Bulk and surface topological indices for a skyrmion string: current-driven dynamics of skyrmion string in stepped samples

Abstract

The magnetic skyrmion is a topological magnetic vortex, and its topological nature is characterized by an index called skyrmion number which is a mapping of the magnetic moments defined on a two-dimensional space to a unit sphere. In three-dimensions, a skyrmion, i.e., a vortex penetrating though the magnet naturally forms a string, which terminates at the surfaces of the magnet or in the bulk. For such a string, the topological indices, which control its topological stability are less trivial. Here, we study theoretically, in terms of numerical simulation, the dynamics of current-driven motion of a skyrmion string in a film sample with the step edges on the surface. In particular, skyrmion–antiskyrmion pair is generated by driving a skyrmion string through the side step with an enough height. We find that the topological indices relevant to the stability are the followings; (1) skyrmion number along the developed surface, and (2) the monopole charge in the bulk defined as the integral over the surface enclosing a singular magnetic configuration. As long as the magnetic configuration is slowly varying, the former is conserved while its changes is associated with nonzero monopole charge. The skyrmion number and the monoplole charge offer a coherent understanding of the stability of the topological magnetic texture and the nontrivial dynamics of skyrmion strings.

Theoretical Studies on Controlling the Chirality of Helical Polarization Vortices in Ferroelectric Nanowires: Implications for Reconfigurable Electronic Devices

“…Interestingly, the polarization texture possesses helical-like precession of the vortex core around the wire axis, which is named helical polarization vortex (HPV) (type IV). This nonaxisymmetric vortex core bears resemblance to skyrmion strings seen in some magnets , or 1D topological strings in multiferroic barium hexaferrite nanocrystals . Since the vortex core in ferroelectric nanodots or nanowires is commonly straight, , such an HPV shown in Figure d exhibits an unusual topological polarization structure.…”

Demonstration of Controlled Skyrmion Injection Across a Thickness Step

“…41,42 This behavior is also very similar to the micromagnetics presented by Koshibae et al, who found that surface pinning restricts the ability of skyrmions near the surface to move past a thickness step while allowing the bulk of the skyrmion past, leading to bent states similar to those in our micromagnetics. 40 As demonstrated by Figure 2f, the result of these considerations is a disordered skyrmion state in the thick region after current pulse. However, there are some important limitations of micromagnetics that restrict their direct comparison to real behavior, and hence require experimental study.…”

“…Previous theoretical works have studied current injection in smaller stepped geometries of skyrmion-containing systems using micromagnetics. , To draw an analogy to these works, we also explicitly simulated a 50 ns STT current pulse (7.5 × 10 11 A m –2 ) applied to the initial state shown in Figure d. The resulting magnetization profile after this current injection is shown in Figure f.…”

SiO4 characterization in a chain and C6 H6 embedded in a Non-kekulean structure for Kulli Temperature indices

“…Many well-known researchers have investigated topological indices in order to learn more about various graph families [7,19]. For example, in Qualitative Structure Property Relationships (QSPR) and Qualitative Structure Activity Relationships (QSAR), topological indices are employed as handy numerical descriptors in comparison with biological, physical or chemical parameters of molecules, which is an advantage of chemical industry, [15,13]. Many researchers have worked on various chemical compounds and computed topological descriptors of various molecular graphs over the last few decades [1,24].…”