A Simple Localized-Itinerant Model for PrAl$\text{}_{3}$: Crystal Field and Exchange Effects

We present a simple magnetic model for PrAl$\text{}_{3}$. The effects of crystal field are treated using a reduced set of levels and the corresponding wave functions are extracted from the actual crystal field levels of Pr$\text{}^{+3}$ in a hexagonal symmetry. The exchange between 4f- and conduction-electrons are dealt within a molecular field approximation. An analytical magnetic state equation is derived and the magnetic behaviour discussed. The parameters of the model are estimated from a fitting of the inverse susceptibility of PrAl$\text{}_{3}$ given in the literature.