Goldstone modes and electromagnon fluctuations in the conical cycloid state of a multiferroic

Using a phenomenological Ginzburg-Landau theory for the magnetic conical cycloid state of a multiferroic, which has been recently reported in the cubic spinel CoCr$_{2}$O$_{4}$, we discuss its low-energy fluctuation spectrum. We identify the Goldstone modes of the conical cycloidal order, and deduce their dispersion relations whose signature anisotropy in momentum space reflects the symmetries broken by the ordered state. We discuss the soft polarization fluctuations, the `electromagnons, associated with these magnetic modes and make several experimental predictions which can be tested in neutron scattering and optical experiments.