Aspects of Complex Magnetism: Vortex Phases, Skyrmion Dynamics, and Chaotic Nano-Oscillators

Project I Vortex Phase in Spiral Antiferromagnets
Spiral antiferromagnets are characterized by a Dzyaloshinskii-Moriya interaction that stabilizes spatially modulated phases of the staggered order parameter. In the framework of a Ginzburg-Landau theory, it is shown that a magnetic field leads to the formation of a topological phase constituting a square lattice of vortices and antivortices. An orthogonal alignment of the antiferromagnetic staggered order parameter with an external magnetic field is energetically favorable since both sublattices of a spiral antiferromagnet cannot minimize their Zeeman energy simultaneously, and energy can be gained from spin canting. This spin-flop mechanism has the same effect as easy-plane anisotropy, which leads the vortices to form topological defects with vanishing core. Thus, the vortex phase is only stable close to the Néel temperature.
At lower temperatures, the square-lattice vortex phase undergoes spontaneous symme- try breaking into a rectangular phase. We investigate the stability of this rectangular phase with respect to mixed DMI and in-plane magnetic fields. Since any modulated magnetic texture induces a ferroelectric polarization, the vortices of both the vortex and the rectangular phase carry an electrical charge which makes them amenable to the ma- nipulation with in-plane electric fields. ... mehrFinally, the relevance of these results for the chiral antiferromagnet Ba2CuGe2O7 is discussed.

Project II High-Energy Magnons of a Skyrmion Lattice
The energy bands of magnons in the skyrmion lattice phase of a chiral magnet, which were recently measured experimentally, show a peculiar, parabola-shaped superstructure when plotted in an extended zone scheme. They are described theoretically in the con- tinuum approximation by a bosonic Bogoliubov-de Gennes equation. In this project, a high-energy approximation is developed, which takes the form of a Schrödinger equa- tion, describing these magnons as charged particles in the emergent magnetic field of the skyrmion lattice.
It is known that charged particles in a periodically modulated magnetic field can form runaway orbits, skipping between regions of positive and regions of negative magnetic field values and effectively behaving as free particles. A semiclassical analysis shows the magnon eigenfunctions corresponding to the parabola-shaped superstructures focus on the runaway orbits in the periodically modulated emergent magnetic field experienced by the magnons in this high-energy description. Hence, they can be explained by classical runaway orbits, skipping along the high-symmetry directions of the skyrmion lattice phase, which may be used as magnon waveguides.

Project III Chaotic Spin-Torque Nano-Oscillator
A spin current transversing a magnetic material exerts a spin-transfer torque onto the magnetic textures, which may lead to oscillations of the magnetization, which constitutes a so-called spin-torque nano-oscillator. Understanding the dynamics of spin-torque nano- oscillators is a prerequisite for applications in reservoir and stochastic computing and designing hardware that emulates artificial neural networks with low power consumption.
This project analyses a specific setup for an antiferromagnetic spin-torque nano-oscillator, where a spin current drives a collinear easy-axis antiferromagnet, including damping, and with an external magnetic field applied perpendicular to it. First, it characterizes the static, uniform states and their excitations, yielding the eigenfrequencies of the nano- oscillator. Next, it analyzes the regular dynamics, investigating the stability of a limit cycle at the spin-flop field. Finally, it is shown by calculating the Lyapunov spectrum that this model features chaotic dynamics intrinsically. The transition to chaos is analyzed us- ing bifurcation diagrams, and it is shown that for large damping, chaos is controlled by period-halving bifurcations.