Orientational dependence of the tails of dipole-broadened NMR spectra in crystals

Abstract

This paper describes experimental and theoretical studies of the tails of the dipole-broadened nuclear magnetic resonance (NMR) absorption spectra of 19F in isomorphic single crystals of BaF2 and CaF2 with the magnetic field directed along three crystallographic axes. The results obtained by directly measuring the derivative of the tail of the NMR absorption spectrum and the falloffs of the Engelsberg-Lowe free precession after Fourier transformation qualitatively agree. It is shown that the shape of the tail is well described by an exponential function in which the orientational dependence of the exponent does not reduce to variation of the second moment. The observed shape of the tail and the orientational dependence of its parameters are explained on the basis of a self-consistent fluctuating-local-field theory. Nonlinear integral equations are derived for the correlation functions, taking into account the changes of the actual number of nearest neighbors caused by the anisotropy of the dipole-dipole interaction and the contribution of lattice sums with loops. The equations are solved numerically. Good agreement is obtained for the computed dropoffs of the free precession, the NMR spectra, and the cross-polarization rates with the experimental results.