# PhD Theses

(2020)**Ivan Ado**

## Quantum transport, spin transfer and damping, and chiral interactions in two-dimensional ferromagnets

This thesis studies effective models of two-dimensional ferromagnets with pronounced spin-orbit coupling. It reports a number of unexpected discoveries. The most glorious discovery came as a result of a completely unsuccessful attempt to compute weak localization correction to the anomalous Hall conductivity. Instead, we accidentally found a set of the leading order Feynman diagrams that were completely overlooked before. They are important not only for the anomalous Hall conductivity, but for some other effects as well. Another pack of results was inferred from a microscopic analysis of spin-transfer torques and Gilbert damping. Surprisingly, for a particular (but essential) model system, their interplay turned out to describe a motion of magnetic textures with the classical drift velocity of conduction electrons. The least awesome finding of the thesis is the identification of three particular crystallographic classes, for which only the anisotropic chiral interactions beyond the Dzyaloshinskii-Moriya interaction can contribute to the micromagnetic energy density.

(2020)**Guus Slotman****Electronic properties of two-dimensional materials and Van der Waals heterostructures**A substantial part of this thesis deals with the interaction between atomically thick layers of different materials stacked together to form new materials called Van der Waals heterostructures. Tuning the materials used in this stacking one can alter the physical properties of the system. Examples include the bandgap and thus the optical properties. These properties can then be further tuned by changing the orientation between the different layers.

In this thesis multiple computational techniques were applied to obtain those properties. The, for this thesis, most important method is called the tight-binding propagation method (TBPM), which allows studying systems of millions of atoms. Being able to study such large systems makes it possible to study realistic real word systems in which, for example, two layers are rotated with respect to each other.

The first part of the thesis deals with graphene-hBN VdW heterostructures. The phonon spectrum is calculated as well as the effects of so called moiré patterns on the electronic properties. We show that the phonon spectrum for a combined graphene-h-BN system is very close to the superposition of the phonon spectra of the constituent layers. In the latter part of the thesis the excitation (plasmon) spectra of graphene on top of various metal substrates is obtained by means of TBPM. We show that due to the moiré reconstructionion graphene on top of ruthenium, another mode appears in the excitation spectrum, which could be used in novel graphene-optoelectronics applications. Similarly, in we studied plasmonic properties of a singlelayer of antimony (or antimonene), one of the more recent additions to the 2D materials library. We show that the spin-orbit coupling is essential in describing the rich excitation spectrum.

(2020)**Marion Barbeau**

## Magnetic Exchange Interactions out of Equilibrium (pdf, 4,7 MB)

Nowadays, there is a huge interest among the scientiﬁc community in order to study magnetic exchange interactions under non-equilibrium conditions, aiming for the possibility of directly control the magnetic order on ultrafast time scales. In this thesis, we study the exchange interactions, especially their competition and the competition between electronic interactions in magnetic systems out of equilibrium. We start by introducing the concept of magnetism in materials as well as the exchange interaction which is the strongest force in magnetic materials. Following that, we discuss the key role of magnetism in data storage technology and how a direct control of the exchange interaction is a prospective candidate for controlling magnetism at the ultimate time scale. Then, we explain different analytical and numerical methods that are used in the thesis in order to obtain the exchange interactions. As a next step, we study the role of orbital degree of freedom in the control of exchange interactions using a two-orbital Hubbard model. This orbital degree of freedom gives rise to two competing exchange interactions: the Heisenberg as well as the biquadratic exchange interaction. In addition, we discuss a novel spin-charge coupling phenomenon which allows the non-resonant and reversible hybridization of a spin and a charge state which, in equilibrium, are separated by a large energy gap. Then, we study the enhancement of screening effects on the Heisenberg exchange interaction out of equilibrium using the Dynamical Mean Field Theory. Finally, we study the possibility of modifying the competing Dzyaloshinskii-Moriya interaction and Heisenberg exchange with an acoustic wave. This is aimed to support the feasibility of strain-induced magnetic Skyrmion creation and annihilation.

**Edo van Veen**(2019)

*Large-scale tight-binding simulations of two-dimensional materials and self-similar systems*Two-dimensional materials have many possible applications in electronics and optics. To further explore these possibilities we need to do realistic modelling of large-scale two-dimensional condensed matter systems. The tight-binding approximation provides a simple and intuitive way to model these systems. When the number of atoms in the model becomes so large that exact diagonalization is no longer an option, we can use tight-binding propagation methods to calculate electronic, transport and optical properties. In this thesis, we employ these methods to study antimonene ribbons and black phosphorus. It turns out we can manipulate the gap in antimonene ribbons by applying external electric fields, and that we can tune the hyperbolic spectrum of black phosphorus by applying strain and electric bias. Then, we investigate the properties of self-similar systems, i.e., fractal systems exhibiting patterns that repeat on different length scales. We show that the conductance of fractals in the Sierpinski carpet family is self-similar. Finally, we show that the optical conductivity of Sierpinski gaskets shows peaks corresponding to each length scale present in the system, and that they feature localized plasmon modes. This thesis also contains a description and manual of the open-source code that was made to do these simulations. With this library it is easy to make large-scale Hamiltonians and use tight-binding propagation methods on it.

