Temperature dependence of the magnetic excitations in singlet-ground-state systems: Paramagnetic and zero-temperature behavior ofPr3Tl and(Pr,La)3Tl

Neutron scattering experiments have shown that the magnetic excitations in polycrystalline ${\mathrm{}(\mathrm{P}\mathrm{r},\mathrm{L}\mathrm{a})\mathrm{}}_3$Tl compounds are only weakly temperature dependent. This contrasts with the strong temperature renormalization predicted by the simple singlet-singlet and singlet-triplet models of induced moment systems. Calculations have been made of the spin-wave dispersion relation at zero temperature using the pseudoboson model and as a function of temperature in the paramagnetic phase using a generalized susceptibility theory including transitions between all levels of the ground multiplet. As the temperature increases it is found that mode-mode interaction between excitations out of the ground state and those out of excited states plays an important role. The temperature dependence of the excitations is found to be weak for most wave vectors and in agreement with experiment. Near the zone center where no experiments were possible the excitations are more strongly temperature dependent.