  The A-site spinel material, CoAl2O4, is a physical realization of the
frustrated diamond-lattice antiferromagnet, a model in which is predicted to
contain unique incommensurate or `spin-spiral liquid' ground states. Our
previous single-crystal neutron scattering study instead classified it as a
`kinetically-inhibited' antiferromagnet, where the long ranged correlations of
a collinear Neel ground state are blocked by the freezing of domain wall motion
below a first-order phase transition at T* = 6.5 K. The current paper expands
on our original results in several important ways. New elastic and inelastic
neutron measurements are presented that show our initial conclusions are
affected by neither the sample measured nor the instrument resolution, while
measurements to temperatures as low as T = 250 mK limit the possible role being
played by low-lying thermal excitations. Polarized diffuse neutron measurements
confirm reports of short-range antiferromagnetic correlations and diffuse
streaks of scattering, but major diffuse features are explained as signatures
of overlapping critical correlations between neighboring Brillouin zones.
Finally, and critically, this paper presents detailed elastic and inelastic
measurements of magnetic correlations in a single-crystal of MnAl2O4, which
acts as an unfrustrated analogue to CoAl2O4. The unfrustrated material is shown
to have a classical continuous phase transition to Neel order at T_N = 39 K,
with collective spinwave excitations and Lorentzian-like critical correlations
which diverge at the transition. Direct comparison between the two compounds
indicates that CoAl2O4 is unique, not in the nature of high-temperature diffuse
correlations, but rather in the nature of the frozen state below T*. The higher
level of cation inversion in the MnAl2O4 sample indicates that this novel
behavior is primarily an effect of greater next-nearest-neighbor exchange.
