical framework will be crucial to describe anticipated experiments on spin-current injection into exotic quantum matter or for manipulating spin-based qubits within a quantum computer by electric currents, where in all such cases the quantum-classical standard model is inapplicable from the outset.
