Reduced Bandgap Energy of Fe, Co, Ni, and (Ag,Fe)‐Doped Ferroelectric PbTiO ₃ Nanoparticles

Using a microscopic model and the Green's function theory, the size and ion doping dependence of the magnetization, bandgap energy, and polarization of PbTiO 3 nanoparticles have been investigated for the first time. Due to surface oxygen vacancies, the spin exchange interaction constants on the surface are tuned compared to those in the bulk. This leads to room temperature ferromagnetism and to smaller bandgap energy with decreasing the size. By transition metal ion doping at the Ti site, different strain appears, which modifies the exchange interaction constants in the doped compounds. So, on a microscopic level the enhanced magnetization and reduced bandgap energy with increasing the doping concentration are explained. In order to maintain the spontaneous polarization and reduce the bandgap energy, the codoped (Ag,Fe) PTO is also studied. There is a good agreement with the experimental data.