Bayesian-inspired hierarchical modeling of angle-dependent electron paramagnetic resonance spectra in (C2H5NH3)2CuCl4

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 βh=0.38 for T>Tc and βl=0.37 for T Bayesian-inspired hierarchical modeling with maximum a posteriori estimation provides a framework for analyzing angle-dependent electron paramagnetic resonance spectra. It quantifies uncertainty, stabilizes parameter estimates, and identifies a structural phase transition.