Of bandits and Bohr magnetons : balancing exploration and exploitation in magnetic landscapes

Résumé :

The energy landscape of strongly interacting magnetic materials is a high-dimensional, rugged terrain populated by a multitude of metastable states with distinct magnetizations, oxidation states, and orbital orders. Identifying the true ground state within this complexity remains a significant hurdle for the computational design of materials with tunable magnetic properties.
Building on the work of Ponet et al. [1,2], we systematically characterize this terrain to reveal the fundamental drivers of its complexity. We trace its origins to a core competition between the DFT functional’s preference for delocalization and the Hubbard +U correction’s drive for localization. This primary conflict is further modulated by a hierarchy of magnetic interactions, including Hund’s coupling, superexchange, and Kugel-Khomskii physics, which collectively define the energetic valleys and barriers across both high and low energy scales.
To overcome these barriers, we propose a novel approach inspired by a completely different field: advertisement/recommendation engines (contextual Bandits) currently powering social media feeds and large parts of the Internet. By leveraging bandit strategies that balance the exploration of unknown configurations with the exploitation of known areas, we demonstrate an efficient method for navigating this landscape. Our results show that these strategies successfully identify the lowest energy states where traditional methods often fail, providing a robust framework for predicting and engineering the properties of strongly correlated magnetic materials.

[1] Ponet, L., Di Lucente, E., & Marzari, N. (2024). The energy landscape of magnetic materials. npj Computational Materials, 10(1), 151.
[2] Haddadi, F., Campi, D., dos Santos, F., Mounet, N., Ponet, L., Marzari, N., & Gibertini, M. (2025). Exploring the magnetic landscape of easily-exfoliable two-dimensional materials (arXiv:2509.09531v2).

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Contact : matteo.dastuto@neel.cnrs.fr