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.
Density functional theory methods are applied to investigate the properties of the new superconductor $beta$-YbAlB$_4$ and its polymorph $alpha$-YbAlB$_4$. We utilize the generalized gradient approximation + Hubbard U (GGA+U) approach with spin-orbit
(SO) coupling to approximate the effects of the strong correlations due to the open $4f$ shell of Yb. We examine closely the differences in crystal bonding and symmetry of $beta$-YbAlB$_4$ and $alpha$-YbAlB$_4$. The in-plane bonding structure amongst the dominant itinerant electrons in the boron sheets is shown to differ significantly. Our calculations indicate that, in both polymorphs, the localized 4$f$ electrons hybridize strongly with the conduction sea when compared to the related materials YbRh$_{2}$Si$_{2}$ and YbB$_{2}$. Comparing $beta$-YbAlB$_4$ to the electronic structure of related crystal structures indicates a key role of the 7-member boron coordination of the Yb ion in $beta$-YbAlB$_4$ in producing its enhanced Kondo scale and superconductivity. The Kondo scale is shown to depend strongly on the angle between the B neighbors and the Yb ion, relative to the $x-y$ plane, which relates some of the physical behavior to structural characteristics.
Using density functional theory we investigate the evolution of the magnetic ground state of NbFe$_{2}$ due to doping by Nb-excess and Fe-excess. We find that non-rigid-band effects, due to the contribution of Fe-textit{d} states to the density of st
ates at the Fermi level are crucial to the evolution of the magnetic phase diagram. Furthermore, the influence of disorder is important to the development of ferromagnetism upon Nb doping. These findings give a framework in which to understand the evolution of the magnetic ground state in the temperature-doping phase diagram. We investigate the magnetic instabilities in NbFe$_{2}$. We find that explicit calculation of the Lindhard function, $chi_{0}(mathbf{q})$, indicates that the primary instability is to finite $mathbf{q}$ antiferromagnetism driven by Fermi surface nesting. Total energy calculations indicate that $mathbf{q}=0$ antiferromagnetism is the ground state. We discuss the influence of competing $mathbf{q}=0$ and finite $mathbf{q}$ instabilities on the presence of the non-Fermi liquid behavior in this material.
We present detailed electronic structure calculations for CaFe2As2. We investigate in particular the `collapsed tetragonal and orthorhombic regions of the temperature-pressure phase diagram and find properties that distinguish CaFe2As2 from other Fe-
pnictide compounds. In contrast to the tetragonal phase of other Fe-pnictides the electronic structure in the `collapsed tetragonal phase of CaFe2As2 is found to be strongly 3D. We discuss the influence of these properties on the formation of superconductivity and in particular we find evidence that both magnetic and lattice interactions may be important to the formation of superconductivity. We also find that the Local Spin Density Approximation is able to accurately predict the ordering moment in the low temperature orthorhombic phase.
