Polarization of an open shell in the presence of spin-orbit coupling

There exist many f transition metal-based materials, with large orbital degeneracy and relatively strong spin-orbit coupling, that exhibits some multipolar order. We perform first-principles calculations on these systems within DFT method plus on-site Coulomb correction and we discuss the results in terms of polarization of the density occupation matrix. The fact that higher multipole polarizations play a larger role than the spin polarization indicates a breakdown of Hund's rules and we suggest a new complementary set of rules —Katt's rules, valid in case of large spin-orbit coupling interaction.