This Tutorial article focuses on magnetic phenomena and material systems that have gained significant importance since the original development of mumax3, but are challenging to simulate for users who rely solely on the originally provided examples. Alongside the physical background, we provide hands-on examples of advanced magnetic systems, including detailed explanations of complete mumax3 input files (13 in total, often showing different ways to achieve things), and highlighting potential pitfalls where applicable. Specifically, we explore two approaches to incorporate spin–orbit torques in mumax simulations, considering the trade-off between versatility and speed. We also examine complex multilayer material stacks, including synthetic antiferromagnets, demonstrating different implementation methods that again vary in speed, versatility, and realism. A key criterion for selecting the optimal simulation strategy is its suitability for modeling systems where the magnetization varies significantly in the third dimension. The material covered in this Tutorial paper includes content developed for the mumax3 workshop presented during the summer of 2020 within the context of the IEEE online spintronics seminar, along with additional new topics. Throughout the explanations, we ensure broad applicability beyond specific examples.

Magnetic domain formation in two-dimensional (2D) materials gives perspectives into the fundamental origins of 2D magnetism and also motivates the development of advanced spintronics devices. However, the characterization of magnetic domains in atomically thin van der Waals (vdW) flakes remains challenging. Here, we employ X-ray photoemission electron microscopy (XPEEM) to perform layer-resolved imaging of the domain structures in the itinerant vdW ferromagnet Fe5GeTe2 which shows near room temperature bulk ferromagnetism and a weak perpendicular magnetic anisotropy (PMA). In the bulk limit, we observe the well-known labyrinth-type domains. Thinner flakes, on the other hand, are characterized by increasingly fragmented domains. While PMA is a characteristic property of Fe5GeTe2, we observe a spin-reorientation transition with the spins canting in-plane for flakes thinner than six layers. Notably, a bubble phase emerges in four-layer flakes. This thickness dependence, which clearly deviates from the single-domain behavior observed in other 2D magnetic materials, demonstrates the exciting prospect of stabilizing complex spin textures in 2D vdW magnets at relatively high temperatures.

Magnetic skyrmions are topologically stabilized nanoscale spin structures that could be of use in the development of future spintronic devices. When a skyrmion is driven by an electric current it propagates at an angle relative to the flow of current—known as the skyrmion Hall angle (SkHA)—that is a function of the drive current. This drive dependence, as well as thermal effects due to Joule heating, could be used to tailor skyrmion trajectories, but are not well understood. Here we report a study of skyrmion dynamics as a function of temperature and drive amplitude. We find that the skyrmion velocity depends strongly on temperature, while the SkHA does not and instead evolves differently in the low- and high-drive regimes. In particular, the maximum skyrmion velocity in ferromagnetic devices is limited by a mechanism based on skyrmion surface tension and deformation (where the skyrmion transitions into a stripe). Our mechanism provides a complete description of the SkHA in ferromagnetic multilayers across the full range of drive strengths, illustrating that skyrmion trajectories can be engineered for device applications. An analysis of skyrmion dynamics at different temperatures and electric drive currents is used to develop a complete description of the skyrmion Hall angle in ferromagnetic multilayers from the creep to the flow regime and illustrates that skyrmion trajectories can be engineered for device applications.

Magnetic skyrmions promise breakthroughs in future memory and computing devices due to their inherent stability and small size. Their creation and current driven motion have been recently observed at room temperature, but the key mechanisms of their formation are not yet well-understood. Here it is shown that in heavy metal/ferromagnet heterostructures, pulsed currents can drive morphological transitions between labyrinth-like, stripe-like, and skyrmionic states. Using high-resolution X-ray microscopy, the spin texture evolution with temperature and magnetic field is imaged and it is demonstrated that with transient Joule heating, topological charges can be injected into the system, driving it across the stripe-skyrmion boundary. The observations are explained through atomistic spin dynamic and micromagnetic simulations that reveal a crossover to a global skyrmionic ground state above a threshold magnetic field, which is found to decrease with increasing temperature. It is demonstrated how by tuning the phase stability, one can reliably generate skyrmions by short current pulses and stabilize them at zero field, providing new means to create and manipulate spin textures in engineered chiral ferromagnets.

Magnetic skyrmions are particle-like chiral twists of the magnetization that promise advances in spin-based data storage and logic device applications. In article number 1805461, Mathias Kläui, Geoffrey S. D. Beach, and co-workers examine current-induced generation of skyrmions in heavy-metal/ferromagnet multilayers and show that Joule heat pulses can drive topological transitions in magnetic textures and enable skyrmion creation on nanosecond timescales.

Magnetic skyrmions are promising candidates for future spintronic applications such as skyrmion racetrack memories and logic devices. They exhibit exotic and complex dynamics governed by topology and are less influenced by defects, such as edge roughness, than conventionally used domain walls. In particular, their non-zero topological charge leads to a predicted ‘skyrmion Hall effect’, in which current-driven skyrmions acquire a transverse velocity component analogous to charged particles in the conventional Hall effect. Here, we use nanoscale pump–probe imaging to reveal the real-time dynamics of skyrmions driven by current-induced spin–orbit torques. We find that skyrmions move at a well-defined angle ΘSkH that can exceed 30° with respect to the current flow, but in contrast to conventional theoretical expectations, ΘSkH increases linearly with velocity up to at least 100 ms−1. We qualitatively explain our observation based on internal mode excitations in combination with a field-like spin–orbit torque, showing that one must go beyond the usual rigid skyrmion description to understand the dynamics. Experiments show that when driven by electric currents, magnetic skyrmions experience transverse motion due to their topological charge — similar to the conventional Hall effect experienced by charged particles in a perpendicular magnetic field.