Magnetodielectric coupling in Mn$_3$O$_4$ and MnCr$_2$O$_4$

We have investigated the temperature and magnetic field dependent dielectric constants of the ferrimagnetic insulators Mn$_3$O$_4$ and MnCr$_2$O$_4$. We have also measured the heat capacity and AC magnetic susceptibility through the multiple spin ordering transitions in these materials. At the zero field T = 42 K and T = 35 K magnetic transitions in Mn$_3$O$_4$ we observed sharp drops in the dielectric constant. In an applied field of 5 kOe, Mn$_3$O$_4$ shows a positive shift in dielectric constant at the intermediate T = 40 K transition in addition to the features observed at zero field. MnCr$_2$O$_4$ also shows features in the dielectric constant at the magnetic transitions at T = 40 K and T = 20 K, though these shifts were approximately 100 times smaller than those observed in Mn$_3$O$_4$. These results will be discussed in the framework of models for coupling the dielectric constant to non-colinear long-range magnetic order.