Phase Diagrams with Data Analytics

The ABO₃ perovskites exhibit complex electron-lattice interactions that complicate the identification of primary pathways to tune physical properties. Representation theory provides a framework us to decompose low-symmetry structures into orthonormal symmetry-breaking lattice modes of the parent aristotype. Statistical analyses may then be used to study structure-property relationships based on these symmetry-modes and macroscopic observables [1]. As test cases, we explore the metal-insulator transitions and complex spin orders of the rare-earth nickelates and spin and orbital orders of vanadate perovskites. Analyses of experimental vs. ab initio data reveal significant differences in predicted trends depending on how the crystal structures were obtained. We show how physical priors can help explain this discrepancy and illustrate why context matters in conducting statistical studies.
[1] P.V. Balachandran et al., Phys. Rev. B. 88, 054101 (2013).