Dynamics of driven antiferromagnetic skyrmions

Abstract

Magnetic Skyrmions are vortex-like quasi-particles stabilized by their topology and exist in several magnetic materials. While originally described by continuous vector fields that ensure topological protection, stable Skyrmions can also form in magnetic lattices, allowing for their experimental observation. Not least due to their potential applications in magnetic storage devices, Skyrmions have gained popularity since their first experimental observation in 2009. Ferromagnetic (FM) Skyrmions are nanometer-sized and can be driven by electric currents. They move as massless particles at an angle to the current flow and, therefore, exhibit the Skyrmion Hall effect. While ferromagnetic Skyrmions are still extensively studied in current research, the field of study evolve further to advanced structures. An emerging topic is the study of antiferromagnetic (AFM) Skyrmions. Unlike their ferromagnetic counterparts, AFM Skyrmions do not exhibit the Skyrmion Hall effect and can reach higher velocities when driven by electric currents, making them more attractive for technological applications. Moreover, AFM Skyrmions have a finite mass and exhibit behavior akin to classical particles, making them a fascinating subject for fundamental research. Theoretical studies of AFM Skyrmions typically focuses on either synthetic antiferromagnets or G-type antiferromagnets, making it crucial to understand the distinctions between them. Synthetic antiferromagnets are a composition of two or more ferromagnetic layers that are coupled antiferromagnetically through a non-magnetic spacer layer. In contrast, G-type antiferromagnets exhibit a chessboard-like structure, where the sublattices are within the same layer. While Skyrmions have been experimentally observed in synthetic antiferromagnets, they remain elusive in other types of antiferromagnetic systems up to now. Both types are considered in this thesis. After introducing classical micromagnetic dynamics and general properties of a magnetic Skyrmion, we will discuss these two realizations of antiferromagnets. Furthermore, we will demonstrate that, independent of the type, the antiferromagnetic system can be treated as two effectively coupled ferromagnetic sublattices. In this thesis, the underlying mechanics of antiferromagnetic Skyrmion dynamics play a crucial role. To investigate them, we utilize the separation into two sublattices and treat the Skyrmions forming on these sublattices as rigid objects. This approach reveals that the driving mechanism of an AFM Skyrmion is due to a small displacement of its sublattice constituents. We develop a formalism that incorporates this mechanism and demonstrate that an AFM Skyrmion eventually mirrors the dynamics of a classical particle with finite mass. Furthermore, this framework allows us to fully characterize the resulting motion of an AFM Skyrmion driven by an external force. We apply this formalism to the case of current-driven Skyrmions, showing that it can predict the dynamics of an antiferromagnetic Skyrmion, regardless of the type of antiferromagnet, in various scenarios, even in fine detail. All results are compared to micromagnetic simulations. As another possibility for driving AFM Skyrmions, we examine spin wave-driven Skyrmions in the second part of this thesis, focusing on a two-dimensional square lattice. We begin with formulating a classical spin wave theory explicitly tailored to this system by linearizing the equations of motion around a homogeneous ground state. This allows us to derive the dispersion relation and characterize different types of spin wave polarization, namely circularly and linearly polarized spin waves. All results are confirmed by simulations. Subsequently, we investigate the impact of spin waves on the Skyrmion. To do so, we simulate an isolated Skyrmion in the lattice and inject the spin wave via edge spin manipulation. Our observations reveal that spin waves generally accelerate the Skyrmion. While linearly polarized spin waves move the Skyrmion in the direction of wave propagation, circularly polarized spin waves induce an additional motion perpendicular to this direction, resulting in a Skyrmion Hall effect. The resulting Skyrmion acceleration depends on the properties of the spin wave, such as its wave number and amplitude. Furthermore, we investigate the impact of damping on spin waves and the resulting Skyrmion motion. We derive an expression for the decay of spin waves as they propagate through the lattice, focusing on the decay length. Additionally, we propose a concept for an antiferromagnetic Skyrmion racetrack that incorporates both spin wave decay and the Skyrmion Hall effect.