Modular development of deep potential for complex solid solutions

The multicomponent oxide solid solution is a versatile platform to tune the delicate balance between competing spin, charge, orbital, and lattice degrees of freedom for materials design and discovery. The development of compositionally complex oxides with superior functional properties has been largely empirical and serendipitous, in part due to the exceedingly complex chemistry and structure of solid solutions that span a range of length scales. The usage of classical molecular dynamics (MD), a powerful statistical method, in computer-aided materials design has not yet reached the same level of sophistication as that in computer-aided drug design because of the limited availability and accuracy of classical force fields for solids. Here, we introduce the strategy of ``modular development of deep potential'' (ModDP) that enables a systematic development and improvement of deep-neural-network-based model potential, termed as deep potential, for complex solid solutions with minimum human intervention. The converged training database associated with an end-member material is treated as an independent module and is reused to train the deep potential of solid solutions via a concurrent learning procedure. We apply ModDP to obtain classical force fields of two technologically important solid solutions, ${\mathrm{Pb}}_{x}{\mathrm{Sr}}_{1\ensuremath{-}x}{\mathrm{TiO}}_{3}$ and ${\mathrm{Hf}}_{x}{\mathrm{Zr}}_{1\ensuremath{-}x}{\mathrm{O}}_{2}$. For both materials' systems, a single model potential is capable of predicting various properties of solid solutions including temperature-driven and composition-driven phase transitions over a wide range of compositions. In particular, the deep potential of ${\mathrm{Pb}}_{x}{\mathrm{Sr}}_{1\ensuremath{-}x}{\mathrm{TiO}}_{3}$ reproduces a few known topological textures such as polar vortex lattice and electric dipole waves in ${\mathrm{PbTiO}}_{3}/{\mathrm{SrTiO}}_{3}$ superlattices, paving the way for MD investigations on the dynamics of topological structures in response to external stimuli. MD simulations of ${\mathrm{Hf}}_{x}{\mathrm{Zr}}_{1\ensuremath{-}x}{\mathrm{O}}_{2}$ reveal a substantial impact of composition variation on both the phase transition temperature and the nature of the high-temperature nonpolar phase.