Robustness and experimental observability of giant resonant spin transfer torque in atomically thin magnetic bilayer tunnel junctions

Cao, Tu, Xiao, and Yao (Chin. Phys. Lett. 37, 107201 (2020)) predicted that a van der Waals tunnel junction whose central region is two ferromagnetic monolayers separated by a nonmagnetic barrier acts as a magnetic Fabry–Pérot cavity: quantum-coherent multiple reflections of the tunneling electron between the two magnets amplify the damping-like spin transfer torque, giving a universal value $(\hbar/2)\tan(\theta/2)$ per transmitted electron over a broad resonance range and per-incidence torques far exceeding $\hbar/2$ near resonance. The prediction rests on idealized assumptions — fully coherent high-quality-factor resonances, spin-conserving nonmagnetic contacts free of Rashba spin–orbit coupling, a bias window overlapping the resonant bilayer bands, and no disorder or thermal smearing. The open problem is to determine quantitatively under which realistic conditions the cavity-amplified torque and the associated spin-filter and spin-pumping functionalities survive — specifically the effect of contact-induced Rashba spin depolarization, the operational bias range relative to the bonding/antibonding bands under detuning of the two wells, and disorder, coherence, and temperature thresholds — and to propose an experimental realization that could observe the giant per-incidence torque in a van der Waals heterostructure.

Background

Spin transfer torque (STT) is the torque exerted on a magnet's magnetization when a spin-polarized current passes through it: each electron exchanges up to $\hbar/2$ of angular momentum with the magnet, so in conventional magnetic tunnel junctions (MTJs, two ferromagnets separated by a nonmagnetic tunnel barrier, the workhorse of STT-MRAM) the damping-like torque per transmitted electron is bounded by $\hbar/2$. The damping-like component of the torque changes the angle $\theta$ between two magnetizations, while the field-like component rotates the pair about their common axis. Van der Waals (vdW) magnets are crystalline magnets that can be exfoliated to a single monolayer, such as the ferromagnetic insulator CrI3, which acts as a spin filter: electrons tunneling through a CrI3 monolayer emerge nearly fully spin-polarized, producing giant tunneling magnetoresistance in vdW tunnel devices. A double-barrier junction with two ferromagnetic monolayers separated by a nonmagnetic barrier realizes two coupled spin-polarized quantum wells whose bonding and antibonding states $\mathcal{E}_{\pm}(\mathbf{k})$ support resonant tunneling: between the well resonances the electron wavefunction undergoes multiple partial reflections, in close analogy to a photon bouncing between the mirrors of a cavity in cavity quantum electrodynamics. Cao, Tu, Xiao, and Yao showed that with this magnetic cavity geometry the multiple impacts of one electron on the two magnets transfer angular momentum repeatedly, so the damping-like torque per electron incidence can reach tens of $\hbar/2$ near resonance (about $15\,\hbar/2$ in their model calculation), and the torque per electron transmission takes a parameter-free universal value $(\hbar/2)\tan(\theta/2)$ across a broad energy range around the resonances — a regime impossible in conventional MTJs, whose total thickness exceeds the electron coherence length, and distinct from earlier resonant-tunneling torque schemes where the magnets sit outside the multi-reflection path so the per-electron torque stays bounded by $\hbar/2$. Rashba spin–orbit interaction is the momentum-dependent spin coupling arising at interfaces that break inversion symmetry, such as the contact between a nonmagnetic electrode and a magnetic monolayer; it can depolarize spins of electrons in the contacts. Spin pumping denotes the emission of a spin current out of a magnet whose magnetization precesses, and spin filtering the production of spin-polarized current by transmission through a magnet — both device functionalities harvest the transmitted or reflected spin current of the bilayer junction and are therefore sensitive to depolarization before readout. The original prediction was obtained in a clean, coherent, zero-temperature model with spin-conserving contacts, and its authors noted that contact Rashba depolarization, bias windows falling below the resonant band edges, detuning $\delta=E_1-E_2$ between the spin-polarized quantum-well levels of the two monolayers, and realistic disorder and temperature all degrade the effect quantitatively, while arguing that the torque itself, being driven by spin-unpolarized incidence and multiple scattering inside the cavity, should be comparatively robust.

Problem Statement

For a vdW double-barrier tunnel junction whose central region is two ferromagnetic monolayers (e.g., CrI3 monolayers) separated by a nonmagnetic barrier, in which coherent multiple reflections between the magnetic layers resonantly amplify the damping-like spin transfer torque — with per-transmission universal value $(\hbar/2)\tan(\theta/2)$ in $\theta$ (the angle between the magnetizations) and per-incidence torques $\gg\hbar/2$ near the bonding/antibonding resonances $\mathcal{E}_{\pm}(\mathbf{k})$ — determine quantitatively the conditions under which this giant torque and the associated spin-current harvesting functionalities survive realistic device conditions, and propose an experimental realization. Concretely, three linked questions, all of which a complete answer must address: (i) quantify contact-induced in-plane Rashba spin–orbit interaction in the nonmagnetic electrodes, the spin depolarization it causes in transmitted and reflected currents, and its impact — if any — on the cavity-amplified torque itself, on spin-filter efficiency, and on spin-pumping readout; (ii) determine the torque as a function of bias-window placement relative to the band edges of $\mathcal{E}_{\pm}(\mathbf{k})$ and detuning $\delta=E_1-E_2$ between the spin-polarized quantum-well levels of the two monolayers, including finite-temperature smearing of the window, and identify the operational bias range in which the per-transmission torque stays at or near the universal value; (iii) establish the disorder strength, phase-coherence length, resonance quality factor, and temperature thresholds that a realistic vdW heterostructure must meet for per-incidence torques exceeding $\hbar/2$ to be observable, together with an experimental protocol (device geometry, contact scheme, measurement and readout) capable of distinguishing the giant STT from Joule-heating and contact spin–orbit-torque artifacts.

References

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