A Multi-Scale Machine Learning Framework for Coupled Chemical, Spin, and Structural Disorder in Alloys
Understanding the thermodynamic properties of disordered magnetic alloys requires a unified treatment of configurational (chemical, spin, etc.) and structural degrees of freedom, which has remained beyond the scope of existing computational frameworks. Here we present a general framework that integrates machine learning models (such as graph neural networks and machine learning interatomic potentials) and statistical sampling methods (such as Monte Carlo and molecular dynamics simulations) to study the coupled chemical, spin, and structural disorder in alloys. We demonstrate the framework on body-centered-cubic Fe-Co alloys with interstitial carbon dopants, where the Fe-Co host exhibits intrinsic chemical and spin disorder, and the interstitial carbon introduces additional structural disorder through local lattice distortions, making the system a prototypical multi-disorder magnetic alloy. The framework predicts the order-to-disorder phase transition temperature and the melting temperature of Fe-Co alloy to be 1,000 K and 1,690 K, in excellent agreement with the experimentally measured values of 1,006 K and approximately 1,700 K, respectively. It also predicts the tetragonal-to-nearly-cubic structural transitions in Fe-Co-C alloy as temperature increases. These results establish the framework as a reliable tool for studying multi-disorder alloys, with applications to complex disordered systems such as high-entropy alloys, multiferroics, and spintronic devices.