We analyze in detail the error that arises from the linearization in linearized augmented-plane-wave (LAPW) basis functions around predetermined energies E l and show that it can lead to undesirable dependences of the calculated results on method-inherent parameters such as energy parameters E l and muffin-tin sphere radii. To overcome these dependences, we evaluate approaches that eliminate the linearization error systematically by adding local orbitals (LOs) to the basis set. We consider two kinds of LOs: (i) constructed from solutions u l (r, E) to the scalar-relativistic approximation of the radial Dirac equation with E > E l and (ii) constructed from second energy derivatives ∂ 2 u l (r, E)/∂E 2 at E = E l . We find that the latter eliminates the error most efficiently and yields the density functional answer to many electronic and materials properties with very high precision. Finally, we demonstrate that the so constructed LAPW+LO basis shows a more favorable convergence behavior than the conventional LAPW basis due to a better decoupling of muffin-tin and interstitial regions, similarly to the related APW+lo approach, which requires an extra set of LOs to reach the same total energy, though.

Chiral magnets are of fundamental interest and have important technological ramifications. The origin of chiral magnets lies in the Dzyaloshinskii-Moriya interaction (DMI), an interaction whose experimental and theoretical determination is laborious. We derive an expression that identifies the electric dipole moment as descriptor for the systematic design of chiral magnetic multilayers. Using density functional theory calculations, we determine the DMI of (111)-oriented metallic ferromagnetic Z/Co/Pt multilayers of ultrathin films. The non-magnetic layer Z determines the DMI at the Co-Pt interface. The results validate the electric and magnetic dipole moments as excellent descriptors. We found a linear relation between the electric dipole moment of Pt, the Allen electronegativity of Z, and the contribution of Pt to the total DMI.

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A hybrid MPI+OpenMP parallelization strategy has been implemented into the density functional theory code FLEUR. Based on the full-potential linearized augmented plane-wave (FLAPW) method, FLEUR is a well-established all-electron code specialized on the simulation of materials properties of crystalline bulk solids and surfaces with significant electronic and magnetic complexity. Developed in over 30 years the Fortran implementation included two layers of MPI-based distributed memory parallelization that serves as a reference for our work. The revised code version shows superior performance, improved scalability and thereby opens the path to exploit current and future high performance computing architectures efficiently. Multiple threads per MPI process can be utilized by interfacing with optimized linear algebra subroutines from the BLAS and LAPACK libraries as well as in code sections with explicit OpenMP statements. We demonstrate that the additional multithreading helps to avoid the communication induced scalability limit of the pure-MPI version and simultaneously boosts the single node-performance on current multi-core systems. This enables FLEUR calculations for unit cells with over 1000 atoms to simulate extended defects, surfaces and disordered solids.

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.