  Doping is a widely used method to tune physical properties of ferroelectric
perovskites. Since doping can induce charges due to the substitution of certain
elements, charge effects shall be considered in doped samples. To understand
how charges can affect the system, we incorporate the dipole-charge interaction
into our simulations, where the pinched hysteresis loops can well be
reproduced. Two charge compensation models are proposed and numerically
investigated to understand how lanthanum doping affect BaTiO$_{3}$'s
ferroelectric phase transition temperature and hysteresis loop. The
consequences of the two charge compensation models are compared and discussed.
