We discuss the interplay between anti-ferromagnetic order and polarizationfluctuations in a magnetic quantum paraelectric. Using an action whereanti-ferromagnetic order parameter couples to the polarization fluctuations andas well as magnetic field, we derive a set of self consistent equations tostudy both the temperature and the magnetic field dependence of the staticdielectric susceptibility. The temperature dependence of dielectricsusceptibility near both the anti-ferromagnetic quantum critical point andferroelectric quantum critical point are described using scaling arguments.Discussions on achieving various quantum critical points in experiments arealso made.
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