Bayesian-inspired hierarchical modeling of angle-dependent electron paramagnetic resonance spectra in (C ₂ H ₅ NH ₃ ) ₂ CuCl ₄

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 over 71 temperature points yielded consistent estimates at lower computational cost. These results indicate 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 βh = 0.38 for T > Tc and βl = 0.37 for T < Tc, with Tc = 206.2 K. Although the 95% Bayesian credible intervals 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.