Temperature Dependence of Exchange-Narrowed Magnetic-Resonance Linewidth

Temperature dependence of exchange-narrowed paramagnetic-resonance linewidths can be inferred by computing second and fourth moments of the resonance line at finite temperature. This procedure is carried out here for two systems in which the moments can be calculated with a minimum amount of approximation: (i) a paramagnet with exchange energy much less than $\mathrm{kT}$ but with Zeeman energy comparable to $\mathrm{kT}$ so that spin ordering takes place solely via a large external field; (ii) an antiferromagnetic linear-chain salt such as Cu${\left(\mathrm{N}{\mathrm{H}}_3\right)}_4$S${\mathrm{O}}_4$·${\mathrm{H}}_2$O for which Zeeman energy is negligible but in which short-range order exists because of an exchange-interaction energy of the order of $\mathrm{kT}$. Dipole-dipole and hyperfine couplings are considered as sources of broadening, and the treatment is confined to spin ½. In either case we find the effective exchange frequency to increase as the temperature is lowered; so the line is narrower at a given temperature than would be expected on the basis of second-moment and susceptibility considerations alone. Linewidth measurements by Date on Cu${\left(\mathrm{N}{\mathrm{H}}_3\right)}_4$S${\mathrm{O}}_4$·${\mathrm{H}}_2$O seem to give some experimental evidence in support of this conclusion.