Evidence of Coulomb correction and spin-orbit coupling in rare-earth dioxides CeO2, PrO2 and TbO2: An ab initio study

► GGA+U implementation lead us to describe correctly the relativistic effect on 4f electrons for CeO2. ► Inclusion of the Hubbard-U parameter & spin-orbit coupling is responsible for ferromagnetic insulating of PrO2 and TbO2. ► Elastic constants calculation proves the mechanical stability of CeO2, PrO2 and TbO2. ► The electronic structure description shows that these compounds are stable in ferromagnetic phases.