Neither of the two typical two-dimensional materials, graphene and single layer MoS ${}_2$ , are good enough for developing semiconductor logical devices. We calculated the electron mobility of 14 two-dimensional semiconductors with composition of MX ${}_2$ , where M (=Mo, W, Sn, Hf, Zr and Pt) are transition metals, and Xs are S, Se and Te. We approximated the electron phonon scattering matrix by deformation potentials, within which long wave longitudinal acoustical and optical phonon scatterings were included. Piezoelectric scattering in the compounds without inversion symmetry is also taken into account. We found that out of the 14 compounds, WS ${}_2$ , PtS ${}_2$ and PtSe ${}_2$ are promising for logical devices regarding the possible high electron mobility and finite band gap. Especially, the phonon limited electron mobility in PtSe ${}_2$ reaches about 4000 cm ${}^2$ ·V ${}^{-1}$ ·s ${}^{-1}$ at room temperature, which is the highest among the compounds with an indirect bandgap of about 1.25 eV under the local density approximation. Our results can be the first guide for experiments to synthesize better two-dimensional materials for future semiconductor devices.

The superexchange theory predicts dominant antiferromagnetic kinetic interaction when the orbitals accommodating magnetic electrons are covalently bonded through diamagnetic bridging atoms or groups. Here we show that explicit consideration of magnetic and (leading) bridging orbitals, together with the electron transfer between the former, reveals a strong ferromagnetic kinetic exchange contribution. First-principles calculations show that it is comparable in strength with antiferromagnetic superexchange in a number of magnetic materials with diamagnetic metal bridges. In particular, it is responsible for a very large ferromagnetic coupling ($-10$ meV) between the iron ions in a ${\mathrm{Fe}}^{3+}\text{−}{\mathrm{Co}}^{3+}\text{−}{\mathrm{Fe}}^{3+}$ complex. Furthermore, we find that the ferromagnetic exchange interaction turns into antiferromagnetic by substituting the diamagnetic bridge with magnetic one. The phenomenology is observed in two series of materials, supporting the significance of the ferromagnetic kinetic exchange mechanism.

In insulating lanthanides, unquenched orbital momentum and weak crystal-field (CF) splitting of the atomic $J$ multiplet at lanthanide ions result in a highly ranked (multipolar) exchange interaction between them and a complex low-temperature magnetic order not fully uncovered by experiment. Explicitly correlated ab initio methods proved to be highly efficient for an accurate description of CF multiplets and magnetism of individual lanthanide ions in such materials. Here we extend this ab initio methodology and develop a first-principles microscopic theory of multipolar exchange interaction between $J$ multiplets in $f$-metal compounds. The key point of the approach is a complete account of Goodenough's exchange mechanism along with traditional Anderson's superexchange and other contributions, the former being dominant in many lanthanide materials. Application of this methodology to the description of the ground-state order in the neodymium nitride with rocksalt structure reveals the multipolar nature of its ferromagnetic order. We found that the primary and secondary order parameters (of $T_{1u}$ and $E_g$ symmetry, respectively) contain non-negligible $J$-tensorial contributions up to the ninth order. The calculated spin-wave dispersion and magnetic and thermodynamic properties show that they cannot be simulated quantitatively by confining to the ground CF multiplet on the Nd sites. Our results demonstrate that the ab initio approach to the low-energy Hamiltonian represents a powerful tool for the study of materials with complex magnetic order.

Compared to isolated ${\mathrm{C}}_{60}^{3-}$ ions, characterized by a three-dimensional equipotential trough at the bottom of the lowest adiabatic potential energy surface (APES), the Jahn-Teller (JT) effect in cubic fullerides is additionally influenced by the interaction of JT distortions at ${\mathrm{C}}_{60}$ sites with vibrational modes of the lattice. This leads to modification of JT stabilization energy and to the warping of the trough at each fullerene site, as well as to the interaction of JT distortions at different sites. Here we investigate these effects in three fcc fullerides with $A=\mathrm{K}$, Rb, Cs and in ${\mathrm{Cs}}_3{\mathrm{C}}_{60}$ with bcc (A15) structure. DFT calculations of orbital vibronic coupling constants at ${\mathrm{C}}_{60}$ sites and of phonon spectra have been done for fully ordered lattices (1 ${\mathrm{C}}_{60}/\mathrm{u}.\mathrm{c}.$). Based on them the elastic response function for local JT distortions has been evaluated and the lowest APES investigated. To this end an expression for the latter as a function of trough coordinates of all sites has been derived. The results show that the JT stabilization energy slightly increases compared to an isolated ${\mathrm{C}}_{60}^{3-}$ and a warping of the trough of a few meV occurs. The interaction of JT distortions on nearest- and next-nearest-neighbor fullerene sites is of similar order of magnitude. These effects arise first of all due to the interaction of ${\mathrm{C}}_{60}$ sites with the displacements of neighbor alkali atoms and are more pronounced in fcc fullerides than in the A15 compound. The results of this study support the picture of weakly hindered independent rotations of JT deformations at ${\mathrm{C}}_{60}$ sites in cubic $A_3{\mathrm{C}}_{60}$.