Ab initio investigation of the spin-reorientation phase transition in PrCo$_{5-x}$Ni$_x$ ($x = 0$–$5$)

The series PrCo$_{5-x}$Ni$_x$ ($x = 0$–$5$) was investigated within the LDA+U+SO method taking into account strong correlations and spin-orbit coupling in Pr-4f, as well as in Ni(Co)-3d states. We give a detailed description of total energies, electronic structure and magnetic moments directions and values for all ions and concentrations considered. It was obtained that the system pass through a continuous spin transition from planar ab to the c axis directions of the Pr ion in agreement with experiments.