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| Home > Publications database > Phonons in Magnetic Systems by means of Density-Functional Perturbation Theory |
| Book/Dissertation / PhD Thesis | FZJ-2025-04180 |
2025
Forschungszentrum Jülich GmbH Zentralbibliothek, Verlag
Jülich
ISBN: 978-3-95806-853-7
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Please use a persistent id in citations: doi:10.34734/FZJ-2025-04180
Abstract: Phonons are quantized vibrational excitations of the crystal lattice. These quasiparticles play a crucial role in understanding many properties of the solid-state system. In this thesis, phonons in terms of dispersion relations and density of states (DOS) are investigated on the basis of the Kohn–Sham density functional theory (DFT), the state-of-the-art ab-initio approach to the electronic structure of specific materials and a proven foundation for the study of lattice vibrations from first-principles. This work relies on the harmonic approximation, in which the properties of phonons are directly related to the second order response of the total energy of the system with respect to the displacement of the atoms in the lattice. Two complementary approaches are used to calculate this response: The first one is the finite displacement (FD) approach, that in which the second order of the energy is approximated as a difference quotient using differences in the forces acting on the atoms. The second one is the density-functional perturbation theory (DFPT), a variational approach that constructs the second order response analytically from the first order response of the wave functions obtained by the self-consistent solution of the Sternheimer equation. In this thesis, I go beyond the conventional application of DFPT to nonmagnetic systems and the conventional realization of DFPT in terms of methods representing the electron wave function in a plane wave (PW) basis and present an implementation in the all-electron full-potential linearized augmented plane-wave (FLAPW) method. This very accurate method, applicable without further ado to all nonmagnetic and magnetic chemical elements of the periodic table, comes with the challenge of an atomic position dependent basis set. I show that the subsequently arising additional matrix elements, so-called correction terms to calculate the response of wave function and energy can be determined accurately. One objective of this thesis is to advance the development of DFPT within the FLAPW method by refining and extending the existing realisation in the community code FLEUR. I present the general theory that leads to the existing implementation and, from this starting point, develop correction terms that improve upon previous results. I extend the framework from the minimum base version towards spin-polarized magnetic systems and systems with more than one atom per unit cell. From the viewpoint of software engineering, I demonstrate efficient integration of DFPT into the existing code, minimizing redundancy and maximizing parallelization options. I benchmark the improved implementation against FD results calculated with FLEUR in conjunction with the phonopy package and obtain an excellent agreement. The validation set spans both materials that were previously established but now show improved results, as well as materials that were previously inaccessible. I calculate both elemental and rare-earth magnets in different magnetic configurations to elucidate, how magnetism and the magnetic order impacts the phonon physics. Finally, I investigate two-dimensional (2D) layered systems and unsupported monolayers. The latter can be efficiently calculated with the thin-film implementation in FLEUR, for which I present an extension to the DFPT plugin.
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