  Changes in the spin configuration of atomically-thin, magnetic van-der-Waals
multilayers can cause drastic modifications in their opto-electronic
properties. Conversely, the opto-electronic response of these systems provides
information about the magnetic state, very difficult to obtain otherwise. Here
we show that in CrCl$_3$ multilayers, the dependence of the tunnelling
conductance on applied magnetic field ($H$), temperature ($T$), and number of
layers ($N$) tracks the evolution of the magnetic state, enabling the magnetic
phase diagram of these systems to be determined experimentally. Besides a
high-field spin-flip transition occurring for all thicknesses, the in-plane
magnetoconductance exhibits an even-odd effect due to a low-field spin-flop
transition. If the layer number $N$ is even, the transition occurs at $\mu_0 H
\sim 0$ T due to the very small in-plane magnetic anisotropy, whereas for odd
$N$ the net magnetization of the uncompensated layer causes the transition to
occur at finite $H$. Through a quantitative analysis of the phenomena, we
determine the interlayer exchange coupling as well as the staggered
magnetization, and show that in CrCl$_3$ shape anisotropy dominates. Our
results reveal the rich behaviour of atomically-thin layered antiferromagnets
with weak magnetic anisotropy.
