As an outstanding information carrier, skyrmion is increasingly widely used in devices based on complex geometries. To achieve the skyrmion-based spintronic devices, a reasonable and feasible nanotrack is essential. In this paper, we conducted a study on the current-driven skyrmion movement in a circular-ring-shaped nanotrack. Our results suggest that the asymmetry of the inside and outside boundary of the circular ring changed the stable position of the skyrmion, causing it to move like the skyrmion Hall effect when driven by currents. Moreover, the asymmetric boundaries have advantages in enhancing or weakening the skyrmion Hall effect. Additionally, we also compared the skyrmion Hall effect from the asymmetric boundary of circular ring nanotracks with that from inhomogeneous DMI. It is found that the skyrmion Hall effect caused by the circular ring is significantly greater than that caused by the inhomogeneous DMI. These results contribute to our understanding of the skyrmion dynamics in confined geometries and offer an alternative method for controlling the skyrmion Hall effect of skyrmion-based devices.

MnSi has played a major role since the late 1970s in developing the theory of helical magnets in non-centro symmetric materials showing Dzyaloshinsky-Moriya interaction (DMI). With a long helimagnetic pitch of 175 \AA~as compared to the lattice d-spacing of 4.55\AA, it was ideal for performing neutron studies especially as large single crystals could be grown. In these studies under the application of a field of 180 mT perpendicular to Q, a so-called A-phase in the B-T phase diagram was found and interpreted as a rotation of the alignment of the magnetic helix away from the pinning axis. After the surprising discovery of the skyrmion lattice in the A-phase in 2009 much interest arose as it could be shown that the magnetic skyrmion lattice is topologically protected. Due to the rigidity of the skyrmionic lattice it is only loosely bound to the crystal lattice and therefore only relatively small current densities can already induce a motion of this lattice. Another very interesting aspect are the excitations in the spin system of MnSi. As the helimagnetic state is characterized by a long pitch of about 175 \AA, the associated characteristic excitations form a band structure due to Umklapp scattering and can only be observed at very small q with energies below 1 meV. We have investigated the the magnons in MnSi in the whole (B,T)-phase diagram starting in the single-k helimagnetic state by applying a small magnetic field B = 100 mT. This way, the complexity of the magnon spectrum is significantly reduced allowing a detailed comparison of the data with theory resulting in a full theoretical understanding of the spin system of MnSi in all its different magnetic phases.

In atomic GdFe$_2$ films capped by 4$d$ and 5$d$ transition metals, we show that skyrmions with diameters smaller than 12 nm can emerge. The Dzyaloshinskii--Moriya interaction (DMI), exchange energy, and the magnetocrystalline anisotropy (MCA) energy were investigated based on density functional theory. Since DMI and MCA are caused by spin--orbit coupling (SOC), they are increased with 5$d$ capping layers which exhibit strong SOC strength. We discover a skyrmion phase by using atomistic spin dynamic simulations at small magnetic fields of $\sim$1 T. In addition, a ground state that a spin spiral phase is remained even at zero magnetic field for both films with 4$d$ and 5$d$ capping layers.