Mn ions' site and valence in PbTiO$_{3}$ based on the native vacancy defects
Mn ions' doping site and valence were studied in PbTiO$_{3}$ (PT) with the native vacancy defects by the first-principles calculations. Firstly, the native vacancy defects of Pb, O and Ti in PT were investigated and it was found that Pb vacancy is preferred to others. And then the growth of Mn doped PT should be preferred to Mn ion substituting for an A-site Pb ion with +3 valence when Pb is deficient under equilibrium conditions driven solely by minimization of the formation energy, and this could result in a larger lattice distortion of PT. In addition, when Mn enters the Pb site, the electronegativity of O becomes weaker which makes the domain movement easier in PT to improve the performance of PT, while Mn ion substitution for a B-site Ti ion is the opposite.