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, following at time 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 T₂, 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 T₁. Except for a small initial oscillation, the amplitudes of successive even or odd echo maxima in CaF₂ are found to decay exponentially with a time constant T₂. 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 ^-5 dependence of T₂ as well as the oscillatory effect. Numerical evaluation of the magnitude of T₂ based on a cumulant-moment approximation gives good agreement with experiment. Further related experiments have been performed by spin-locking the F^19 magnetization in long pulses of low amplitude. These experiments are intended to simulate the multiple-pulse sequences by replacing the coherent-pulse train with its mean field. The results reveal considerable oscillatory effects due to mutual exchange of energy between the Zeeman and dipolar subsystems in the rotating reference frame. A theoretical analysis is given which supports these effects. An estimate is made of the Zeeman dipolar cross-relaxation time, and is compared with Provotorov's theory as modified by Walstedt. In the multiple-pulse experiment, the "solid-echo" amplitude modulation may be ascribed to mutual energy exchange between the rf Zeeman energy in the zeroth Fourier harmonic of the pulse train (the mean pulse field) and the dipolar energy. Because of the higher harmonics in the Fourier expansion, however, the initial oscillatory effects disappear as increases.