Multiferroicity in V-doped PbTiO₃

We report \emph{ab initio} predictions on the proper multiferroic (ferromagnetic, insulating and ferroelectric) character of PbTiO$_{3}$ doped with vanadium. V impurities coupled ferromagnetically carry a magnetization of 1 $\mu_{\rm B}$ each. The coupling is expected to be strong, since the paramagnetic solution is higher by 150 meV/vanadium, and no stable antiferromagnetic solution was found. The electronic gap in the doped system is about 0.2-0.3 eV in GGA, hence the system is properly multiferroic. V doping increases the spontaneous polarization in PbTiO$_{3}$, with an approximate percentual rate of 0.7 $\mu$C/cm$^{2}$.