This thesis illustrates the use of the nuclear magnetic resonance (NMR) technique as a local probe for the study of static and dynamic magnetism in the iron-based superconductors.

First, a Korringa ratio analysis of 59Co and 75As NMR data reveals the existence of ferromagnetic (FM) spin fluctuations in SrCo2As2 and the hole- and electron-doped BaFe2As2 families of iron-pnictide superconductors. The analysis further shows that the FM fluctuations compete with AFM fluctuations to suppress superconductivity in these materials. The FM fluctuations are thus a crucial ingredient to understanding the variability of the superconducting transition temperature (Tc) and the shape of the superconducting dome in these and other iron-pnictide families.

Secondly, a study of KFe2As2 under pressures up to 2.1 GPa reveals a crossover between a high-temperature incoherent, local-moment behavior and a low-temperature coherent behavior at a crossover temperature, T*. The T* is found to increase monotonically with pressure, consistent with increasing hybridization between localized 3d orbital-derived bands with the itinerant electron bands. No anomaly in T* is seen at the critical pressure where a change of slope of Tc(p) has been observed. In the superconducting state, two-component nuclear spin-lattice relaxation is observed at low temperatures, suggesting the existence of two distinct local electronic environments.

Finally, 77Se-NMR studies of FeSe subjected to external pressure and sulfur doping are presented. In pure FeSe under pressure, the NMR spectra reveal the existence of a short-range, local nematic ordered state above the bulk nematic ordering temperature. Furthermore, this local nematic order does not compete with low-energy AFM spin fluctuations. In sulfur-doped FeSe(1−x)Sx, the observed behavior of the magnetic fluctuations parallels the Tc, providing strong evidence for the primary importance of magnetic fluctuations for superconductivity, despite the presence of nematic quantum criticality in this system.