A Foraging Guide to the Magnetic Landscape: Balancing Exploration and Exploitation in the Hunt for the Ground State

The energy landscape of correlated magnetic materials is a high-dimensional, rugged terrain populated by a multitude of metastable states with distinct magnetizations, oxidation states, and orbital orders. This makes identifying the true ground state a significant computational challenge and poses significant hurdles in attempting to design materials with tunable magnetic properties.

Building on the work of Ponet et al. [1], we characterize this complex terrain. We trace the ruggedness to a set of competing tensions, such as the DFT tendency towards delocalization and the Hubbard +U correction driving localization instead. This competition is further modulated by a hierarchy of magnetic interactions, including Hund's coupling, superexchange and Kugel-Khomskii physics. This complex interplay creates the very "valleys" and "barriers" that define the ruggedness in both high and low energy scales.

Taking inspiration from animal foraging behavior, where efficient search requires balancing "exploration" of new territory with "exploitation" of known resources, we leverage this insight to devise metaheuristic strategies that successfully navigate this landscape and hunt down the true ground state.

[1] L. Ponet, E. di Lucente & N. Marzari, npj Computational Materials 10, 137 (2024).