  We have investigated the structural, magnetic, thermodynamic, and dielectric
properties of polycrystalline CoCr$_2$O$_4$, an insulating spinel exhibiting
both ferrimagnetic and spiral magnetic structures. Below $T_c$ = 94 K the
sample develops long-range ferrimagnetic order, and we attribute a sharp phase
transition at $T_N$ $\approx$ 25 K with the onset of long-range spiral magnetic
order. Neutron measurements confirm that while the structure remains cubic at
80 K and at 11 K; there is complex magnetic ordering by 11 K. Density
functional theory supports the view of a ferrimagnetic semiconductor with
magnetic interactions consistent with non-collinear ordering. Capacitance
measurements on CoCr$_2$O$_4$, show a sharp decrease in the dielectric constant
at $T_N$, but also an anomaly showing thermal hysteresis falling between
approximately $T$ = 50 K and $T$ = 57 K. We tentatively attribute the
appearance of this higher temperature dielectric anomaly to the development of
\textit{short-range} spiral magnetic order, and discuss these results in the
context of utilizing dielectric spectroscopy to investigate non-collinear
short-range magnetic structures.
