  Transition metal dichalcogenides (TMDs) combine interesting optical and
spintronic properties in an atomically-thin material, where the light
polarization can be used to control the spin and valley degrees-of-freedom for
the development of novel opto-spintronic devices. These promising properties
emerge due to their large spin-orbit coupling in combination with their crystal
symmetries. Here, we provide simple symmetry arguments in a group-theory
approach to unveil the symmetry-allowed spin scattering mechanisms, and
indicate how one can use these concepts towards an external control of the spin
lifetime. We perform this analysis for both monolayer (inversion asymmetric)
and bilayer (inversion symmetric) crystals, indicating the different mechanisms
that play a role in these systems. We show that, in monolayer TMDs, electrons
and holes transform fundamentally differently -- leading to distinct
spin-scattering processes. We find that one of the electronic states in the
conduction band is partially protected by time-reversal symmetry, indicating a
longer spin lifetime for that state. In bilayer and bulk TMDs, a hidden
spin-polarization can exist within each layer despite the presence of global
inversion symmetry. We show that this feature enables control of the interlayer
spin-flipping scattering processes via an out-of-plane electric field,
providing a mechanism for electrical control of the spin lifetime.
