Dielectric and Spin Susceptibilities using Density Functional Theory

The response of a system to some external perturbation is almost ubiquitous in Physics. The application of perturbation theory through an electronic structure method such as Density Functional Theory has had significant contributions over the last few decades. Its implementation, aptly named Density Functional Perturbation Theory has seen use in a number of ab initio calculations on a variety of physical properties of materials which depend on their lattice-dynamical behaviour. Specific heats, thermal expansion, infrared, Raman and optical spectra are to name just a few. Understanding the complex phenomena has significantly corroborated the current understanding of the quantum picture of solids. The Sternheimer scheme falls under the umbrella of methods to compute response functions in Time-Dependent Density Functional Theory. Initially developed to study the electronic polarisability, it is now commonly utilised in the field of lattice dynamics to study phonons and related crystal properties. The Sternheimer equation has also been used to model spin wave excitations by computation of the magnetic susceptibility. The poles of the susceptibility are known to correspond to magnon excitations and these computations have been corroborated by experimental inelastic neutron scattering data. These excitations are of a transverse nature, in that they involve fluctuations of the magnetisation perpendicular to a chosen z axis. The lesser-known longitudinal excitations involve fluctuations of the magnetisation along z, an investigation of collective modes present in transition metals may be carried out from self-consistent computations of the Sternheimer equation. The dielectric response is an important linear response function in solid-state physics. Its computation from first principles provides an invaluable tool in the characterisation of optical properties and can be compared to the experimental method of spectroscopic ellipsometry.

The work in this thesis concerns the implementation of the Sternheimer method in computing the dynamical response from either an external plane wave or spin-polarised perturbation. These response functions are the dielectric and spin (magnetisation) susceptibilities respectively.

The scheme to compute the frequency-dependent dielectric response is implemented in a plane-wave pseudopotential DFT package. Calculations are performed on the semiconducting systems of Silicon, Gallium Arsenide, Zinc Oxide and perovskite Methylammonium Lead Triiodide. The overall shape of the dielectric spectra is in good agreement with spectroscopic ellipsometry data, however, there is a shift which is attributed to the limitations of DFT.

The scheme developed to compute longitudinal spin dynamics is applied to the transition
metal systems of body-centred cubic Iron and face-centred cubic Nickel. In a similar manner to another first principles approach, a single dominant peak is shown to be present in the magnetisation channel with the charge dynamics being effectively null in comparison. However, the exact position of these peaks is not in agreement with the other approach, a discussion is made regarding difficulties pertaining to self-consistent optimisation.