Title: Magnetic-field induced spiral order in the electric polarization

Abstract: We present a phenomenological model for magnetoelectricity in multiferroic materials. The distinctive feature of the model is a two-component complex order parameter that encodes the electric polarization, along with a direct coupling between the polarization and magnetic field. Our model effectively elucidates that a sufficiently strong magnetic field can destroy electric polarization. Furthermore, the transition field strength diminishes with rising temperature, following a power-law relation with the exponent being precisely worked out. At lower field strength, the electric polarization takes a spiral order in the magnetic field, with the spiral wavelength inversely proportional to the magnetic field strength. We anticipate these predictions can be experimentally tested in future studies on multiferroic materials.