Phonons from Density-Functional Perturbation Theory using the All-Electron Full-Potential Linearized Augmented Plane-Wave Method FLEUR

Phonons are quantized vibrations of a crystal lattice that play a crucial role in understanding many properties of solids. Density functional theory (DFT) provides a state-of-the-art computational approach to lattice vibrations from first-principles. We present a successful software implementation for calculating phonons in the harmonic approximation, employing density-functional perturbation theory (DFPT) within the framework of the full-potential linearized augmented plane-wave (FLAPW) method as implemented in the electronic structure package FLEUR. The implementation, which involves the Sternheimer equation for the linear response of the wave function, charge density, and potential with respect to infinitesimal atomic displacements, as well as the setup of the dynamical matrix, is presented and the specifics due to the muffin-tin sphere centered LAPW basis-set and the all-electron nature are discussed. As a test, we calculate the phonon dispersion of several solids including an insulator, a semiconductor as well as several metals. The latter are comprised of magnetic, simple, and transition metals. The results are validated on the basis of phonon dispersions calculated using the finite displacement approach in conjunction with the FLEUR code and the phonopy package, as well as by some experimental results. An excellent agreement is obtained.Comment: 44 pages, 6 figure

Density-Functional Perturbation Theory within the All-Electron Full-Potential Linearized Augmented Plane-Wave Method: Application to Phonons

Solids consisting of periodic lattice structures exhibit vibrational modes of their atomic nuclei. In the context of a quantum-mechanical description, the excitations of the collective lattice vibrations are quantized and behave like particles. These quasiparticles are called phonons and essential for describing a diverse spectrum of central solid properties and phenomena. Density-Functional Theory (DFT) according to Kohn and Sham has established itself as a very successful, state-of-the-art, material-specific, theoretical, and computational framework. It enables us to calculate the phonon modes with very high predictive power from the first principles of quantum mechanics for describing electrons and ions. Two different approaches to obtaining phonon properties are employed: (i) the Finite Displacement (FD) ansatz, where the second-order derivatives of the total energy with respect to atomic displacements are approximated by difference quotients that involve the forces exerted on the atoms due to their finite displacement, and (ii) the Density-Functional Perturbation Theory (DFPT), a variational approach delivering the desired second-order derivatives from linear responses to an infinitesimal displacement wave. The ambition of this dissertation is to pursue a DFPT beyond the common frameworks with plane-wave basis functions. It is realized by means of the Full-Potential Linearized Augmented Plane-Wave (FLAPW) method, an all-electron electronic-structure method based on muffin-tin (MT) spheres circumscribing the atomic nuclei. The FLAPW method is known for providing the density-functional answer to arbitrary material systems, i.e., independent of which chemical element in the periodic table is chosen. I report on the implementation and validation of the DFPT approach within the FLAPW method in terms of the newly-developed computer program juPhon. Its algorithm describes the properties of phonons in harmonic approximation and is based on the input of the FLEUR code, which is a DFT implementation utilizing the aforementioned FLAPW ansatz. In detail, I elucidate the numerical challenges and show how they have been surmounted enabling us to reliably set up a dynamical matrix, the associated phonon energies of which are many orders of magnitude smaller than the ground-state energy of a crystal. This covers (i) implementing the self-consistent Sternheimer equation, which determines the first-order variations of the charge density as well as the effective potential due to the presence of the displacement wave, and (ii) accounting for the features of the LAPW basis-set. Owing to the displaced atoms, the latter entails considering both Pulay basis-set corrections and discontinuities at the MT-sphere surfaces in the section-wise defined LAPW basis and the potentials. While the Pulay terms compensate for the representation of the wave functions outside the Hilbert space spanned by the finite LAPW basis-set, the discontinuities require the introduction of surface integral contributions. Decisive has amongst others been a sustainable programming paradigm, making juPhon become a complex and sophisticated testing and application software. Within this thesis, I finally benchmark the juPhon phonon dispersions of bulk fcc Cu, Au, Al, Ne, and Ar as well as bcc Mo by comparing them with respective FD computations and experimental reference data. These results show a good agreement

Fermi surfaces, spin-mixing parameter, and colossal anisotropy of spin relaxation in transition metals from ab initio theory

The Fermi surfaces and Elliott-Yafet spin-mixing parameter (EYP) of several elemental metals are studied by ab initio calculations. We focus first on the anisotropy of the EYP as a function of the direction of the spin-quantization axis [B. Zimmermann et al., Phys. Rev. Lett. 109, 236603 (2012)]. We analyze in detail the origin of the gigantic anisotropy in 5d hcp metals as compared to 5d cubic metals by band structure calculations and discuss the stability of our results against an applied magnetic field. We further present calculations of light (4d and 3d) hcp crystals, where we find a huge increase of the EYP anisotropy, reaching colossal values as large as 6000% in hcp Ti. We attribute these findings to the reduced strength of spin-orbit coupling, which promotes the anisotropic spin-flip hot loops at the Fermi surface. In order to conduct these investigations, we developed an adapted tetrahedron-based method for the precise calculation of Fermi surfaces of complicated shape and accurate Fermi-surface integrals within the full-potential relativistic Korringa-Kohn-Rostoker Green function method

Calculation Of Phonon Spectra With The FLAPW Method Using Density Functional Perturbation Theory

Computing phonons applying density functional perturbation theory (DFPT) within all-electron DFT methods is a well-known challenge due to the displacement of muffin-tin spheres and sphere-centered basis functions. In this talk, we present our current results of the phonon dispersion based on our implementation of the DFPT approach in the FLEUR code [1] (www.flapw.de), an implementation of the full-potential linearized augmented plane wave (FLAPW) method. We highlight the good agreement of our preliminary results with phonon dispersions obtained with the finite displacement method for which the FLEUR code has been combined with the phonopy tool (www.phonopy.github.io/phonopy/). We discuss the numerical challenges involved in calculating meV quantites on top of large ground state energies typical for all-electron methods and how we addressed them

FLEUR

FLEUR is an all-electron DFT code based on the full-potential linearized augmented plane-wave method (FLAPW). It is mainly developed at the Forschungsentrum Jülich, Germany and available for the materials research community