Prediction and Understanding of Functional Topological and Spintronic Materials from First Principles

In this thesis we use first-principles density functional theory (DFT) and related methods to predict and understand the properties of two categories of materials with particular promise for technological applications: topological semimetals, and antiferromagnets whose magnetic order can be controlled by electrical current./nTopological semimetals (TSMs), a subset of topological materials which are the particular focus of the first part of this thesis, have robust band crossings in reciprocal space protected by crystalline symmetries and characterized by mathematical invariants. They exhibit a variety of exotic phenomena such as ultrahigh mobility of electrons, giant magnetoresistance, and chiral anomalies. Moreover, analogously to the better known topological insulators (TIs), the ``bulk-boundary correspondence", related to the change in topological invariant in going from material to vacuum, implies the existence of electronic states localized at the compound surface which can differ significantly from the semimetallic bulk states in TSMs. The development of group-theoretical methods to identify TSMs and TIs have revealed that TSMs are far more ubiquitous than initially hypothesized; to date over $10000$ candidates have been identified. While this might seem to imply that the goal of harnessing properties of TSMs for practical purposes is a solved problem, most candidate materials have one or more features which make experimental manipulation and detection of the topological properties difficult if not impossible. If the symmetry-protected band crossings occur at energies far from the Fermi level, or if they are obscured by other trivial bands at the same energy, the topological signatures will be obscured. Thus, the identification of specific materials, structural motifs, and possible tuning parameters through which one can realize ``functional" TSMs is highly desirable.\\indent The first section of this thesis describes a set of studies focused on the interplay of symmetry, orbital character and magnetism in yielding electronic structures with controllable TSM features near the Fermi level and free from interfering trivial bands. First, we use a combination of DFT and tight-binding to examine the electronic structure of a previously synthesized compound, $\mathrm{TiRhAs}$. We find that $\mathrm{TiRhAs}$ hosts a topological nodal line protected by a mirror plane nearly exactly at the Fermi level, with no other energetically degenerate trivial bands. Next, in combination with experimental ARPES data which confirmed our DFT findings, we investigate the transition metal dichalcogenide (TMD) $\mathrm{NiTe_2}$, and find that is a Dirac semimetal with a bulk tilted Dirac cone and topological surface states. While previous isostructural $\mathrm{MX_2}$ ($\mathrm{M}=\mathrm{Pd}$, $\mathrm{Pt}$: $\mathrm{X}=\mathrm{Te}$, $\mathrm{Se}$) compounds have been shown to host similar ``ladders" of topologically protected bulk and surface states, the features of interest occur at large binding energies which render their topological properties irrelevant to transport. We show that the increased hybridization between $\mathrm{Ni}$ $\mathrm{d}$ and $\mathrm{Te}$ $\mathrm{p}$ states as compared to the other $\mathrm{MX_2}$ compounds is responsible for tuning the Dirac cone very close to the Fermi level; thus substitution of the transition metal element is an effective method for designing functional TSMs within this class of TMDs. Finally, we examine the possibility of realizing TSM features in compounds isostructural to the multiferroic hexagonal manganites. This was motivated by the numerous order parameters in multiferroic compounds which can be controlled by external fields; thus, a multiferroic compound with TSM features in a particular phase would provide an opportunity to switch from nontrivial to trivial topology by tuning of the ferroic order parameters. We find through our DFT calculations that by enforcing a metastable ferromagnetic order in the nonpolar centrosymmetric phase, hexagonal $\mathrm{YCrO_3}$ and $\mathrm{YVO_3}$ become topological nodal line semimetals, in contrast to the insulating band structures that occur with the ground state antiferromagnetic order of the transition metal ions.\ \indent The second section of this thesis focuses on first-principles characterization of ``functional materials" in which the feature to leverage for functionality is magnetic, rather than topological, order. We focus on antiferromagnetic (AFM) materials. There has been a recent surge of interest in using AFMs rather than their traditional ferromagnetic (FM) counterparts for spintronic devices whose magnetic order can be manipulated by an electrical current. The vanishing bulk magnetization of AFMs makes them particularly robust to magnetic field perturbations, and the limiting rate of spin dynamics (i.e. the rate at which spins can rotate) in AFMs is order $\sim \mathrm{THz}$ as opposed to $\sim \mathrm{GHz}$ for FMs.\ \indent Our studies focus on one example, the iron-intercalated TMD, $\mathrm{Fe_{1/3}NbS_2}$. The triangular lattice of $\mathrm{Fe}$ ions has an antiferromagnetic (AFM) order which can be manipulated with electrical pulses of very low current density. While numerous experimental characterizations have been performed on this compound, ambiguities regarding the magnetic ground state, spin exchange constants, and the specifics of the current-induced magnetization dynamics, remain. In one study, we calculate the nearest-neighbor Heisenberg exchange constants in $\mathrm{Fe_{1/3}NbS_2}$ and find that competition between strong nearest-neighbor interplanar and intraplanar $\mathrm{Fe}$ exchange constants is responsible for an observed half-magnetization plateau. In the second part of our first-principles characterization of $\mathrm{Fe_{1/3}NbS_2}$, we explore the working hypothesis that the current-induced manipulation of AFM order, which is detected by changes in electrical resistance, is due to a repopulation of three energetically equivalent AFM domains on the triangular lattice. Based on calculated conductivity tensors within a constant relaxation time approximation with experimentally proposed AFM magnetic orders, we verify that the transport parallel to the $\mathrm{Fe}$ layers is anisotropic, a necessary condition for the domain repopulation hypothesis. Finally, by comparing our ab-initio transport with experimental changes in resistance for specific pulse directions, we infer the likely current-domain response for $\mathrm{Fe_{1/3}NbS_2}$, that is, which domains are favored for a given current direction.

Advisor: Neaton, Jeffrey B