Role of the rare-earth doping on the multiferroic properties of BaTiO$_3$: First-principles calculation

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