  The competition between different forms of order is central to the problem of
strong correlation. This is particularly true of frustrated systems, which
frequently exist at or near to a zero-temperature critical point. Here we show
that a state with a half-magnetization plateau but no long range order can
arise when a three dimensional frustrated antiferromagnet is tuned to a
critical point bordering a metamagnetic state. We use classical Monte Carlo
simulation and low-temperature expansion techniques to accurately characterize
this `spin pseudogap' state, and show how its properties relate to those of the
critical point. Our results provide an example of three dimensional spin model
which can be used to study the relationship between gap and `pseudogap', - i.e.
long range and preformed local order - near a metamagnetic critical point.
