Limitations of the Method of Moments for Unlike-Spin Broadening

The magnetic resonance line-shape analysis based on the second and fourth moments of the frequency distribution, as originally formulated by Van Vleck, is shown to give incorrect results in the presence of the combined conditions (a) rapidly modulated (i.e., narrowed) interactions with unlike-spin species and (b) like-spin broadening comparable to (or greater than) that from mechanism (a). A new line-shape analysis is given based on density-matrix perturbation theory which specifically treats the case of rapidly modulated unlike-spin coupling. The results are compared with the moment analysis and applied to several examples from the literature. The case of the ¹⁹F NMR linewidth in antiferromagnetic MnF₂ is discussed in considerable detail, including a detailed evaluation of the ¹⁹F-¹⁹F Suhl-Nakamura coupling. Experimental results are reported for the inhomogeneous ¹⁹F line broadening in a MnF₂ crystal of excellent quality, allowing a comparison of measured and calculated free-induction decay times. Contrary to the earlier "method-of-moments" analysis, in which the ¹⁹F line was thought to be narrowed by the combined effect of ¹⁹F-⁵⁵Mn dipolar coupling and ⁵⁵Mn-⁵⁵Mn Suhl-Nakamura interaction, we find the linewidth to be accounted for by ¹⁹F-¹⁹F spin-spin interactions alone. This conclusion is in agreement with the new line-shape theory.