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We present a detailed study of the zone-center phonons and magnetoelectric interactions in Ni3V2O8. Using combined neutron scattering, polarized infrared (IR) measurements and first-principles LDA+U calculations, we successfully assigned all IR-active modes, including eleven B2u phonons which can induce the observed spontaneous electric polarization. We also calculated the Born-effective charges and the IR intensities which are in surprisingly good agreement with the experimental data. Among the eleven B2u phonons, we find that only a few of them can actually induce a significant dipole moment. The exchange interactions up to a cutoff of 6.5 A are also calculated within the LDA+U approach with different values of U for Ni, V and O atoms. We find that LSDA (i.e. U = 0) gives excellent results concerning the optimized atomic positions, bandgap and phonon energies. However, the magnitudes of the exchange constants are too large compared to the experimental Curie–Weiss constant, Θ. Including U for Ni corrects the magnitude of the superexchange constants but opens a too large electronic bandgap. We observe that including correlation at the O site is very important to get simultaneously the correct phonon energies, bandgap and exchange constants. In particular, the nearest and next-nearest exchange constants along the Ni-spine sites result in incommensurate spin ordering with a wavevector that is consistent with the experimental data. Our results also explain how the antiferromagnetic coupling between sublattices in the b and c directions is consistent with the relatively small observed value of Θ. We also find that, regardless of the values of U used, we always get the same five exchange constants that are significantly larger than the rest. Finally, we discuss how the B2u phonons and the spin structure combine to yield the observed spontaneous polarization. We present a simple phenomenological model which shows how trilinear (and quartic) couplings of one (or two) phonons to two spin operators perturbatively affects the magnon (i.e. electromagnon) and phonon energies.

We report on the magnetic properties of multiferroic hexagonal HoMnO3 single crystals and polycrystalline samples with micrometer and nanometer particle size. We have studied the in-plane and out-of-plane magnetization of HoMnO3 single crystals under low applied magnetic fields in the temperature range below TNeel = 72 K and observe the bifurcation of zero-field-cooled and field-cooled curves at the Mn spin reorientation transition temperature at 34 K. In addition, the c-axis magnetization shows a ferrimagnetic-like behavior which may relate to the magnetic Ho 3+ and Mn 3+ domain boundary structures and sensitively respond to changes of the magnetic structure such as spin rotations at the phase transitions near 5 and 34 K. We also studied the particles' size dependent magnetic behavior in the HoMnO3 polycrystalline samples and observe the presence of a net magnetic moment at the surface due to the large surface/volume ratio. Below the Ho 3+ ordering temperature of 5 K, magnetization curves as a function of applied magnetic field, in contrast to those for the single crystal, show hysteresis behavior with coercivity, which increases with diminishing particle size.