Nuclear Magnetic Resonance in Solids: Thermodynamic Effects of a Pair of rf Pulses

A discussion is given of the effects of a pair of pulses of rf magnetic field (at the NMR frequency) on the Zeeman and dipolar energies of the spin system in a solid. Zeeman order is partly transformed into dipolar order when the two pulses have different rf phases. A theoretical calculation provides a very simple relation between the efficiency of this transfer of energy (as a function of the characteristics of the pulses and their time separation) and the magnitude and shape of the dipolar component of the free-precession signal. This prediction has been verified quantitatively in the case of the ${\mathrm{F}}^{19}$ spins in a Ca${\mathrm{F}}_{2}$ crystal with the large magnetic field in a [100] direction. A maximum efficiency of transfer of Zeeman energy into dipolar energy of 56% has been obtained with a $\frac{\ensuremath{\pi}}{2}$ phase shift between a first $\frac{\ensuremath{\pi}}{2}$ pulse and a second $\frac{\ensuremath{\pi}}{4}$ pulse, separated by a time of the order of ${T}_{2}$. (An ideal adiabatic demagnetization in the rotating frame would have an efficiency of 100%.) The experimental results also indicate that the ${\mathrm{F}}^{19}$ spin system reaches internal quasiequilibrium in a time of the order of a few ${T}_{2}$ after the pulse pair. It is also shown that the use of a pair of rf pulses (both of the same rf phase this time) leads to a new method for measuring the complete shape of free-precession signals, which avoids the usual difficulties due to the finite recovery time of the observation circuit.