Anomalous Hall effect and magnetic orderings in nano-thick V$_{\mathrm{5}}$S$_{\mathrm{8}}$

The rise of graphene marks the advent of two-dimensional atomic crystals, which have exhibited a cornucopia of intriguing properties, such as the integer and fractional quantum Hall effects, valley Hall effect, charge density waves and superconductivity, to name a few. Yet, magnetism, a property of extreme importance in both science and technology, remains elusive. There is a paramount need for magnetic two-dimensional crystals. Here we show that nano-thick V$_{\mathrm{5}}$S$_{\mathrm{8}}$ is ferromagnetic at low temperatures. In particular, we employ the anomalous Hall effect, combined with magnetoresistance, to probe the magnetic ordering in V$_{\mathrm{5}}$S$_{\mathrm{8}}$ down to 3.2 nm. With decreasing thickness, a transition from antiferromagnetism to ferromagnetism is evident. The results represents a significant step toward magnetic two-dimensional crystals.