Evidence for Strong Quadrupolar Pair Interactions in Rare-Earth Palladium BronzesRPd3S4

We report an evidence of order due to quadrupolar pair interactions, taking place along the rare-earth ( $R$) series of $R{\mathrm{Pd}}_3{\mathrm{S}}_4$ slightly above their dipolar magnetic order. Specific-heat measurements proved that the $R$ ions in these bronzes possess highly degenerate ground states, which may cause large orbital effects at low temperatures. The magnetic ordering temperatures much exceed those predicted by the de Gennes scaling at both ends of the $R$ series. The fact suggests that orbital effects dominate over the ordinary exchange-type dipolar interactions. The presumed quadrupolar ordering temperatures, on the other hand, scale with the squared Stevens factor along the $R$ series, indicating that quadrupolar pair interactions via conduction electrons are responsible for the ordering.