Ab initio calculations of spin wave excitation spectra from time-dependent density functional theory

The topic of this work is the quantum-mechanical description of elementary magnetic excitations, so-called spin waves. The theoretical foundation of spin-wave excitations is systematically worked out, the central points of a computer implementation is presented, and results are finally shown. A central property of these calculations is that no material-specific parameters are used, instead only the true interactions within the system of valence electrons is used. Such calculations are called ab initio calculations or calculations from first principles. The basis of the calculations if provided by the density functional theory (DFT). Its central theorem is that the state of a quantum-mechanical many-electron system is not only given through the many-particle wavefunction, but the properties of the system are specified as well through the electron density. This lays the foundation for practical computer calculations. A crucial restriction is given by the limitation of the DFT to ground-state properties. Any excitated states of the systems – which include the spin-wave excitations that are in the focus of this work – are by definition beyond the applicability of the DFT. However, the time-dependent extension of the DFT, the time-dependent density functional theory (TDDFT), enhances the scope of the conventional DFT towards charge-neutral excitations. The essential quantity which describes the response of a system to an external excitation (and which thus describes elementary excitations) is the magnetic response function. The focus in this work lies on the spin- flip response function. It describes the reaction of a quantum-mechanical system in answer to an change of the system's total spin by +1 or -1. Such an elementary spin excitation is called spin wave, since it can visualized in the Heisenberg model as a wave-like displacement which propagates through the system. From a mathematical point of view, the spin-flip response function contains the elementary magnetic excitations as poles in its Lehmann representation. In the following, the formalism of spin-flip response is applied to the homogeneous electron gas, which is a standard model for the study of solid-state electronic properties. In this framework, the crucial quantities can be determined analytically. In this system, two kinds of elementary magnetic excitations can be distinguished. On the one hand, the additional spin can be taken up by a single electron by flipping its spin; this one-particle excitations are called spin-flip or Stoner excitations. On the other hand, there are spin excitations which involve the whole electronic system; these collective excitations are called spin waves. In real systems this differentiation cannot be clearly applied. In order to extend the investigation to real materials, the mathematical methods are presented which are used for the realization of the DFT and TDDFT calculations. This includes the FLAPW method (full-potential linearized augmented plane-wave method) and the mixed-basis method. Both methods use basis sets in order to represent the one-particle wavefunction. After applying these methods, the calculations of the determination of the ground-state properties (the DFT calculation) and the subsequent determination of the magnetic excitation properties (the TDDFT calculation) turn into matrix computations. In the results chapter the developed method is applied, and the different convergence parameters are analyzed. Further, the simple transition methods Iron, Cobalt and Nickel are calculated. The magnetic excitation spectra are investigated, in particular with regard to different crystal structures and anisotropies with respect to the excitation momentum q. The results are compared to experiments and to other TDDFT calculations, as well as to calculations based on the frozen-magnon method. Further perspectives for development and application are given in the concluding chapter.

Grantor dc:publisher

Publikationsserver der RWTH Aachen University

Year dc:date

2012

Author dc:creator

• Niesert, Manfred

Contributors dc:contributor

• Blügel, Stefan

• info:eu-repo/classification/ddc/530
• Magnetismus
• Dichtefunktionalformalismus
• Spinwelle
• Physik
• Spinwellen
• magnetism
• density functional theory
• spin waves

Statement dc:rights

• info:eu-repo/semantics/openAccess

Language dc:language

eng

Identifier

https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-124425%22

OAI identifier oai:identifier

oai:publications.rwth-aachen.de:62952