Spin roton in flattened dipolar binary condensates

A confined dipolar Bose-Einstein condensate can develop a finite-momentum roton instability, which has been observed in recent experiments. Here we consider a flattened two-component dipolar condensate, produced by trapping along one direction. This system exhibits roton instabilities with density- and spin-character. We find that the spin-roton instability marks the transition to a patterned immiscible ground state. We develop a theory for the ground states and excitations of this system and apply this to locating the conditions where the spin-roton forms.