Spin-orbit torque (SOT)-mediated magnetization switching is crucial for developing high-performance SOT magnetoresistive random access memory (SOT-MRAM). SOT-MRAM offers advantages over spin-transfer torque MRAM, including faster write speed, lower write energy, and higher endurance. A typical SOT-MRAM cell incorporates a magnetic tunnel junction (MTJ) atop a heavy metal layer. An in-plane charge current generates a perpendicular spin current via the spin Hall effect (SHE), which then switches the magnetization of the overlaying magnetic layer. While SOT can switch both perpendicular and in-plane magnetization, perpendicular switching is preferred for SOT-MRAM due to its speed and scalability. However, conventional SOT-mediated perpendicular switching usually necessitates an in-plane bias magnetic field, which is undesirable due to reduced thermal stability and potential crosstalk between cells. Several methods have been proposed to achieve field-free SOT-mediated perpendicular magnetization switching. These include creating asymmetric multilayer stacks (e.g., thickness gradients), introducing a built-in in-plane bias field (using a reference layer or an antiferromagnetic heavy metal), incorporating ferroelectric layers, adding another heavy metal layer to generate competing spin currents, applying an out-of-plane charge current, and engineering the geometry of the ferromagnetic layer. This research focuses on an approach that doesn't require architectural changes to a standard SOT-MRAM cell, utilizing the interplay of lateral size, interfacial DMI strength, and current density.

The paper reviews various existing methods for achieving field-free SOT-mediated perpendicular magnetization switching. These methods broadly fall into categories such as modifying the material stack structure to create asymmetry, incorporating additional magnetic or antiferromagnetic layers to generate built-in fields, using electric field effects from ferroelectric layers, adding a second heavy metal layer to manipulate spin currents, introducing an out-of-plane current, and modifying the geometry of the ferromagnetic layer itself. The authors highlight the limitations of these previous approaches, primarily focusing on their incompatibility with the architecture of standard SOT-MRAM cells and the complexities they introduce into device fabrication. The current work proposes an alternative method that avoids these shortcomings, emphasizing its compatibility with existing technology.

The study employed both micromagnetic simulations using the commercial μ-Pro package and the open-source MuMax3 package, along with atomistic spin dynamics (ASD) simulations using an in-house developed package called AtomMag. The micromagnetic simulations modeled a 40 nm diameter MgO/Co₂₀Fe₆₀B₂₀(1.1 nm) bilayer nanodisk on a Pt layer, discretizing the CoFeB layer into cuboids. The Landau-Lifshitz-Gilbert (LLG) equation, including a spin-orbit torque (SOT) term, was solved numerically. The effective magnetic field included contributions from exchange energy, interfacial DMI energy, Heisenberg exchange anisotropy, magnetostatic stray field, and anisotropy energy (uniaxial and shape anisotropy). The SOT term was derived from the spin Hall effect, considering the transfer of angular momentum from the Pt layer. Simulations used a forth-order Runge-Kutta method with a time interval of 0.005 (dimensionless). MuMax3 simulations were used for validation. ASD simulations utilized a 2D hexagonal lattice of Co atoms to model the system, again solving the LLG equation with an SOT term. The effective field included contributions from dipole-dipole interaction, uniaxial magnetic anisotropy, interfacial DMI, Heisenberg exchange interaction, and thermal fluctuation field. The SOT term was incorporated similarly to the micromagnetic model. The LLG equation was solved using a forth-order Runge-Kutta method with a time interval of 1 fs. A machine learning model, specifically a decision-tree regression model, was trained on approximately 1000 groups of micromagnetic simulation data to predict the equilibrium magnetization as a function of disk diameter, DMI strength, and current density. The model was trained using Scikit-learn and tested with 80 additional datasets.

The simulations revealed that field-free SOT perpendicular switching is achievable within an intermediate range of current density, disk diameter, and DMI strength. A two-step switching process was observed: a >90° switching followed by relaxation to the fully reversed state. The >90° switching involved deterministic nucleation of a reversed domain in a specific region of the disk, driven by the synergistic action of SOT and DMI. The growth of the reversed domain was found to be two-dimensional and well-described by the Kolmogorov-Avrami equation. The ASD simulations provided atomic-scale insights into the nucleation process, revealing variations in switching speed across different nucleation clusters. The machine learning model demonstrated high accuracy (>90% R² score) in predicting the equilibrium magnetization state for given parameters, significantly accelerating the design process compared to extensive micromagnetic simulations. The switching was shown to be repeatable using both unipolar and bipolar current pulses, highlighting the flexibility of the proposed method. The analysis showed that for optimal switching, both the current density and DMI strength must be in an intermediate range; too low and switching would not occur, while too high and the resulting domain wall structure would prevent relaxation to the desired state. The size of the nanomagnet is also critical, with smaller diameters resulting in stronger perpendicular magnetic anisotropy (PMA) and less tilting of the magnetization, which hinders switching.

The findings demonstrate a practical and efficient approach for field-free SOT-mediated perpendicular magnetization switching in SOT-MRAM devices. The method's compatibility with the standard SOT-MRAM architecture is a significant advantage over previously reported techniques. The successful switching relies on a delicate balance between the SOT, DMI, and geometrical confinement. The two-step switching mechanism is shown to be robust and deterministic, and the repeatable switching capability, using unipolar or bipolar pulses, provides design flexibility. The atomic-scale analysis from ASD simulations complements the micromagnetic results, offering insights into the fundamental nucleation processes. The machine learning model provides a powerful tool to quickly and accurately predict the switching behavior, accelerating the design and optimization of such devices.

This research successfully demonstrates a field-free SOT-mediated perpendicular magnetization switching method that is compatible with the standard SOT-MRAM cell architecture. The method relies on the interplay of lateral size, DMI strength, and current density. A two-step switching process is identified and analyzed using micromagnetic and ASD simulations, complemented by a highly accurate machine learning model for efficient parameter optimization. Future research could explore the impact of other material parameters or explore novel architectures that further enhance switching performance and energy efficiency.

The study primarily relies on computational simulations. While the simulations were validated using two different micromagnetic packages, experimental validation is still necessary to fully confirm the findings. The ASD simulations were performed on a simplified 2D model, which may not fully capture all aspects of the three-dimensional system. The machine learning model's accuracy depends on the quality and quantity of the training data; more data might improve its performance. The parameter ranges investigated might not be exhaustive, and further investigation may reveal additional optimal conditions.