Ferroelectricity in the incommensurate helical magnetic phase (below $T_N$, 43 K) of alpha (α) CaCr${}_2$O${}_4$ has been confirmed by pyroelectric measurements. Magnetoelectric and magnetodielectric coupling exist below $T_N$ and are proportional to the square of magnetic field. From symmetry analysis we suggest that the presence of an external electric field destabilizes the symmetrical 2221′ phase and stabilizes 21′ symmetry. This provides a unique system in which polarization varies as the fourth-degree of the order-parameter amplitude and exhibits a vanishingly small value below the first-order transition at $T_N$, as observed experimentally.

• Received 22 April 2011

DOI:https://doi.org/10.1103/PhysRevB.84.064129