By establishing magnetic order in a square lattice compound, we introduce the first magnetic “new fermion.”

We have theoretically investigated, by ab initio techniques, the phonon properties of several semiconductors with chalcopyrite structure. Comparison with experiments has led us to distinguish between materials with $d$ electrons in the valence band (e.g., CuGaS${}_2$, AgGaS${}_2$) and those without $d$ electrons (e.g., ZnSnAs${}_2$). The former exhibit a rather peculiar nonmonotonic temperature dependence of the energy gap which, so far, has resisted cogent theoretical description. We analyze this nonmonotonic temperature dependence by fitting two Bose-Einstein oscillators with weights of opposite sign leading to an increase at low temperatures and a decrease at higher temperatures and find that the energy of the former correlates well with characteristic peaks in the phonon density of states associated with low-energy vibrations of the $d$-electron elements. We hope that this work will encourage theoretical investigations of the electron-phonon interaction in this direction, especially of the current ab initio type.

Specific heat measurements and theoretical calculations reveal an intimate analogy between EuTiO3 and SrTiO3. For EuTiO3, a hitherto unknown specific heat anomaly is discovered at temperatures TA= 282(1)K, which is analogous to the well-known specific heat anomaly of SrTiO3 at the temperature TA= 105K caused by an antiferrodistortive transition. Because the zone center soft phonon mode observed in both systems can be modeled with the same parameters, we ascribe the new 282(1)K instability of EuTiO3 to an antiferrodistortive phase transition. The higher transition temperature of EuTiO3 as compared to SrTiO3 results from spin-phonon coupling.

We report ab initio calculations of the electronic band structure and the phonon dispersion relations of the zincblende-type mercury chalcogenides ($\beta \text{-HgS}$, HgSe, and HgTe). The latter have been used to evaluate the temperature dependence of the specific heat, which has been compared with experimental data. The electronic band structure of these materials has been confirmed to have an inverted direct gap of the $\alpha$-tin type, which makes HgSe and HgTe semimetallic. For $\beta \text{-HgS}$, however, our calculations predict a negative spin-orbit splitting that restores semiconducting properties to the material in spite of the inverted gap. We have calculated the spin-orbit induced linear terms in $\mathbf{k}$, which appear at the ${\Gamma }_8$ valence bands. We have also investigated the pressure dependence of the crystal structure and the phonons.