Inversion symmetric materials are forbidden to show an overall spin texture in their band structure in the presence of time-reversal symmetry. However, in van der Waals materials which lack inversion symmetry within a single layer, it has been proposed that a layer-dependent spin texture can arise leading to a coupled spin-layer degree of freedom. Here we use time-resolved Kerr rotation in inversion symmetric WSe$_{2}$ and MoSe$_{2}$ bulk crystals to study this spin-layer polarization and unveil its dynamics. Our measurements show that the spin-layer relaxation time in WSe$_2$ is limited by phonon-scattering at high temperatures and that the inter-layer hopping can be tunned by a small in-plane magnetic field at low temperatures, enhancing the relaxation rates. We find a significantly lower lifetime for MoSe$_{2}$ which agrees with theoretical expectations of a spin-layer polarization stabilized by the larger spin-orbit coupling in WSe$_2$.
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