NMR Spin Dynamics in Solids. II. Pulse Experiments in Two-Spin-Species Systems

A theoretical and experimental study is made of the response of a two-ingredient spin system when repeatedly pulsed at resonance by a number of 90° rf pulses. With a long train of 90° pulses, a sustained chain of solid echoes was produced for ${\mathrm{Na}}^{23}$ in NaF. The peak echo amplitude was found to decay nonexponentially for short times (i.e., the first few echoes), settling down for long times to an exponential decay characterized by a time constant $T_{2\epsilon }$. A theoretical expression for $T_{2\epsilon }$ derived in a similar manner to that for a single-ingredient spin system, described previously by Waugh and Wang and by Mansfield and Ware, does not fit the experimental data. A more general theoretical approach to the multiple-pulse experiments is developed, based on the use of a logarithmic operator. Using this formalism together with a line-narrowing model similar to Anderson's theory of spectral line narrowing in solids in the presence of an exchange interaction, a new expression for $T_{2\epsilon }$ is derived. Some related long-pulse experiments have been performed in which the ${\mathrm{Na}}^{23}$ magnetization following an initial 90° pulse is spin-locked in a low rf field. These experiments simulate the mean rf field in the multiple-pulse experiment. Oscillation of the spin-locked magnetization is observed. Theoretical expressions are derived which describe these oscillations, and their relation to the multiple-pulse experiments is discussed. Mentioned briefly are some multiple-pulse experiments on ${\mathrm{F}}^{19}$ in Ca${\mathrm{F}}_2$ doped with paramagnetic impurities; also discussed briefly are some earlier multiple-pulse double-resonance experiments carried out on both nuclear species in NaF.