Topological solitons in two-dimensional chiral magnets

Li, Xinye; Melcher, Christof (Thesis advisor); Gustafson, Stephen (Thesis advisor); Westdickenberg, Maria Gabrielle (Thesis advisor)

Aachen : RWTH Aachen University (2020, 2021)
Dissertation / PhD Thesis

Dissertation, RWTH Aachen University, 2020


The goal of the this thesis is to study a wide variety of topological solitons in two-dimensional magnets without inversion symmetry analytically and numerically.We first consider the magnetic chiral skyrmions with an energy functional, including exchange energy, Dzyaloshinskii-Moriya and Zeeman interactions in low-temperature regime, where the magnetization has constant modulus. We prove the local stability of isolated axisymmetric chiral skyrmions in the presence of arbitrary perturbations under the sufficiently large Zeeman field. As a consequence, we show the axisymmetric symmetric solution is a traveling wave profile of the Landau-Lifshitz-Gilbert equation with spin transfer torques and the traveling wave solution exists with a small in-plane spin velocity. In the second part we investigate the pattern formation in the high-temperature regime for magnetizations with variable modulus governed by Ginzburg-Landau energy functional including exchange energy, Dzyaloshinskii-Moriya, in-plane anisotropy and Landau energy. We identify the emerging patterns based on equivariant bifurcation theory and investigate their stabilities. In particular, the vortex-antivortex configurations on square lattices are stable under the sufficiently large in-plane anisotropy and skyrmion configurations on hexagonal lattices are unstable.The third part is concerned with a numerical method to approximate the solutions derived in the second part. Combining Fourier spectral method and a modified Crank-Nicolson scheme, we validate our findings in the second part, especially the stability condition of quadratic vortex-antivortex lattices. In the forth part we extend the numerical method used in the third part to the low-temperature regime for energy functional considered in the first part. In numerical experiments, rich patterns such as isolated skyrmion, elongated skyrmion, skyrmionium and skyrmion lattices are observed.