  The ground state of BaFe12O19 (BFO) is controversial as three different
quantum states, namely quantum paraelectric, frustrated antiferroelectric and
quantum electric dipole liquid (QEDL), have been proposed. We have investigated
the quantum critical behavior of BFO as a function of chemical pressure (a
non-thermal variable) generated by smaller isovalent ion Ca2+ at the Ba2+ site.
Analysis of synchrotron x-ray diffraction data confirms that Ca2+ substitution
generates positive chemical pressure. Our dielectric measurements reveal that
Ca2+ substitution drives BFO away from its quantum critical point (QCP) and
stabilizes a quantum electric dipolar glass state whose dielectric peak
temperature (Tc) increases with increasing Ca2+ content as Tc ~ (x-xc)1/2, a
canonical signature of quantum phase transitions. Our dielectric measurements
reveal that pure BFO is slightly away from its QCP with a Tc of 2.91 K.
Specific heat measurements reveal excess specific heat of non-Debye and
non-magnetic origin with linear temperature dependence below Tc which could be
due to QEDL state of BFO.
