A quantitatively constrained framework for defect identification in oxides: application to Cr ³⁺ centers in PbTiO ₃

Identifying paramagnetic defect centers in ferroelectric oxides is challenging due to the large configurational space of dopants and the strong sensitivity of spectroscopic signatures to local structure. In this work, we present a unified framework for assigning Cr³⁺ defect centers in PbTiO₃ by combining machine-learning-based structural optimization with quantitatively constrained zero-field splitting (ZFS) analysis. A comprehensive set of substitutional and charge-compensated Cr defect models was constructed and relaxed using the CHGNet interatomic potential. Local Cr-O coordination geometries were then extracted and used as input for superposition-model calculations of ZFS parameters, which were systematically fitted to experimental EPR data under strict bounds on both intrinsic and structural variations. By jointly evaluating ZFS mismatches, parameter stability, and independent structural quality metrics, we establish objective criteria to discriminate physically plausible defect configurations from unphysical ones. This analysis enables consistent assignment of the experimentally observed EPR centers C1-C4 to a limited subset of defect models, while excluding the majority of bulk-like configurations. In particular, the dominant bulk center C1 is reproduced by low-distortion Ti-site substitution models involving long-range defect interactions. Although certain bulk-based configurations provide partial agreement for the nanopowder-specific center C4, the absence of a fully consistent bulk solution indicates a size-dependent origin associated with more complex local environment, such as surface-related coordination effects. The methodology introduced here is general and transferable, providing a robust route for defect identification in functional oxides that integrates machine-learning structural fidelity with physically constrained spectroscopic modeling.