  Superfluids with a tendency towards periodic crystalline order have both a
phonon and roton like spectrum of collective modes. The softening of the roton
spectrum provides one route to a supersolid. We show that roton softening
occurs in 87Rb spinor condensates once dipolar interactions and spin dynamics
are taken into account. By including the effects of a quasi-two-dimensional
geometry and rapid Larmor precession, we show a dynamical instability develops
in the collective mode spectrum at finite wavevectors. We construct phase
diagrams showing a variety of instabilities as a function of the direction of
the magnetic field and strength of the quadratic Zeeman shift. Our results
provide a possible explanation of current experiments in the Berkeley group
Phys. Rev. Lett. 100:170403 (2008).
