Graphene has emerged as the foremost material for future two-dimensional spintronics due to its tuneable electronic properties. In graphene, spin information can be transported over long distances and, in principle, be manipulated by using magnetic correlations or large spin-orbit coupling (SOC) induced by proximity effects. In particular, a dramatic SOC enhancement has been predicted when interfacing graphene with a semiconducting transition metal dechalcogenide, such as tungsten disulphide (WS$_2$). Signatures of such an enhancement have recently been reported but the nature of the spin relaxation in these systems remains unknown. Here, we unambiguously demonstrate anisotropic spin dynamics in bilayer heterostructures comprising graphene and WS$_2$. By using out-of-plane spin precession, we show that the spin lifetime is largest when the spins point out of the graphene plane. Moreover, we observe that the spin lifetime varies over one order of magnitude depending on the spin orientation, indicating that the strong spin-valley coupling in WS$_2$ is imprinted in the bilayer and felt by the propagating spins. These findings provide a rich platform to explore coupled spin-valley phenomena and offer novel spin manipulation strategies based on spin relaxation anisotropy in two-dimensional materials.
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