Electron paramagnetic resonance (EPR) spectroscopy is a powerful technique for probing magnetic and structural properties in functional materials. However, conventional least-squares analysis methods often fail to propagate uncertainty across related measurements, such as angle-resolved spectra. To address this, we employed a Bayesian-inspired hierarchical modeling framework to consistently estimate spectral parameters across multiple datasets. This framework was implemented for asymmetric EPR spectra of the layered perovskite (C2H5NH3)2CuCl4, which exhibits two-dimensional magnetism and potential multiferroicity. Spectral parameters, including g-values and linewidths, were comprehensively estimated across 24 angular datasets. For temperature dependence, a reduced model using three principal directions over 71 temperature points yielded consistent estimates at lower computational cost. Analysis under the hierarchical model indicates a structural phase transition at a critical temperature (Tc). Simultaneous scaling-law fits of the temperature dependence of the CuCl6 octahedral tilt angle on both sides of the transition, assuming a common Tc, yielded critical parameters of Formula: see text for Formula: see text and Formula: see text for Formula: see text, with Formula: see text K. Although the 95% Bayesian credible intervals under this hierarchical model were too broad to assign a definitive universality class, the results support a second-order phase transition. To interpret spectral asymmetry, we tested a twin-domain model, which proved insufficient. In contrast, a direct maximum a posteriori (MAP) optimization incorporating absorption and dispersion components successfully reproduced the observed spectra and yielded physically plausible parameters. These results demonstrate that this Bayesian-inspired hierarchical modeling framework provides a practical basis for uncertainty quantification, model evaluation, and structural interpretation in EPR spectroscopy.
Manaka et al. (Wed,) studied this question.