[en] We measured the temperature-dependent infrared reflectivity spectra of MnF₂ between 4 and 600 K. We show that the phonon spectrum undergoes a clear renormalization at T_N. The ab initio calculation we performed on this compound accurately predicts the magnitude and the direction of the changes in the phonon parameters across the antiferromagnetic transition, showing that they are mainly induced by the magnetic order. In this material, we found that the dielectric constant is mostly from phonon origin. The large change in the lattice parameters with temperature seen by x-ray diffraction as well as the A_2u phonon softening below T_N indicate that magnetic order induced distortions in MnF₂ are compatible with the ferroelectric instabilities observed in TiO₂, FeF₂ and other rutile-type fluorides. This study also shows the anomalous temperature evolution of the lower energy E_u mode in the paramagnetic phase, which can be compared to that of the B_1g phonon seen by Raman spectroscopy in many isostructural materials. This was interpreted as being a precursor of a phase transition from rutile to CaCl₂ structure which was observed under pressure in ZnF₂.

[en] This paper proposes the direct calculation of the microscopic contributions to the magneto-electric coupling, using ab initio methods. The electrostrictive and the Dzyaloshinskii–Moriya contributions were evaluated individually. For this purpose a specific method was designed, combining density functional theory calculations and embedded fragment, explicitly correlated, quantum chemical calculations. This method allowed us to calculate the evolution of the magnetic couplings as a function of an applied electric field. We found that in YMnO₃ the Dzyaloshinskii–Moriya contribution to the magneto-electric effect is three orders of magnitude weaker than the electrostrictive contribution. Strictive effects are thus dominant in the magnetic exchange evolution under an applied electric field, and by extension in the magneto-electric effect. These effects however, remain quite small, and the modifications of the magnetic excitations under an applied electric field will be difficult to observe experimentally. Another important conclusion is that it can be shown that the linear magneto-electric tensor is null due to the inter-layer symmetry operations. (paper)