Abstract
High quality single crystals of BaFe$_{12}$O$_{19}$ were grown with the floating zone technique in flowing oxygen atmosphere of 100 atm. BaFe$_{12}$O$_{19}$ melts incongruently in atmospheric oxygen. High oxygen pressure above 50 atm modifies the melting behavior to be congruent, which allows for the crystal growth with the crucible-free floating zone technique. Single crystal neutron diffraction were measured to determine the nuclear and magnetic structures at 4 K and 295 K. At both temperatures, there exist local electric dipoles formed by the off-mirror-plane displacements of magnetic Fe$^{3+}$ ions at the bypyramidal sites. The displacement at 4 K is about half of that at room temperature. The temperature dependence of specific heat shows no anomaly associated with the long range polar ordering in the temperature range of 1.90-300~K. The inverse dielectric constant along $\emph{c}$ axis shows a $T^2$ temperature dependence below 20 K and then following by a plateau below 10 K, recognized as quantum paraelectric features. Further cooling below 1.4 K, the upturn region was clearly revealed and indicates BaFe$_{12}$O$_{19}$ is a critical quantum paraelectric system with Fe$^{3+}$ ions playing roles for both magnetic and electric dipoles.
