Ca-induced phonon softening in BaTiO3 revealed by inelastic x-ray and neutron scattering

We performed inelastic x-ray and neutron scattering (IXS and INS) experiments for $(\mathrm{Ba},\phantom{\rule{0.16em}{0ex}}\mathrm{Ca})\mathrm{Ti}{\mathrm{O}}_{3}$ single crystals to elucidate the effect of Ca doping on the atomic dynamics. Dispersion relations of transverse phonons in $\mathrm{BaTi}{\mathrm{O}}_{3}, (\mathrm{B}{\mathrm{a}}_{0.9}\mathrm{C}{\mathrm{a}}_{0.1})\mathrm{Ti}{\mathrm{O}}_{3}$, and $(\mathrm{B}{\mathrm{a}}_{0.8}\mathrm{C}{\mathrm{a}}_{0.2})\mathrm{Ti}{\mathrm{O}}_{3}$ were determined. The $A$-site--O vibrational mode as well as the acoustic mode were observed both by IXS and INS, whereas the Ti--O soft mode was detected only by INS. It was found that the $A$-site--O vibration exhibits significant softening with increasing Ca concentration, while the Ti--O soft mode is almost unaffected by the Ca doping. This finding is discussed in comparison with the polarization hysteresis loops and piezoelectric coefficients of $(\mathrm{Ba},\phantom{\rule{0.16em}{0ex}}\mathrm{Ca})\mathrm{Ti}{\mathrm{O}}_{3}$. It is indicated that the softening of the $A$-site--O vibration contributes to the enhancement of the piezoelectricity of Ca-doped $\mathrm{BaTi}{\mathrm{O}}_{3}$-based materials.