PhD Theses

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.

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.

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.

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.

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 = 2N 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)).

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.

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.

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.