**Koen Reijnders**(2019)

## Semiclassical dynamics of charge carriers in graphene

In this PhD thesis, the dynamics of charge carriers in graphene are studied using the semiclassical approximation. Graphene, a monolayer of carbon atoms, has unusual electronic properties, because the effective behavior of its electrons is described by the Dirac equation. Consequently, electrons that are normally incident on a potential barrier are transmitted with unit probability, so-called Klein tunneling. In the first part of this thesis, the transmission coefficient for angular incidence is derived for smooth potential barriers. In the second part, we consider electronic optics, in particular the focusing of electrons. First, a detailed description of lensing by potential barriers is constructed, so-called Veselago lensing. Subsequently, the influence of trigonal warping on the focusing is studied. We find very good agreement between our semiclassical theory and tight-binding calculations. Finally, focusing of electrons by two-dimensional potential wells is studied. We show that the semiclassical phase can have a significant effect on the position of the intensity maximum. This thesis also contains a careful review of the different semiclassical methods that are used.

**Hylke Donker**(2018)## Quantum decoherence and measurement in small spin systems

During the inception of quantum mechanics, the founding fathers were shaken by the conceptual difficulties that arise when interpreting their new theory. De- spite the tremendous technological development that we have seen the last cen- tury, the most pressing interpretational questions in quantum physics—such as collapse of the wave function—still stands tall, as a widely accepted resolution is yet to be found.

Nevertheless, some concrete proposals were formulated to resolve some of these problems, perhaps most notably the theory of decoherence. But these solutions have been tested—almost without exception—on simplistic, usually non-interacting, analytically tractable models. This work considers the quantum dynamics of (small) ensembles of spin-1/2 particles. Quantum spin simulations are an ideal test bed to verify and explore assumptions of decoherence and quantum measurement theory. The freedom offered by numerical spin calculations can be used to construct a wide range of systems with specific features (e.g., conserved quantities). Par- ticular models can be dissected by removing idealisations that are introduced to make such systems analytically tractable. In this way, it is possible to study the general applicability of concepts underlying decoherence- and quantum measure- ment theory. Furthermore, the accuracy of the simulations can be controlled, which make it possible to separate quantum correlations effects from numerical errors. Due to the exponential growth of the Hilbert space—

*d*= 2*N*for spin- 1/2—calculations have to be limited to a fairly small set of spins (around twenty in this dissertation). Nevertheless, by a suitable choice of the Hamiltonian—such as a spin-glass type for a thermal reservoir—finite size effects can be partially negated. Assumptions of decoherence and quantum measurement are put to the test by numerically solving the Schr¨odinger equation to evolve the wave function*|ψ*(0)*) → |ψ*(*t*)*)*for given initial conditions*|ψ*(0)*)*.**Erik van Loon**(2018)

## Collective phenomena in strongly correlated systems

The electrons in materials are not independent particles, the Coulomb interaction leads to correlation. Such a correlated system is usually impossible to solve exactly, but it is possible to develop efficient (numerical) approximations. This thesis describes the dual boson approach to strongly correlated systems. This method is based on using an exactly solvable interacting reference model, which describes local correlation effects, as a starting point to which non-local correlations are added perturbatively. This thesis describes the theory behind this method, some aspects of practical implementations, as well as numerical tests and benchmark to establish the overall reliability. In addition, the dual boson method is applied to describe monolayer NbS_2, dipolar fermions in optical lattices and long wavelength collective charge excitations in the Hubbard models.

**Remko Logemann**(2017)

## Geometry, magnetism and electronic structure of transition-metal oxide and carbide clusters

The clusters in this thesis are sub-nanometer particles containing 1 to 20 atoms. As clusters form the transition from the single atom to the bulk, they serve as an interesting model system to study material properties at the smallest size range. In order to study the cluster properties, we first calculate the geometric structure of the Fe_{x}O_{y}clusters using density functional theory and our implemented genetic algorithm. To successfully identify their structure, we calculate their vibrational spectra for comparison with experiments. As a starting point to study the magnetic interactions in clusters, we first perform a systematic comparison between two approaches for spin polarization on oxygen in typical bulk transition metal (TM) oxides such as NiO, MnO and hematite. In hematite, both models result in non-Heisenberg behavior. The bulk magnetic properties of hematite undergo drastic modifications in the cluster form. The atomic moments on oxygen in clusters are significantly enhanced compared to hematite. Furthermore, the exchange interactions in FexOy clusters are an order of magnitude stronger compared to bulk hematite. In the final part of this thesis NbC and TaC clusters are studied and compared to IR-UV spectroscopy to identify their electronic and geometric structure.

