Theoretical Study of Co-Doping Effects with Different Ions on the Multiferroic Properties of BiFeO3 Nanoparticles

Using a microscopic model and the Green's function theory, the size and co-doping effects on the multiferroic and optical (band gap) properties of BiFeO₃ (BFO) nanoparticles are investigated. The magnetization increases, whereas the band gap energy decreases with decreasing nanoparticle size. The substitution with Co/Mn, Nd/Sm, Ce/Ni, and Cd/Ni is discussed and explained on a microscopic level. By the ion co-doping appear different strains due to the difference between the doping and host ionic radii, which leads to changes in the exchange interaction constants for tuning all properties. It is observed that by co-doping with Nd/Sm at the Bi site or with Co/Mn at the Fe site, the multiferroic properties are larger than those by doping with one ion. Moreover, by doping with Ni, the multiferroic properties are reduced. But by adding another ion (for example Ce or Cd), an increase in these properties is obtained. This shows the advantages of the co-doping, its flexibility, and its greater possibility of tuning the multiferroic properties compared to single ion substitution. The band gap energy decreases for all co-dopants. The polarization increases with increasing magnetic field. This is evidence of magnetoelectric coupling, which is enhanced by co-doping with Co/Mn. The observed theoretical results are in good qualitative agreement with the existing experimental data.