NMR Spin Dynamics in Solids. I. Artificial Line Narrowing and Zeeman Spin-Spin Relaxation in the Rotating Frame

An experimental and theoretical study is made of the response of a single-magnetic-species spin system to a coherent train of resonant 90° rf pulses of spacing $2\tau$, following at time $\tau$ an initial preparatory 90° pulse. The rf phase of the coherent pulses is shifted 90° with respect to the initial pulse. It is shown that this pulse sequence will produce a sustained "solid-echo" chain for times much greater than $T_2$, i.e., approaching the spin-lattice relaxation time. This therefore shows promise as a new method of chemical-shift measurement in solids, as well as a direct method of measuring the rotating-frame spin-lattice relaxation time $T_{1\rho }$. Except for a small initial oscillation, the amplitudes of successive even or odd echo maxima in Ca${\mathrm{F}}_2$ are found to decay exponentially with a time constant $T_{2\epsilon }$. It is shown theoretically that a simple diagonal assumption for the density matrix plus the rotational symmetry properties of the dipolar Hamiltonian to 90° pulses could explain the observed ${\tau }^{-5\mathrm{}}$ dependence of $T_{2\epsilon }$ as well as the oscillatory effect. Numerical evaluation of the magnitude of $T_{2\epsilon }$ based on a cumulant-moment approximation gives good agreement with experiment.