Hidden ordered frequencies in disordered magnetic systems: An inverse analysis of µSR spectra

Abstract Strong magnetic disorder can suppress observable muon-spin precession, making it difficult to distinguish genuinely disordered magnetic states from magnetic states containing characteristic internal-field contributions masked by random-field broadening. We introduce Convolution-Constrained Inverse $\mu$SR Analysis (CCI-$\mu$SR), a framework combining zero-field (ZF) and transverse-field (TF) measurements to investigate potentially hidden characteristic internal-field contributions. Disorder-induced broadening inferred from model-based ZF analysis is incorporated as a constraint in TF fitting, restricting the range of admissible local-field descriptions. We demonstrate the approach using the pyrochlore iridate Y$_{1.8}$Cu$_{0.1}$Ca$_{0.1}$Ir$_2$O$_7$, where strong damping obscures coherent oscillations. Conventional Fourier analysis does not resolve a distinct internal-field frequency, while unconstrained Prony reconstruction yields model-dependent estimates. The CCI-$\mu$SR framework provides a physically constrained description compatible with a strongly broadened quasistatic magnetic component. Profile-$\chi^2$ analysis supports a finite characteristic internal-field frequency in ZF within the adopted model. The complementary TF analysis demonstrates that a strongly broadened finite-frequency contribution remains compatible with the measured response, even when it cannot be independently resolved or uniquely distinguished from a zero-frequency alternative. These findings highlight the ability of CCI-$\mu$SR to assess potentially hidden magnetic contributions through jointly constrained ZF and TF descriptions, while explicitly identifying the limitations of frequency reconstruction.