Magnetism in the diluted induced moment system (La,Pr)$_{6}$Ni$_{2}$Si$_{3}$

Pr$_{6}$Ni$_{2}$Si$_{3}$ crystallizes in a complex hexagonal structure with two distinct Pr sites with no point symmetry, thus the 2J+1=9 ground state levels are CEF-split into singlets. Single-crystal magnetization and specific heat measurements suggest that this splitting is large compared to the ordering temperature. As CEF-induced singlets are nonmagnetic, any ordered magnetic moment is induced by magnetic interactions. Pr$_{6}$Ni$_{2}$Si$_{3}$ orders with a ferromagnetic component parallel to the c-axis at $\sim $40K, whereas La$_{6}$Ni$_{2}$Si$_{3}$ appears to be nonmagnetic. Upon substitution of Pr by La the ordering temperature decreases more rapidly than predicted by a rule of mixtures. For substitutions of more than 50{\%} La, no ordering is observed above 5 K. For 50{\%} La, both AC and DC magnetization measurements suggest superparamagnetic or spin glass type behavior. This behavior will be discussed in terms of clusters of Pr ions with size-dependent moment and anisotropy.