Response of the electric field gradient in ion implanted BaTiO$_{3}$ to an external electric field

Single crystalline, ferroelectric BaTiO$_{3}$ as material with the highest piezoelectric constants among the perovskites with ordered sublattices was implanted with $^{111}$In($^{111}$Cd). The electric field gradient at the Ti position was measured with perturbed $\gamma-\gamma$-angular correlation spectroscopy (PAC) while the crystal was exposed to an external electric field. A quadratic dependence could be observed: $\nu_{Q}$(E) = (34.8(1) + 0.16(4) E/kV/mm + 0.080(2) E$^{2}$/kV$^{2}$/mm$^{2}$) MHz. Point charge model calculations reproduce the linear change of Vzz, but not the quadratic term. The polarizability of the host ions of BaTiO$_{3}$ is known to be nonlinear with respect to an electric field. The resulting quadratic shift of the electron density is reflected in the strength of the EFG.