Restoration of the Korringa Relation in Disordered Liquid Systems via Transverse Relaxation (T₂)

This study resolves the apparent breakdown of the Korringa relation in disordered liquid metals by investigating Ga-based alloys (EGaIn and Galinstan). By integrating temperature-dependent Knight shifts (K) with longitudinal (T₁) and transverse (T₂) relaxation measurements, we demonstrate that deviations from classical behavior arise from neglecting transverse spin dephasing induced by structural and electronic disorder. While solid-state alloys follow the conventional Korringa law, the liquid phase exhibits significant discrepancies between T₁ and T₂ due to enhanced electron scattering and fluctuating hyperfine fields. By explicitly incorporating T₂ into a modified framework, the proportionality between the Knight shift and nuclear relaxation is quantitatively restored. This establishes transverse relaxation as a critical parameter for describing nuclear spin dynamics in complex liquid metals, reinforcing NMR as a powerful local probe for optimizing next-generation liquid metal technologies.