We discuss a model nonfrustrated magnetoelectric in which a sufficiently strong magnetoelectric coupling produces an incommensurate magnetic order leading to ferroelectricity. Properties of the magnetoelectric in the magnetic field directed perpendicular to the wave vector describing the spin helix are considered in detail. Analysis of the classical energy shows that in contrast to the naive expectation, the onset of ferroelectricity occurs at a field H (c1) that is lower than the saturation field H (c2). We have H (c1) = H (c2) at large enough magnetoelectric coupling. We show that at H = 0, ferroelectricity occurs at T = T (FE) < T (N). A qualitative discussion of the phase diagram in the H-T plane is presented within the mean-field approach.
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