Quantum spin transfer torque induced nonclassical magnetization dynamics and electron-magnetization entanglement

Abstract

The standard spin-transfer torque (STT)-where spin-polarized current drives dynamics of magnetization viewed as a classical vector-requires noncollinearity between electron spins carried by the current and magnetization of a ferromagnetic layer. However, recent experiments [A. Zholud et al., Phys. Rev. Lett. 119, 257201 (2017)] observing magnetization dynamics in spin valves at cryogenic temperatures, even when electron spin is collinear to magnetization, point at overlooked quantum effects in STT which can lead to highly nonclassical magnetization states. Using fully quantum many-body treatment, where an electron injected as spin-polarized wave packet interacts with local spins comprising the anisotropic quantum Heisenberg ferromagnetic chain, we define quantum STT as any time evolution of local spins due to initial many-body state not being an eigenstate of electron+local-spins system. For time evolution caused by injected spin-↓ electron scattering off local ↑-spins, entanglement between electron subsystem and local spins subsystem takes place leading to decoherence and, therefore, shrinking of the total magnetization but without rotation from its initial orientation which explains the experiments. Furthermore, the same processes-entanglement and thereby induced decoherence-are present also in standard noncollinear geometry, together with the usual magnetization rotation. This is because STT in quantum many-body picture is caused only by electron spin-↓ factor state, and the only difference between collinear and noncollinear geometries is in relative size of the contribution of the initial separable state containing such factor state to superpositions of separable many-body quantum states generated during time evolution.The standard spin-transfer torque (STT) [1], predicted in the seminal work of Slonczewski [2] and Berger [3], is a phenomenon where a flux of spin-polarized electrons injected into a ferromagnetic metal (FM) layer drives its magnetization dynamics. The origin of STT is transfer of spin angular momentum from electrons to local magnetic moments of the FM layer, so it is fundamentally a nonequilibrium quantum many-body physics effect. Nevertheless, local magnetic moments are typically treated as classical vectors of fixed length [1, 4] whose dynamics is governed by the Landau-Lifshitz-Gilbert (LLG) equation [5] extended by adding the STT term [6][7][8] T ∝ ŝ e × S(r).(1)Thus, the nonequilibrium spin density ŝ e caused by flowing electrons must be noncollinear to the direction of local spin S(r) [i.e., to the local magnetization proportional to local spin], to drive magnetization dynamics in such a classical picture. The dynamics can include oscillations or complete reversal, whose conversion into resistance variations has emerged as a key resource for next generation spintronic technologies, such as nonvolatile magnetic random access memories, microwave oscillators, microwave detectors, spin-wave emitters, memristors and artificial neural networks [9][10][11].For example, passing current through ...

Quantum many-body states and Green functions of nonequilibrium electron-magnon systems: Localized spin operators vs. their mapping to Holstein-Primakoff bosons

“…Instead, current-driven magnetization reversal due to spin torque [43] is standardly modeled by the LLG equation [44], which can be combined in multiscale fashion with steady-state [45] or time-dependent quantum transport calculations [46][47][48][49][50][51][52] considering single-particle quantum Hamiltonians for electrons. However, such hybrid quantum-classical theories, which treat electrons quantum-mechanically and employ classical dynamics of localized spins via the LLG equation, are justified only in the limit of very large localized spins S → ∞ and → 0 (while S × → 1) [3,51], as well as in the absence of entanglement [3,53,54] between quantum states of localized spins. For example, in the emerging concept of quantum spin torque [53][54][55][56][57], describing transfer of angular momentum between spins of flowing electrons and localized spins in situations [58] where the latter must be described by quantum-mechanical operators, the whole system of electrons and localized spins must be described by a quantum many-body Hamiltonian [as exemplified by Eqs.…”

Effects of the dynamical magnetization state on spin transfer

“…We consider an electron initially propagating in a nonmagnetic medium, and subsequently scattered by a ferromagnet (FM) modeled as a chain of n = 10 localized spins-1/2. In the tight-binding approximation, this system can be described by the Hamiltonian [23,30]…”

“…In the semiclassical approximation, the magnitude of magnetization in ferromagnets is fixed, so ST is forbidden by angular momentum conservation if the electron is spin-polarized collinearly with the magnetic order. However, recent experimental measurements [20,21] and theoretical studies [22][23][24][25][26] revealed a contribution to ST, termed the quantum ST, which persists in the collinear geometry. In ferromagnets, this effect becomes noticeable only at cryogenic temperatures.…”

“…Theoretical studies have shown that ST leads to quantum entanglement between conduction electrons and magnetization [23,25], and can also mediate entanglement within the magnetic system [26], with possible applications in quantum information technologies [28,29]. Furthermore, it was shown that the conservation of the total energy and linear momentum of the quasiparticles involved in ST, the electrons and the magnons, can impose substantial constraints on the magnetization dynamics induced by ST, and on scattering of electrons by magnetic systems [30].…”

From MTJ Device to Hybrid CMOS/MTJ Circuits: A Review

“…Much research on STT induced magnetization dynamics has been reported from time to time [102,[105][106][107][108][109]. Magnetization dynamics of both iMTJ and pMTJ can be easily understand using the LLGS equation.…”