Direct Transition From a Disordered Phase to an Incommensurate Multiferroic on a Triangular Lattice

Competing interactions and geometric frustration provide favorable conditions for exotic states of matter. Case in point are magnetic ferroelectrics, or multiferroics, where inversion symmetry breaking magnetism acts as an electric field [1-5]. Complicating their interpretation and application, multiferroic states were so far only encountered as products of secondary phase transitions from ferroelectric or magnetic states of matter. We report a first direct transition from a paramagnetic and paraelectric phase to an incommensurate multiferroic in the triangular lattice antiferromagnet RbFe(MoO4)2 (RFMO). A magnetic field extinguishes the electric polarization when the symmetry of the magnetic order changes and ferroelectricity is only observed when the magnetic structure has chirality and breaks inversion symmetry. Multiferroic behavior in RFMO provides a theoretically tractable example of ferroelectricity from competing spin interactions. A Landau expansion that describes the magneto-electric coupling takes a simple form and explains the simple relation of the temperature dependence of the electric and magnetic order parameters. Our quantitative determination of the magneto-electric coupling constant is a direct guide towards the design of multifunctional materials for device applications.