Skyrmions and Monopoles in Chiral Magnets & Correlated Heterostructures

The first part of this thesis is called "Skyrmions and Monopoles in Chiral Magnets" and concerned with topological spin textures in chiral magnets. The second part, "Correlated Heterostructures", studies layered, strongly correlated devices within the framework of dynamical mean-field theory. In magnets without inversion symmetry, so called chiral magnets, weak spin-orbit coupling leads to the formation of smooth twisted magnetic structures with a long period. Recently, a new magnetic phase of a lattice of topologically stable whirl-lines was discovered. In the first chapter we introduce the concept of a such a whirling texture and briefly mention its occurrence in other areas of physics. In chapters 2 we review the Ginzburg-Landau theory for chiral magnetic structures describing their equilibrium properties followed by a description of a numerical minimisation technique to explore the mean-field configuration of the free energy functional. In chapter 3 we review the Langevin description for a system at finite temperature and concentrate on especially on the description of magnetic systems. The describe how a numerical integration of the equations of motion, a stochastically differential equation, can be achieved to compute ensemble-averaged quantities. Chapter 4 we present the discovery of emergent magnetic monopoles as the driving mechanism behind topological phase transitions from the Skyrmion lattice into topologically trivial phases. We describe how a Skyrmion lattice unwinds due to the motion of magnetic monopoles in the system as seen both in experiment and numerical simulations. We investigate how the energetics of and forces between monopoles and antimonopoles influence their creation rate and dynamics. In chapter 5 we turn to the dynamical properties of single Skyrmions in ferromagnetic backgrounds. In a first approach we study analytically the fluctuations around the mean-field configuration and determine the spectrum of the bound states, the scattering solutions and their phase shifts and coupling mechanism to the collective Skyrmion coordinate. By integrating out the fluctuations we discover a strongly frequency-dependent effective mass for the collective Skyrmion coordinate. We approach the same question from a different angle in the second part of the chapter. Here we start from numerical simulations of the stochastic Landau-Lifshitz-Gilbert equation and determine the coefficients of the effective equations of motion from a statistical analysis of the collective coordinate fluctuations. We find a strongly frequency-dependent effective mass and a new peculiar damping mechanism proportional to the acceleration of the Skyrmion that we call 'gyro-damping'. The second part of this thesis explores the interface effects in strongly correlated heterostructures. Multilayered heterostructures in the nano sized realm (also known as multilayered nanostructures) are the most common electronic devices. A classic multilayered nanostructure is a tunnel junction consisting of two metallic leads connected by a ``weak link'', often a conventional band insulator. The connection between the two leads is thus governed by inherently quantum mechanical effects. We begin with an introduction to model Hamiltonians, in particular the Hubbard and the single impurity Anderson model. The second chapter describes the static mean-field treatment of anti-ferromagnetic order in the Hubbard model. Chapter 3 introduces the reader to the dynamical mean-field theory (DMFT) and describes extensions of the DMFT to system with antiferromagnetic order. The DMFT maps the lattice problem onto an effective impurity problem. In chapter 4 we review how the single impurity Anderson model can be solved using the numerical renormalisation group (NRG). The generalisation of DMFT to inhomogenous, layered systems is given in chapter 5 including the effects of long-range Coulomb interactions on the Hartree level. Here we also outline our generalisation of the inhomogenous DMFT to systems with antiferromagnetic order. In chapter 6 we derive expressions for the layer-resolved optical conductivity and the Hall conductivity. We apply the former to the Mott-Band-Mott heterostructure where we study the transport properties of the two-dimensional metallic state at the interface where we find a rich temperature dependence. In chapter 7 we turn to the question how the transmission amplitude through a Mott insulator in a linear potential depends on temperature.