Simultaneous optimization of lattice and spin configurations in atomic scale simulation of magnetic materials

Large scale atomistic simulations involving spin-lattice coupling are at the forefront of research in condensed matter physics and materials science. A key challenge lies in determining the ground state configurations of spins and lattices given this strong coupling, complicated by their evolution adherence to distinct governing equations. Unlike first-principles calculations, where the magnetic configuration is naturally determined by minimizing the electronic energy, no existing algorithm can simultaneously optimize both lattice and spin degrees of freedom at the atomic scale. This paper introduces a synergistic optimization framework for lattice and spin optimization in magnetic materials, overcoming the conventional separation approach. Employing a ``pseudoatomic'' method, the simultaneous optimization of atomic and spin configurations enhances accuracy and speed, enabling both atomic scale precision and large scale calculations. Applied to face-centered-cubic iron and ${\mathrm{BiFeO}}_{3}$, this approach demonstrates effective convergence, offering a robust tool for complex spin-lattice coupling problems, which paves a path for addressing high-dimensional optimization problems.