The nature of the lattice instability connected to the structural transition and superconductivity of (Sr,Ca)$_3$Ir$_4$Sn$_{13}$ is not yet fully understood. In this work density functional theory (DFT) calculations of the phonon instabilities as a f
unction of chemical and hydrostatic pressure show that the primary lattice instabilities in Sr$_3$Ir$_4$Sn$_{13}$ lie at phonon modes of wavevectors $mathbf{q}=(0.5,0,0)$ and $mathbf{q}=(0.5,0.5,0)$. Following these modes by calculating the energy of supercells incorporating the mode distortion results in an energy advantage of -14.1 meV and -9.0 meV per formula unit respectively. However, the application of chemical pressure to form Ca$_3$Ir$_4$Sn$_{13}$ reduces the energetic advantage of these instabilities, which is completely removed by the application of a hydrostatic pressure of 35 kbar to Ca$_3$Ir$_4$Sn$_{13}$. The evolution of these lattice instabilities is consistent with experimental phase diagram. The structural distortion associated with the mode at $mathbf{q}=(0.5,0.5,0)$ produces a distorted cell with the same space group symmetry as the experimentally refined low temperature structure. Furthermore, calculation of the deformation potential due to these modes quantitatively demonstrates a strong electron-phonon coupling. Therefore, these modes are likely to be implicated in the structural transition and superconductivity of this system.
First principles density functional theory (DFT) is used to investigate the electronic structure of beta-MnO2. From collinear spin polarized calculations we find that DFT+U_Eff predicts a gapless ferromagnet in contrast with experiment which indicate
s an insulating antiferromagnet. The inclusion of anisotropic Coulomb and exchange interactions in the DFT+U approach, defining U and J explicitly, corrects these errors and leads to an antiferromagnetic ground state with a fundamental gap of 0.8 eV consistent with low temperature experiments. To our knowledge, this work on beta-MnO2 represents the first demonstration of a case in which the application of fully anisotropic interactions in DFT+U determines the magnetic order and consequent band gap, while the more commonly used effective U approach fails. Such effects are argued to be of importance in many insulating materials. The mechanism leading to an increase in band gap due to anisotropic interactions is highlighted by analytical calculation of DFT+U d-orbital eigenvalues obtained within a Kanamori-type model. Magnetic coupling constants obtained by the fitting of a Heisenberg spin Hamiltonian to the energies of a range of magnetic states assist in rationalizing the finding that anisotropic interactions enhance the stability of the experimentally observed helical antiferromagnetic order. The plane wave PAW method yields poorer results for the exchange couplings than full-potential LAPW calculations. Finally, we compare the DFT+U results with exchange couplings obtained from hybrid functionals. It is argued that anisotropic interactions should be included in DFT+U if the results are to be properly compared with those from hybrid functionals.
