Ginzburg-Landau theory for the conical cycloid state in multiferroics: Applications to CoCr2O4

We show that the cycloidal magnetic order of a multiferroic can arise in the absence of spin and lattice anisotropies, e.g., in a cubic material, and this explains the occurrence of such a state in CoCr2O4. We discuss the case when this order coexists with ferromagnetism in a so-called conical cycloid state and show that a direct transition to this state from the ferromagnet is necessarily first order. On quite general grounds, the reversal of the direction of the uniform magnetization in this state can lead to the reversal of the electric polarization as well without the need to invoke toroidal moment as the order parameter.