Predicting dynamic spin splitting in 2D hybrid organic-inorganic perovskites via machine learning model

Hybrid organic–inorganic perovskites (HOIPs) have emerged as a promising class of materials for optoelectronic and spintronic applications. Layered two-dimensional (2D) HOIP variants have received considerable attention, primarily due to their unique properties that can be modulated through the tailored selection of both organic and inorganic components. The spin splitting in the band structure due to the strong spin–orbit coupling is one of the most intriguing properties of such 2D HOIPs materials for their potential utility in spintronics. In addition to observing the spin splitting in equilibrium due to the non-centrosymmetric structure, the possibility of having dynamic spin splitting at room temperature of the otherwise centrosymmetric systems has become a topic of great debate. While modern first-principles molecular dynamics (FPMD) simulation is able to address such a question in principle by taking into account the lattice anharmonicity in electronic structure calculation, the finite-size error poses a great challenge in practice. In this work, we employ a machine learning (ML) model to overcome this practical limitation to investigate the dynamic spin splitting in phenylethyl ammonium lead iodide 2D HOIP. Specifically, we use the deep potential molecular dynamics approach [Zeng et al., J. Chem. Phys. 159(5), 054801 (2023)] for ML FPMD simulation, and we also develop a surrogate model for predicting the spin splitting based on the recent finding that relates the spin splitting to structural descriptors in 2D HOIPs. Our work shows that even in globally centrosymmetric structures, the inclusion of lattice anharmonicity can induce dynamic spin splitting at room temperature.