Role of the rare-earth doping on the multiferroic properties of BaTiO3: First-principles calculation

Ab-initio spin-polarized Density Functional Theory plus U is used to study the electronic and magnetic properties of tetragonal doped barium titanate (Ba$_{1-x}$Eu$_x$O$_3$) system for different europium (Eu$^{3+}$) concentrations. For this study, Projector Augmented Wave (PAW) method a Perdew-Zunger (LSDA) approximation, which has been exchange correlation energy, have considered taking into account supercell model. In model, spin polarization as well Hubbard's potential correction electron-electron Coulomb interactions in rare-earth ions partially filled f-orbitals. The bands-structure reveals that band-gap energy dielectric decreases with increase doping concentration. On other hand, modern theory also shows spontaneous electric increases content, whereas states-density ferromagnetic characteristics (with non-zero total magnetization), without an applied field, Ba$_{1-x}$Eu$_x$O$_3$ system. reveal be strongly dependent on interaction strong localized Eu 4f-states crystal lattice.