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Atomistic simulations hold significant value in clarifying crucial phenomena such as phase transitions and energy transport in materials science. Their success stems from the presence of potential energy functions capable of accurately depicting the relationship between system energy and lattice changes. In magnetic materials, two atomic scale degrees of freedom come into play: the lattice and the spin. However, accurately tracing the simultaneous evolution of both lattice and spin in magnetic materials at an atomic scale is a substantial challenge. This is largely due to the complexity involved in depicting the interaction energy precisely, and its influence on lattice and spin-driving forces, such as atomic force and magnetic torque, which continues to be a daunting task in computational science. Addressing this deficit, we present DeepSPIN, a versatile approach that generates high-precision predictive models of energy, atomic forces, and magnetic torque in magnetic systems. This is achieved by integrating first-principles calculations of magnetic excited states with deep learning techniques via active learning. We thoroughly explore the methodology, accuracy, and scalability of our proposed model in this paper. Our technique adeptly connects first-principles computations and atomic-scale simulations of magnetic materials. This synergy presents opportunities to utilize these calculations in devising and tackling theoretical and practical obstacles concerning magnetic materials.

Atomic simulations hold significant value in clarifying crucial matters such as phase transitions and energy transport in materials science. Their success stems from the presence of potential energy functions capable of accurately depicting the relationship between system energy and lattice changes. In magnetic materials, two atomic scale degrees of freedom come into play: the lattice and the magnetic moment. Nonetheless, precisely portraying the interaction energy and its impact on lattice and spin-driving forces, such as atomic force and magnetic torque, remains a formidable task in the computational domain. Consequently, there is no atomic-scale approach capable of elucidating the evolution of lattice and spin at the same time in magnetic materials. Addressing this knowledge deficit, we present DeepSPIN, a versatile approach that generates high-precision predictive models of energy, atomic forces, and magnetic torque in magnetic systems. This is achieved by integrating first-principles calculations of magnetic excited states with advanced deep learning techniques via active learning. We thoroughly explore the methodology, accuracy, and scalability of our proposed model in this paper. Our technique adeptly connects first-principles computations and atomic-scale simulations of magnetic materials. This synergy presents opportunities to utilize these calculations in devising and tackling theoretical and practical obstacles concerning magnetic materials., 8 pages, 4 figures