Double-Tunnel-Junction Structure

• Double-Tunnel-Junction Structure is a multilayer MTJ design that employs dual tunnel barriers, heavy metal spacers, and magnetic layers to generate coupled spin dynamics via RKKY and iDMI interactions.
• It leverages strong spin–orbit coupling from the heavy metal spacer to induce chiral spin textures and modulate both regular and chaotic oscillation regimes.
• The structure enables advanced applications such as MRAM, spin-torque oscillators, and magnonic logic by precisely controlling spin-transfer torque and damping parameters.

A double-tunnel-junction structure, in the context of advanced spintronic and magnetic tunnel junction (MTJ) devices, refers to an architecture where two tunnel barriers and multiple magnetic layers are arranged to create coupled spin-dynamic regimes, typically separated by heavy metal (HM) spacers. Such structures enable complex spin interactions including antiferromagnetic (AFM)–ferromagnetic (FM) coupling, enhanced spin–orbit effects, and tailored non-linear dynamics useful for next-generation magnetic memory, spin-torque oscillators (STOs), and magnonic applications. The discussion below synthesizes the detailed spin dynamics, governing interactions, and operational regimes as illuminated by SAFM|HM|FM double-barrier MTJ systems (Devi et al., 2023).

1. Structural Overview and Layer Composition

The canonical double-barrier MTJ structure studied is composed of three magnetic layers: a synthetic antiferromagnet (SAFM) serving as a reference, an HM spacer (typically providing strong spin–orbit coupling), and a ferromagnetic (FM) layer coupled to the SAFM. An additional ferromagnetic layer (FM₁) acts as a control or polarizing electrode. This arrangement leverages both the exchange coupling typical of standard MTJs and the additional complexity introduced by interlayer RKKY and Dzyaloshinskii–Moriya interactions (DMI).

• SAFM: Used as a reference layer with inherently low net magnetization but robust AFM ordering.
• HM Spacer: Provides large spin–orbit coupling (SOC) and is essential for inducing potent interfacial effects, such as DMI and field-like spin–orbit torques.
• FM Layer(s): The free and control layers can be tuned to provide desired switching properties, oscillation dynamics, and polarization channels.

The HM not only enhances SOC but also facilitates exchange interactions between FM and AFM (via RKKY), while promoting interfacial DMI at broken inversion symmetry locations.

2. Dominant Interactions: RKKY and Interfacial DMI

The fundamental spin dynamics within these double-barrier structures are governed by a balance between the RKKY interaction and interfacial Dzyaloshinskii–Moriya interaction (iDMI):

• RKKY (Ruderman–Kittel–Kasuya–Yosida) Interaction: Mediated by conduction electrons within the HM, this interaction couples AFM–FM or FM–FM layers, promoting parallel or antiparallel spin alignment (ferromagnetic or antiferromagnetic coupling).
• Interfacial DMI: Arises due to strong SOC and broken inversion symmetry at HM interfaces. This antisymmetric exchange induces chiral spin textures, supporting phenomena such as skyrmion formation or non-collinear magnetization.
• Spin–Orbit Coupling (SOC): The strength of SOC in the HM layer critically dictates the magnitude of both iDMI and additional field-like torques.

The device’s behavior is further modulated by external magnetic fields and spin-transfer torque (STT), typically induced by spin-polarized current injection through FM₁.

3. Spin Dynamics and Magnetization Regimes

The time evolution of the magnetization (FM) and AFM order parameter is governed by coupled Landau–Lifshitz–Gilbert–Slonczewski (LLGS) equations, explicitly incorporating damping (α_m, α_n), effective fields, and STT:

$$\begin{aligned} \dot{m} &= -\gamma m \times H_m - \alpha_m \dot{m} - n \times (\gamma H_n - \alpha_n \dot{n}) + T_\mathrm{STT}^m \ \dot{n} &= -m \times (\gamma H_n - \alpha_n \dot{n}) - n \times (\gamma H_m - \alpha_m \dot{m}) + T_\mathrm{STT}^n \end{aligned}$$

where $H_m$, $H_n$ are effective fields derived from an energy functional including anisotropy, iDMI, RKKY, external field, and exchange contributions.

