Microscopic Inhomogeneous Broadening and Nuclear Spin-Spin Interactions

We study here the effects that random inhomogeneities have both on the nuclear spin-spin interaction via virtual spin-wave excitations in magnetically ordered systems [the Suhl-Nakamura (S-N) interaction] and on dipolar interactions. Two models are proposed to explain the experimental observation that the nuclear transverse relaxation rates ($\frac{1}{T_2}$) often are smaller than predicted by the S-N or dipolar theories for the perfect crystal, and that the spin-echo envelope decays are exponential in time rather than Gaussian. For both models, the method of moments is employed, and it is shown that the transformation from Gaussian to cutoff Lorentzian behavior may be characterized by the behavior of the quantity $\frac{{\left(M_4\right)}_{\mathrm{in}}}{{{\left(M_2\right)}_{\mathrm{in}}}^2}$. Assuming the magnitude of the inhomogeneous broadening to be the same, a proportionately greater reduction occurs in ${{\left(M_2\right)}_{\mathrm{in}}}^{\mathrm{S}-\mathrm{N}}$ than in ${{\left(M_2\right)}_{\mathrm{in}}}^{\mathrm{dip}}$ when the range of the S-N interaction is large (i.e., $\frac{H_A}{H_E}\ll 1$). The inhomogeneous model as applied to the dipolar interaction compares favorably with Portis's spectral diffusion theory. The limitations of the applicability of the model theories to comparison with experiment are considered. Finally, a number of serious errors in the S-N theory, as applied to Mn${\mathrm{F}}_2$, are corrected.