Determination of complex magnetism in a homologous series of compounds.

Pr$_{(n+1)(n+2)}$Ni$_{n(n-1)+2}$Si$_{n(n+1)}$, where n = 2, 3, and 4, forms a homologous series of hexagonal compounds whose basic structural unit is a trigonal prism of Pr atoms with its axis parallel to the c-axis. Between 100 and 400 K, their dc susceptibility, $\chi {\rm s}$ measured with H$\vert \vert $c and H$\bot $c on a single crystal follows a Curie-Weiss law. $_{ }$In all compounds, the component of M$\vert \vert $c orders ferromagnetically with T$_{c}$ increases with n. For H$\bot $c, a peak is observed in the low-field M vs T plots below T$_{c}$ suggesting antiferromagnetic order. For H$\bot $c at 5 K, all three compounds exhibit a metamagnetic transition between 2 T and 3 T. Based on the systematics of the properties of the members of the series, a model for site specific interactions has been developed for comparison with first principles calculations.