Towards a microscopic model of magnetoelectric interactions in Ni₃V₂O₈

We develop a microscopic magnetoelectric coupling in Ni₃V₂O₈ (NVO) which gives rise to the trilinear phenomenological coupling used previously to explain the phase transition in which magnetic and ferroelectric order parameters appear simultaneously. Using combined neutron scattering measurements and first-principles calculations of the phonons in NVO, we identify eleven phonons which can induce the observed spontaneous polarization. A few of these phonons can actually induce a significant dipole moment. Using the calculated atomic charges, we find that the required distortion to induce the observed dipole moment is very small (∼0.001 Å) and therefore it would be very difficult to observe the distortion by neutron-powder diffraction. Finally, we identify the derivatives of the exchange tensor with respect to atomic displacements, which are needed for a microscopic model of a spin-phonon coupling in NVO. We also analyze two toy models to illustrate that although the Dzyaloshinskii-Moriya interaction is often very important for coexisting of magnetic and ferroelectric order, it is not the only mechanism when the local site symmetry of the system is low enough. In fact, this coexistence can arise in NVO only due to the symmetric exchange anisotropies.