Statistical deep learning prediction of defect densities in ferromagnetic materials

Developments in deep learning techniques show promise in material science to predict new materials and physical properties [1]. Deep learning requires training a model on large volumes of data and is inherently a process that is statistical in nature. Here, we present a novel application of deep learning applied to magnetic materials while considering defects. This approach defines defect density parameters in the material, similar to random telegraph noise [2], that can be integrated into a pseudospectral Landau-Lifshitz (PSLL) approach [3] to generate the data. To test the applicability of this approach to more complex topological structures in higher dimensions, we leverage the CNN over domain wall profiles to recover the defect parameter thresholds for specific domain wall width and energy. The CNN recovered and predicted the correct relationship between statistical defect parameters and the corresponding domain wall width and energy solutions of the PSLL solver. We have shown a method for learning and predicting the average effect of defects in the profile of magnetic solitons. This work will inform novel approaches to predict the material parameters and features required to stabilize higher-dimensional topological states in new materials.

[1] M. Raissi, P. Perdikaris, and G. E. Karniadakis, J. Comp. Phys. 378, 668-707 (2019)

[2] S. Machlup, J. Appl. Phys. 25, 341-343 (1954)

[3] K. Rockwell, et al., Phys. Rev. B 109, L180404 (2024)