²³Na relaxometry: An overview of theory and applications

²³Na is a nuclear magnetic resonance (NMR)-active isotope with a nuclear spin quantum number of 3/2. ²³Na relaxation phenomenon is at the core of ²³Na NMR measurement and analysis. Due to the dominance of quadrupolar interaction, the relaxation behavior of ²³Na is physically and mathematically more complex than that of a typical spin-1/2 isotope. In this review, we overview the semi-classical Redfield theory for deriving the formulations of ²³Na relaxation. We show that the relaxation behaviors of ²³Na can be quantitatively described by constructing the spectral density functions based on the second-order perturbation theory. In addition, we summarize the applications of ²³Na relaxometry in different research fields, including biomedicine, sodium ion batteries, and quantum information processing. Because sodium is an essential element in our body, food and industrial materials, the research on sodium by ²³Na NMR emerges as important future directions. The theoretical and practical understandings on ²³Na relaxation are the step stones for mastering advanced ²³Na NMR techniques.