Nuclear Magnetic Resonance in the Demagnetized State

A discussion is given of experimental results and theoretical considerations which apply in the case of complete adiabatic demagnetization in the rotating frame (ADRF) for nuclear spin systems in solids. Although the net magnetization in this state is zero, both continuous wave and pulse signals are predicted and readily observed at the normal resonance frequency. These signals appear to be much like the derivative of the signals observed in the normal nuclear magnetic resonance (NMR) cases with amplitudes comparable to normal NMR signal amplitudes and they persist for times comparable with $T_1$ at high fields even when the line is purely homogeneously broadened. A simple heuristic theory is used to calculate, after ADRF, the shape of the free-induction decay and the form of the absorption at $\omega \approx 0, \Omega , \mathrm{and} 2\Omega$, where $\Omega$ is the resonance frequency of the spin system. The density matrix method is then used to calculate line shapes and free-induction decay signals which are found to be in agreement with experiment and the heuristic model calculation. The concept of spin temperature is used to calculate the effect of applying an rf field to produce a line asymmetry in a homogeneously broadened system. It is also shown that, in general, the free induction decay signal is not the Fourier transform of the line shape and homogeneously broadened lines do not saturate uniformly. In addition, it is found experimentally that ADRF is reversible, spin systems are coupled, spectra at low frequency and double the resonance frequency are observed, and spin-system relaxation times vary rapidly with field at low dc fields but are of order of $T_1$ at high fields.