We discuss the interplay between anti-ferromagnetic order and polarization
fluctuations in a magnetic quantum paraelectric. Using an action where
anti-ferromagnetic order parameter couples to the polarization fluctuations and
as well as magnetic field, we derive a set of self consistent equations to
study both the temperature and the magnetic field dependence of the static
dielectric susceptibility. The temperature dependence of dielectric
susceptibility near both the anti-ferromagnetic quantum critical point and
ferroelectric quantum critical point are described using scaling arguments.
Discussions on achieving various quantum critical points in experiments are
also made.Comment: Published version, 7 pages, 3 figures;
http://dx.doi.org/10.1016/j.physleta.2012.07.01