Quadrupolar exchange effects on the dynamics of high-temperature paramagnets

The spin dynamics of paramagnets with both isotropic dipolar and isotropic quadrupolar exchange terms in the spin-spin interaction Hamiltonian is investigated in the high-temperature limit. In particular, lowest-order integral equations for the dynamical two point correlation functions, which are measurable in magnetic resonance and ultrasonic magnetic resonance experiments are derived by the use of a previously developed diagrammatic technique. These equations are valid for all values of the dipolar to quadrupolar exchange energy ratio and for all values of the spin quantum number $S$. A systematic study of the numerical solutions to these equations is then made for $1\le S\le \frac{7}{2}$ and for various combinations of dipolar and quadrupolar exchange energies. The results of these calculations for the case of $S=\frac{7}{2}$ are used in the following paper to help explain the observed nuclear acoustic resonance spectra in ${\mathrm{Ta}}^{181}$.