High-Performance Computing Approach to Hybrid Functionals in the All-Electron DFT Code FLEUR

Virtual materials design attempts to use computational methods to discover new materials with superior properties within the vast space of all conceivable materials. Density-functional theory (DFT) is central to this field, enabling scientists to predict material properties from first principles, i.e. without relying on external parameters or experimental values. While standard DFT is capable of predicting many materials with satisfying accuracy, it struggles with some properties such as details of the electronic structure or certain material classes, e.g. materials exhibiting strongly correlated electrons. This has created a need for methods with greater predictive power. One such class of methods are hybrid exchange-correlation functionals which combine the exact Hartree-Fock exchange with local exchange-correlation functionals, resulting in highly accurate predictions for many insulating or semiconductor materials. However, the computational cost of hybrid functionals increases rapidly with system size and limits their application to small systems. This thesis aims to solve the computational challenge posed by hybrid functionals in large systems by utilizing the massive computational power of today’s supercomputer

Fast All-Electron Hybrid Functionals and Their Application to Rare-Earth Iron Garnets

Virtual materials design requires not only the simulation of a huge number of systems, but also of systems with ever larger sizes and through increasingly accurate models of the electronic structure. These can be provided by density functional theory (DFT) using not only simple local approximations to the unknown exchange and correlation functional, but also more complex approaches such as hybrid functionals, which include some part of Hartree–Fock exact exchange. While hybrid functionals allow many properties such as lattice constants, bond lengths, magnetic moments and band gaps, to be calculated with improved accuracy, they require the calculation of a nonlocal potential, resulting in high computational costs, that scale rapidly with the system size. This limits their wide application. Here, we present a new highly-scalable implementation of the nonlocal Hartree-Fock-type potential into FLEUR—an all-electron electronic structure code that implements the full-potential linearized augmented plane-wave (FLAPW) method. This implementation enables the use of hybrid functionals for systems with several hundred atoms. By porting this algorithm to GPU accelerators, we can leverage future exascale supercomputers which we demonstrate by reporting scaling results for up to 64 GPUs and up to 12,000 CPU cores for a single k-point. As proof of principle, we apply the algorithm to large and complex iron garnet materials (YIG, GdIG, TmIG) that are used in several spintronic applications

Mixed topology ring states for Hall effect and orbital magnetism in skyrmions of Weyl semimetals

As skyrmion lattices are attracting increasing attention owing to their properties driven by real-space topology, properties of magnetic Weyl semimetals with complex k-space topology are moving into the focus of research. We consider Hall transport properties and orbital magnetism of skyrmion lattices imprinted in topological semimetals by employing a minimal model of a mixed Weyl semimetal which, as a function of the magnetization direction, exhibits two Chern insulator phases separated by a Weyl state. We find that while the orbital magnetization is topologically robust and Hall transport properties exhibit a behavior consistent with that expected for the recently discovered chiral Hall effect [F. R. Lux et al., Phys. Rev. Lett. 124, 096602 (2020)], their evolution in the region of the Chern insulator gap is largely determined by the properties of the so-called mixed topology ring states, emerging in domain walls that separate the skyrmion core from the ferromagnetic background. In particular, we show that these localized ring states possess a robust orbital chirality which reverses sign as a function of the skyrmion radius, thereby mediating a smooth switching dynamics of the orbital magnetization. We speculate that while the emergent ring states can possibly play a role in the physics of Majorana states, probing their properties experimentally can provide insights into the details of skyrmionic spin structures

Spin and orbital transport in rare-earth dichalcogenides: The case of EuS 2

We perform first-principles calculations to determine the electronic, magnetic, and transport properties of rare-earth dichalcogenides, taking a monolayer of H-phase EuS2 as a representative. We predict that the H phase of the EuS2 monolayer exhibits a half-metallic behavior upon doping with a very high magnetic moment. We find that the electronic structure of EuS2 is very sensitive to the value of Coulomb repulsion U, which effectively controls the degree of hybridization between Eu f and S p states. We further predict that the nontrivial electronic structure of EuS2 directly results in a pronounced anomalous Hall effect with nontrivial band topology. Moreover, while we find that the spin Hall effect closely follows the anomalous Hall effect in the system, the orbital complexity of the system results in a very large orbital Hall effect, whose properties depend very sensitively on the strength of correlations. Our findings thus promote rare-earth-based dichalcogenides as a promising platform for topological spintronics and orbitronics

The chiral Hall effect in canted ferromagnets and antiferromagnets

The anomalous Hall effect has been indispensable in our understanding of numerous magnetic phenomena. This concerns both ferromagnetic materials, as well as diverse classes of antiferromagnets, where in addition to the anomalous and recently discovered crystal Hall effect, the topological Hall effect in noncoplanar antiferromagnets has been a subject of intensive research in the past decades. Here, we uncover a distinct flavor of the Hall effect emerging in generic canted spin systems. We demonstrate that upon canting, the anomalous Hall effect acquires a contribution which is sensitive to the sense of imprinted vector chirality among spins. We explore the origins and basic properties of corresponding chiral Hall effect, and closely tie it to the symmetry properties of the system. Our findings suggest that the chiral Hall effect and corresponding chiral magneto-optical effects emerge as useful tools in characterizing an interplay of structure and chirality in complex magnets, as well as in tracking their chiral dynamics and fluctuations