The Dzyaloshinskii-Moriya (DM) interaction, an antisymmetric exchange interaction, is critical in creating chiral magnetic orders like spin spirals, skyrmions, and Néel domain walls. These structures, driven by spin currents, are topologically protected and hold promise for storage-class magnetic memories. The DM interaction arises at interfaces of ferromagnetic and non-magnetic layers with strong spin-orbit coupling, but accurately determining its strength (DM exchange constant) is challenging. Existing methods often rely on analyzing magnetic system dynamics, which are influenced by factors like domain wall pinning due to the magnetic anisotropy distribution. This distribution is difficult to control and assess, adding uncertainty to DM constant estimation. The equilibrium magnetic domain structure, determined by energy minimization (including magnetostatic, magneto-elastic, anisotropy, Heisenberg exchange, and DM exchange energies), inherently contains information about the DM exchange constant. While the size of skyrmions can provide clues, imaging them with sufficient resolution remains difficult. This research proposes a novel approach: using pattern recognition and machine learning to extract the DM exchange constant from readily obtainable micrometer-scale magnetic domain images. The approach eliminates the need for complex dynamic analyses and provides a simpler, more robust estimation method.

Previous research on determining the DM interaction often relied on analyzing the dynamics of magnetic systems. Methods include studying current or field-induced domain wall motion, spin wave propagation, and current/field dependence of magnetization reversal. However, these methods present difficulties due to model-dependence and the influence of random domain wall pinning from the magnetic anisotropy distribution. Other studies focused on extracting information from the size of skyrmions, but imaging these nanoscale structures requires sophisticated techniques. This work builds upon these previous efforts by introducing a novel machine learning approach that bypasses these limitations.

The researchers employed a convolutional neural network (CNN) for pattern recognition. To train the network, a large dataset of simulated magnetic domain images was generated using micromagnetic simulations. These simulations solved the Landau-Lifshitz-Gilbert equation with thermal noise, varying parameters such as the DM exchange constant (*D*), anisotropy distribution (*σ*), and other material properties (exchange stiffness constant *A_ex*, saturation magnetization *M_s*, uniaxial magnetic anisotropy energy density *K_u*). The CNN architecture consisted of twelve layers, ten convolutional and two fully connected, using ReLU activation and Huber loss for optimization. The Adam algorithm was used for training, employing a commercial deep learning tool (Sony Neural Network Console). The network was trained on 100,000 simulated images and validated on 10,000. The trained CNN was then used to analyze experimentally obtained magnetic domain images from Co-based heterostructures (Si sub./Ta (*d*)/Pt (2.6 nm)/Co (0.9 nm)/MgO (2 nm)/Ta (1 nm)), with varying Ta seed layer thickness (*d*). The experimental images were acquired using a magnetic microscope with a magnetic tunnel junction (MTJ) sensor. The experimental DM exchange constant was also independently determined using a conventional method involving magnetic field-induced switching of magnetization. To account for experimental conditions, the *M_s* and *K_eff* values from experiments were used in the training images generated for simulation, along with literature values for *A_ex*. Thermal fluctuations were also simulated using a Langevin field. Data augmentation, including image rotation, was employed to increase the training dataset size for improved accuracy.

The trained CNN accurately estimated the DM exchange constant (*D*) and the distribution of the effective perpendicular magnetic anisotropy energy (*σ*) from the simulated images. The root mean square error for *D* was approximately 0.05 mJ/m², and for *σ* it was approximately 0.005. When applied to experimental images, the CNN's estimations of *D* showed good agreement with the values obtained from the conventional experimental method. The *d*-dependence of the estimated *D* matched the experimental trend, demonstrating the system's ability to identify changes in *D* due to changes in the Ta seed layer thickness. The estimations of *σ* showed a monotonic decrease with increasing *d*, which correlates with the trend observed in *K_eff*, suggesting a relationship between *σ* and the Pt/Co layer texture. The stark contrast in the *d*-dependence of *D* and *σ* highlights the CNN's capacity to independently determine multiple material parameters if they are not correlated. The simulations involved varying the anisotropy distribution pattern and initial magnetization configuration to generate diverse domain structures for training. The research also tested a residual network (RN) architecture, with the results suggesting better performance with CNN.

The successful application of machine learning to extract material parameters from a single image significantly simplifies the experimental process for determining the DM exchange constant. The method overcomes the limitations of dynamic analysis methods, such as model-dependence and the influence of random anisotropy distribution. The high accuracy achieved in estimating *D* and *σ*, with the good agreement between the CNN's estimations and the conventional experimental method, validates the efficacy of this approach. The ability to independently estimate multiple parameters demonstrates the potential of this technique to be extended for simultaneous estimation of other material parameters, further simplifying materials research. This approach is crucial for accelerating the development of next-generation magnetic memory technologies that rely on controlled chiral magnetic orders.

This study demonstrated a novel method for determining the DM exchange constant and magnetic anisotropy distribution using pattern recognition and machine learning. A CNN accurately estimated these critical parameters from single magnetic domain images, showing good agreement with experimental results. This approach simplifies experimental procedures, improves accuracy, and provides a powerful tool for materials research in magnetic memory technologies. Future research could explore the application of this approach to other material systems and the integration of more sophisticated machine learning algorithms to further enhance accuracy and efficiency.

The current study relies on micromagnetic simulations to generate the training dataset, which may not perfectly capture all the complexities of real materials. The accuracy of the method is also dependent on the quality and resolution of the experimental images and the choice of machine learning architecture and hyperparameters. While the CNN model demonstrated promising results, the study used a specific type of microscope (MTJ sensor). Adapting the method for use with other microscopy techniques might require further adjustments and retraining.