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Electric manipulation of magnetic properties is a key problem of materials research. To fulfil the requirements of modern electronics, these processes must be shifted to high frequencies. In multiferroic materials this may be achieved by electric and magnetic control of their fundamental excitations. Here we identify magnetic vibrations in multiferroic iron-borates which are simultaneously sensitive to external electric and magnetic fields. Nearly 100 % modulation of the terahertz radiation in an external field is demonstrated for SmFe3(BO3)4. High sensitivity can be explained by a modification of the spin orientation which controls the excitation conditions in multiferroic borates. These experiments demonstrate the possibility to alter terahertz magnetic properties of materials independently by external electric and magnetic fields.

Electric and magnetic properties of multiferroic GdMn 2 O 5 in external magnetic fields were investigated to map out the magnetoelectric phases in this material. Due to strong magnetoelectric coupling, the dielectric permittivity is highly sensitive to phase boundaries in GdMn 2 O 5 , which allowed to construct the field-temperature phase diagrams. Several phase transitions are observed which are strongly field-dependent with respect to field orientation and strength. The phase diagram for a magnetic field along the crystallographic a-axis corresponds well to a polarization step, as induced by 90 • rotation of Gd magnetic moments. Our results support the model of two ferroelectric sublattices, Mn-Mn and Gd-Mn with strong R-Mn (4f -3d) interaction for the polarization in RMn 2 O 5 .

Violation of time reversal and spatial inversion symmetries has profound consequences for elementary particles and cosmology. Spontaneous breaking of these symmetries at phase transitions gives rise to unconventional physical phenomena in condensed matter systems, such as ferroelectricity induced by magnetic spirals, electromagnons, non-reciprocal propagation of light and spin waves, and the linear magnetoelectric (ME) effect—the electric polarization proportional to the applied magnetic field and the magnetization induced by the electric field. Here, we report the experimental study of the holmium-doped langasite, HoxLa3−xGa5SiO14, showing a puzzling combination of linear and highly non-linear ME responses in the disordered paramagnetic state: its electric polarization grows linearly with the magnetic field but oscillates many times upon rotation of the magnetic field vector. We propose a simple phenomenological Hamiltonian describing this unusual behavior and derive it microscopically using the coupling of magnetic multipoles of the rare-earth ions to the electric field.