  Transition metal dichalcogenide (TMD) monolayers are interesting materials in
part because of their strong spin-orbit coupling. This leads to intrinsic
spin-splitting of opposite signs in opposite valleys, so the valleys are
intrinsically spin-polarized when hole-doped. We study spin response in a
simple model of these materials, with an eye to identifying sharp collective
modes (i.e, spin-waves) that are more commonly characteristic of ferromagnets.
We demonstrate that such modes exist for arbitrarily weak repulsive
interactions, even when they are too weak to induce spontaneous ferromagnetism.
The behavior of the spin response is explored for a range of hole dopings and
interaction strengths.
