Nuclear-Magnetic-Resonance Spin-Lattice Relaxation in High and Low Fields

Abstract

An experimental and theoretical study is presented of the magnetic-field dependence of nuclear-magnetic-resonance (NMR) spin-lattice relaxation in solids. Theoretically, density-matrix methods are used along with the spin-temperature assumption to derive an expression for the field dependence of the relaxation time ${T}_{1}$ in the laboratory and rotating reference frames. It is shown that with the assumptions of extreme narrowing and cubic symmetry, the ratio of the Zeeman relaxation time to the dipolar relaxation time should be two for a one-ingredient crystal in both the laboratory and rotating reference frames. The ratio of the Zeeman ${T}_{1}$ to the dipolar ${T}_{1}$ is also calculated for two-ingredient crystals. To test the theory, measurements were made of the field dependence of the laboratory- and rotating-frame spin-lattice relaxation times of the sodium nuclei in NaCl. There is a large discrepancy between the calculated and measured ratios of high-field to low-field relaxation times in both frames. The origin of the discrepancy is not fully understood.