Magnetic Frustration, Phase Competition, and the Magnetoelectric Effect in NdFe_{3}(BO_{3})_{4}

We present an element selective resonant magnetic x-ray scattering study of NdFe3(BO3)4 as a function of temperature and applied magnetic field. Our measurements show that the magnetic order of the Nd sublattice is induced by the Fe spin order. When a magnetic field is applied parallel to the hexagonal basal plane, the helicoidal spin order is suppressed and a collinear ordering, where the moments are forced to align in a direction perpendicular to the applied magnetic field, is stabilized. This result excludes a noncollinear spin order as the origin of the magnetically induced electric polarization in this compound. Instead our data imply that magnetic frustration results in a phase competition, which is the origin of the magnetoelectric response.