**Inka Locht**(2017)

## Theoretical methods for the electronic structure and magnetism of strongly correlated materials

Doctoral dissertation, Uppsala: Acta Universitatis Upsaliensis

In this work we study the interesting physics of the rare earths, and the microscopic state after ultrafast magnetization dynamics in iron. Moreover, this work covers the development, examination and application of several methods used in solid state physics.

In the first part we apply density functional theory plus dynamical mean field theory within the Hubbard I approximation to describe the interesting physics of the rare-earth metals. We calculate a wide range of properties of the rare-earth metals and find a good correspondence with experimental data.

In the second part of this thesis we develop a model, based on statistical arguments, to predict the microscopic state after ultrafast magnetization dynamics in iron. Our model makes it possible to compare the measured data to results that are calculated from microscopic properties.

In the last part of this work we examine several methods of analytic continuation that are used in many-body physics to obtain physical quantities on real energies from either imaginary time or Matsubara frequency data. We compare the reliability and performance of these methods for both one and two-particle Green's functions.**Frank Buijnsters**(2016)

## Linear and nonlinear excitations in magnetic films

Spin waves are excitations which propagate through a magnetic material and thus transfer information. Their strong sensitivity to the magnetic nanostructures in the magnetization field through which they propagate makes them highly controllable. As such, they might enable a future generation of information-processing components (magnonics / magnon spintronics). Thin magnetic films often show a patchwork of domains of alternating magnetization directions. The boundaries between such domains (domain walls) are interesting structures in themselves, with a very peculiar dynamics. An important result of my research is that the phase of spin waves passing through a domain wall can be shifted by up to 180º by switching the domain wall between its two equivalent stable equilibrium states. Through constructive and destructive interference, this turns the domain wall into a spin-wave switch or memory element. Translating the theoretical model of magnetization dynamics (the LLG equation) into concrete predictions for the behavior of spin waves often requires us to solve large eigenvalue, optimization, scattering, or time-integration problems numerically. Part of this thesis is concerned with the further development of such techniques. At the same time, I seek to explain all significant numerical results with mathematically simpler analytical models in order to gain a deeper insight into the essence of the physical behavior.

**Merel van Wijk**(2015)

## Friction and structure of graphitic systems

**Inka Locht**(2015)

## Cohesive and Spectroscopic properties of the Lanthanides within the Hubbard I Approximation (pdf, 4.5 MB) (pdf, 4,5 MB)

We describe the rare-earth elements using the Hubbard I approximation. We show that the theory reproduces the cohesive properties, like the volume and bulk modulus, and we find an excellent agreement between theory and experiment for the (inverse) photo emission spectra of the valence band. In addition we reproduce the spin and orbital moments of these elements. This licentiate thesis contains an introduction to the cohesive, magnetic and spectral properties of the rare-earth elements, to density functional theory and to density functional theory in combination with dynamical mean-field theory within the Hubbard I approximation. We also focus on some technical details, e.g. the optimal basis used in the electronic structure code and the role of charge self-consistency in properly describing the valence electrons.

**Lars Peters**(2015)

## Theory of electronic structure and magnetism of rare-earth and transition-metal clusters

This thesis covers a theoretical study of the electronic and magnetic properties of rare-earth and transition-metal clusters. More precisely, we study these complicated systems with density functional theory and extensions to it. For example, we combine density functional theory with experiment (Born-Haber cycle) to obtain the number of 4f-electrons in the rare-earth clusters. On the other hand, we use the so called LDA+U approximation, i.e. static mean field approximation, for an investigation of the magnetic properties. Then, for the spectral properties of the rare-earth clusters we combine density functional theory with dynamical mean field theory in the limit of zero hybridization, i.e. Hubbard-I approximation. Finally, we also employ this method to calculate in great accuracy both spin and orbital moments of Cobalt clusters.

**Mikhail A. Akhukov**(2013)

## Structure and magnetism of defected carbon materials

**Kostya Zakharchenko**(2011)

## Temperature effects on graphene: from flat crystal to 3D liquid

**Igor di Marco**(2009)

## Correlation effects in the electronic structure of transition metals and their compounds

**Oksana Manyuhina**(2009)

## Frustration in soft matter: interplay between order and curvature

**Claudio Fusco**(2005)

## Friction and diffusion dynamics of adsorbates at surfaces

**Luca Consoli**(2002)

## Nonlinear dynamics of incommensurately contacting surfaces: a model study