Study of the structure and dynamics of magnetic skyrmions
Keywords: resonant elastic x-ray scattering
magnetic skyrmions
magnetic solitons
micromagnetism

Magnetic skyrmions (skyrmions hereafter) are recently discovered localized vortexlike magnetic structures, defined by their unit topological winding number. From this nontrivial topology, skyrmions inherit unusual physical properties. They have been shown to be particularly robust to deformation, and so they are often referred to as being “topologically protected”. In conductive materials, they appear to source electric and magnetic fields. When driven by an applied force, their topology prevents them from moving collinearly with the direction of the applied force; the angle by which they are deflected is known as the skyrmion Hall angle. Large skyrmion Hall angles are known to decrease the depinning threshold for motion under external drives, and skyrmions are known to be sensitive to ultra-low current density spin-transfer and spin-orbit torques.
These factors, combined with their nano-scale size, have generated excitement around the prospect that skyrmions could find use as a next-generation information carrier. This led to the publication of dozens of skyrmionic device schematics, each more ingenious than the last. Despite this flurry of applied research, magnetic skyrmions are still far from finding technological use. This can be attributed to two key issues. The first is materials problem; while there are dozens of materials systems that host these topological whirls, no material is known to host skyrmions with the three necessary characteristics of having a diameter on the order of 10 nm, stability at room temperature, and stability at remanence (although, FeGe and CoxZnyMnz satisfy the first two criteria, and many magnetic multilayers meet the last two). The second issue is a lack of physical understanding of the structure and dynamics of magnetic skyrmions, which will be the focus of this thesis.
The structural investigation begins with the establishment of the necessary mathematical framework; magnetic skyrmions, and the magnetization textures they coexist with, are first constructed and investigated analytically. Then, the twodimensional morphology of lattices of these objects is investigated experimentally using resonant elastic x-ray scattering, and the first measurement of the magnetic soliton lattice above room temperature is presented, alongside the first measurement of the skyrmion liquid phase. Following this 2D study, the fascinating threedimensional structure of skyrmions is probed; a mathematical discussion of the conical modulation of skyrmion strings is followed by an experimental and theoretical study of the surface-pinned nature of skyrmions.
An important model for the description of skyrmion dynamics is Thiele’s equation, but this equation suffers from the prerequisite that one must have a priori knowledge of the interaction potential between the magnetization structures whose motion it describes, and their environment. To extend the cases in which Thiele’s equation can be used, a general form of the interaction potential between any two magnetization configurations is derived and benchmarked. Thiele’s equation in the presence of external spin-transfer torque, spin-orbit torque, and magnetic field gradient drives is derived; this is used to show that, when skyrmions are driven by spinorbit torque down a nanowire, they are only negligibly deflected by the non-uniform magnetic field generated by the current through the wire. Using the knowledge of skyrmion-skyrmion interactions and their coupling to external fields, the properties of large systems of skyrmions are studied numerically by integrating Thiele’s equation, revealing the strain and defect driven dynamics of skyrmion crystals. Finally, the first technique that allows for the determination of the all-important skyrmion Hall angle from the skyrmion lattice state is discussed, and used experimentally to perform the first measurement of the skyrmion Hall angle in FeGe.