  The magnetic state of atomically thin semiconducting layered antiferromagnets
such as CrI$_3$ and CrCl$_3$ can be probed by forming tunnel barriers and
measuring their resistance as a function of magnetic field ($H$) and
temperature ($T$). This is possible because the tunneling magnetoresistance
originates from a spin-filtering effect sensitive to the relative orientation
of the magnetization in different layers, i.e., to the magnetic state of the
multilayers. For systems in which antiferromagnetism occurs within an
individual layer, however, no spin-filtering occurs: it is unclear whether this
strategy can work. To address this issue, we investigate tunnel transport
through atomically thin crystals of MnPS$_3$, a van der Waals semiconductor
that in the bulk exhibits easy-axis antiferromagnetic order within the layers.
For thick multilayers below $T\simeq 78$ K, a $T$-dependent magnetoresistance
sets-in at $\sim 5$ T, and is found to track the boundary between the
antiferromagnetic and the spin-flop phases known from bulk magnetization
measurements. The magnetoresistance persists down to individual MnPS$_3$
monolayers with nearly unchanged characteristic temperature and magnetic field
scales, albeit with a different dependence on $H$. We discuss the implications
of these finding for the magnetic state of atomically thin MnPS$_3$ crystals,
conclude that antiferromagnetic correlations persist down to the level of
individual monolayers, and that tunneling magnetoresistance does allow
magnetism in 2D insulating materials to be detected even in the absence of
spin-filtering.
