Regularized dynamical decoupling noise spectroscopy - a decoherence descriptor for radicals in glassy matrices

Decoherence arises from a fluctuating spin environment, captured by its noise spectrum S(omega). Dynamical decoupling (DD) with n pi pulses extends the dephasing time if the associated filter function attenuates S(omega). Inversely, DD noise spectroscopy (DDNS) reconstructs S(omega) from DD data by approximating the filters pass band by a delta-function. This restricts application to qubit-like spin systems with inherently long dephasing times and/or many applicable pulses. We introduce regularized DDNS to lift this limitation and thereby infer S(omega) from DD traces of paramagnetic centers in glassy o-terphenyl and water-glycerol matrices recorded with n <= 5. For nitroxide radicals at low temperatures, we utilize deuteration to identify distinct matrix- and spin center-induced spectral features. The former extends up to a matrix-specific cut-off frequency and characterizes nuclear spin diffusion. We demonstrate that rotational tunneling of intramolecular methyl groups drives the latter process, whereas at elevated temperatures S(omega) reflects the classical methyl group reorientation. Ultimately, S(omega) visualizes and quantifies variations in the electron spins couplings and thus reports on the underlying spin dynamics as a powerful decoherence descriptor.