  We present the magnetic properties of complete solid solutions of
ZnCr$_2$O$_4$ and CoCr$_2$O$_4$: two well-studied oxide spinels with very
different magnetic ground states. ZnCr$_2$O$_4$, with non-magnetic $d^{10}$
cations occupying the A site and magnetic $d^3$ cations on the B site, is a
highly frustrated antiferromagnet. CoCr$_2$O$_4$, with magnetic $d^7$ cations
(three unpaired electrons) on the A site as well, exhibits both N\'eel
ferrimagnetism as well as commensurate and incommensurate non-collinear
magnetic order. More recently, CoCr$_2$O$_4$ has been studied extensively for
its polar behavior which arises from conical magnetic ordering. Gradually
introducing magnetism on the A site of ZnCr$_2$O$_4$ results in a transition
from frustrated antiferromagnetism to glassy magnetism at low concentrations of
Co, and eventually to ferrimagnetic and conical ground states at higher
concentrations. Real-space Monte-Carlo simulations of the magnetic
susceptibility suggest that the first magnetic ordering transition and features
of the susceptibility across $x$ are captured by near-neighbor self- and
cross-couplings between the magnetic A and B atoms. We present as a part of
this study, a method for displaying the temperature dependence of magnetic
susceptibility in a manner which helps distinguish between compounds possessing
purely antiferromagnetic interactions from compounds where other kinds of
ordering are present.
