Dynamical instability of the XY spiral state of ferromagnetic condensates

We calculate the spectrum of collective excitations of the XY spiral state prepared adiabatically or suddenly from a uniform ferromagnetic F=1 condensate. For spiral wavevectors past a critical value, spin wave excitation energies become imaginary indicating a dynamical instability. We construct phase diagrams as functions of spiral wavevector and quadratic Zeeman energy.