  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.
