A Machine-Learned Spin-Lattice Interatomic Potential for Dynamic Simulations of Defective Magnetic Iron

Critical components in many technologies for power generation, sensing, computation and communications exploit magnetic materials. Their viability in extreme environments, efficacy and performance depend upon magnetic phenomena and rely heavily on materials development for continued improvement. Theoretical understanding of how magnetic properties relate to the underlying microstructure provides valuable insight for tuning characteristic properties and determining the viability and fatigue of aged materials. Iron based alloys are particularly important industrial materials which may obtain a wide variety of complex magnetic states which significantly affect the materials mechanical properties. Nonetheless, studies often explicitly neglect magnetic degrees of freedom. The development of a general-purpose spin-lattice interatomic potential has proven to be a challenge [1,2].<br/><br/>We successfully develop a first of its kind machine-learned spin-lattice potential (MSLP) that can perform dynamic simulations of magnetic materials that includes explicit non-collinear magnetic and lattice degrees of freedom as well as changes in the length of the magnetic moments [3]. The physics-informed MSLP was achieved by supplementing a spin-lattice Hamiltonian with a neural network term [4]. The neural network was trained to a large database of configurations represented using a proper mix of local configurational and magnetic descriptors to provide data-driven corrections to unknown physics in the conventional spin-lattice Hamiltonian. It reproduces the energies of various magnetic states of BCC and FCC phases at different volumes as well as the complex magnetic configurations in the vicinity of a vacancy and self-interstitial atoms. This includes the reversal and quenching of magnetic moments at the defect core. The MSLP results are all in quantitative agreement with density functional theory calculations.<br/><br/>The Curie temperature is calculated using spin-lattice dynamics [5] and is in good agreement with experiments. The new machine-learned potential can perform scalable dynamic simulation with good stability at high temperature. We then apply the potential to study the magnetic structure near different mesoscopic scale dislocation loops in iron at finite temperatures. Such an investigation has not previously been possible with current state of the art theoretical or experimental methods. The effect of radiation induced defects on the interaction of magnetic fluctuations and lattice vibrations is examined. The MSLP developed in this work transcends current treatments using DFT and molecular dynamics, in addition to other spin-lattice potentials which only treat near-perfect crystal cases, enabling simultaneous evaluation of mechanical deformations, magnetic fluctuations and defect properties at mesoscopic scales for the first time.<br/><br/>[1] Nikolov et al npj Comput. Mater. 7, 153 (2021)<br/>[2] Novikov et al npj Comput. Mater. 8, 13 (2022)<br/>[3] J. Chapman & P.-W. Ma, https://arxiv.org/abs/2205.04732<br/>[4] Behler, J. & Parrinello, M. Phys. Rev. Lett. 98 (2007), 146401; Behler, J. J. Chem. Phys. 134 (2011), 074106<br/>[5] Ma, P.-W. & Dudarev, S. L. Phys. Rev. B 83 (2011), 134418; Ma, P.-W. & Dudarev, S. L. Phys. Rev. B 86 (2012), 054416; Ma, P.-W., Dudarev, S. L. & Woo, C. H. Comput. Phys. Commun. 207 (2016), 350.<br/><br/>This work has been carried out within the framework of the EUROfusion Consortium, funded by the European Union via the Euratom Research and Training Programme (Grant Agreement No 101052200 — EUROfusion). The views and opinions expressed herein do not necessarily reflect those of the European Commission. This work also received funding from the Euratom research and training programme 2019-2020 under grant agreement No. 755039. We acknowledge funding by the RCUK Energy Programme (Grant No. EP/W006839/1), and EUROfusion for providing access to Marconi-Fusion HPC facility in the generation of data used in this manuscript.