Relaxation dynamics in strongly coupled spin systems in zero- to ultralow-field NMR spectroscopy

Nuclear spin population lifetimes encode information regarding molecular-tumbling regimes and interatomic distances in solution with sub-nanometer resolution. In the zero- to ultralow-field (ZULF) regime, population and coherence decays reveal complex behavior due to strong coupling between nuclear spins. We describe herein polarization lifetimes measured for a 13C-labeled formic acid sample, with an atomic-magnetometer-based ZULF setup, and present a theoretical framework to understand and model the observed effects. Individual peaks resolved by quadrature detection show different signal decay depending on the shuttling profile from a (pre)polarizing region to the detection region at ultralow fields, the strength of the measurement field, and the nutation angle induced by the excitation pulse. The relaxation model incorporates field-dependent dipole-dipole interactions and random field fluctuations. The multiexponential dynamics of spin populations is a general feature of any heteronuclear spin system at ultralow fields. The control of resonance peak lifetimes could be used for optimizing ZULF experiments, for spectral assignment, and for deriving structural and dynamical features of molecules by interpreting relaxation processes at nano- to microtesla magnetic fields.