Incommensurate phases induced by an electric field

All magnetic symmetry classes for which the two-dimensional representations are physically irreducible are enumerated. These representations admit of the Lifshitz invariant induced by an external electric field aligned parallel to the principal axis of the crystal. In the majority of the cases, this field does not split two-dimensional representations into one-dimensional representations and, therefore, an incommensurate phase arises in an arbitrarily weak field. The representations of the magnetic classes C _4h and C′_4h are considered in close detail. The components of the toroidal momentum are chosen as the components of the order parameter.