No abstract

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.

The magnetic and magnetoelectric properties of rare-earth (R = Tm, Ho, and Tb) aluminum borates were studied. Magnetic susceptibility of the crystals was examined. The dependencies of the magnetic susceptibility on the magnitude and direction of magnetic field were calculated. The quantum theory of magnetoelectric effect in Tm, Ho, and Tb aluminum borates has been developed and the dependencies of the polarization on the magnetic field and temperature were obtained. A comparison of the theoretical and experimental data was performed, ascertaining their consistency.Index Terms-Aluminum borates, crystal-field parameters, magnetoelectric materials, rare-earth ions.