A spectrum of dynamical regimes emerges depending on the relative strengths of RKKY and iDMI:

• Regular Oscillations: For $K_D < K_R$, i.e. weak iDMI, regular spin precession is observed at low STT. Increasing STT converts these to damped oscillations with rapid decay.
• Sustained and Periodic Oscillations: For $K_D \approx K_R$ (comparable iDMI and RKKY), moderate STT allows for robust, persistent oscillations. The system may initially exhibit chaotic trajectories but ultimately settles into periodic or aperiodic oscillation depending on STT and external fields.
• Self-Similar/Aperiodic Dynamics: Dominant iDMI ($K_D > K_R$) engenders intermittent, aperiodic, or chaotic oscillations, highly sensitive to STT perturbation and the presence/absence of additional interfacial fields (e.g., Néel field).

External SOC and magnetic fields further modulate decay times, periodicity, and transition points between these regimes. Notably, periodic oscillations dominate in RKKY-dominated systems under low fields; moderate-to-high fields are necessary for sustained oscillation in iDMI-dominated systems.

4. Mathematical Modelling and Bifurcation Phenomena

Detailed modeling utilizes coupled LLGS equations and their representation in polar coordinates (angles Θ, Φ). Fixed points and bifurcations of the dynamical system are investigated parametrically, with saddle-node bifurcation and chaos emerging under moderate N-type interfacial field and suitable combinations of STT, iDMI and RKKY.

The magnon dispersion is obtained via linearization of the LLGS equations, identifying optical and acoustic modes, with magnon lifetimes ($\tau$) enhanced by stronger iDMI. Damping matrices with off-diagonal ($\alpha_c$) components are analyzed for their impact on oscillatory decay and magnon relaxation.

5. Oscillation and Magnon Lifetime Characteristics

The device exhibits:

• Transition from regular to damped oscillations at increasing STT for weak iDMI.
• Sustained oscillations for matched iDMI and RKKY.
• Self-similar aperiodic or chaotic oscillations in iDMI-dominated systems, especially without additional N-type interfacial field.
• Control of decay times via SOC: longer lifetimes at moderate SOC, nonlinear characteristics arising with further SOC enhancement (dependent on iDMI/RKKY balance).
• Magnon lifetime enhancement by increasing iDMI for both optical and acoustic modes.

6. Applications, Implications, and Tuning Parameters

This class of double-barrier MTJ structures is well-suited for:

• Spin Torque Oscillators (STOs): Controlled nonlinear/chaotic oscillation regimes for microwave generation and neuromorphic systems.
• Magnonic Logic Devices: Tunable magnon lifetime for improved information encoding using spin waves.
• MRAM: Energy-efficient switching at reduced critical STT values with enhanced thermal stability due to HM-induced double-interface coupling.

Critical device parameters for regime control:

• STT magnitude: Drives transitions between oscillatory and chaotic regimes.
• SOC strength: Modulates decay times and introduces nonlinearity.
• External magnetic field: Sets threshold for oscillation periodicity and sustained behavior.
• iDMI/RKKY ratio: Principal determinant for oscillation type and bifurcation thresholds.

7. Future Directions

The theoretical framework suggests further work in:

• Experimental verification of predicted regimes (chaos, bifurcation, magnon lifetime).
• Thermal fluctuation/noise incorporation into the LLGS modeling, affecting stability and coherence.
• Device scaling to nanometric dimensions, evaluating thermal/electric stability.
• Exploration of multilayer/hybrid structures for enhanced dynamic tunability and circuit integration.
• Optimization of off-diagonal damping and iDMI to facilitate magnonic device operation.

In conclusion, SAFM|HM|FM double-barrier MTJ structures leverage strong interlayer coupling and interfacial phenomena (RKKY, iDMI, SOC) to engineer complex and controllable spin dynamics, essential for high-performance oscillators, magnonic logic, and advanced spintronic memory technologies (Devi et al., 2023).