Generation of stable skyrmion lattices and displacement of trains of individual skyrmions along a magnetic racetrack by short current pulses are demonstrated at room temperature in ultrathin metallic ferromagnets.

Magnetic skyrmions are topological quasiparticles of great interest for data storage applications because of their small size, high stability, and ease of manipulation via electric current. However, although models exist for some limiting cases, there is no universal theory capable of accurately describing the structure and energetics of all skyrmions. The main barrier is the complexity of non-local stray field interactions, which are usually included through crude approximations. Here we present an accurate analytical framework to treat isolated skyrmions in any material, assuming only a circularly-symmetric 360° domain wall profile and a homogeneous magnetization profile in the out-of-plane direction. We establish the first rigorous criteria to distinguish stray field from DMI skyrmions, resolving a major dispute in the community. We discover new phases, such as bi-stability, a phenomenon unknown in magnetism so far. We predict materials for sub-10 nm zero field room temperature stable skyrmions suitable for applications. Finally, we derive analytical equations to describe current-driven dynamics, find a topological damping, and show how to engineer materials in which compact skyrmions can be driven at velocities >1000 m/s.

We develop an accurate analytical model for the stray field energy of parallel stripe domains in multilayer films with perpendicular magnetic anisotropy, taking into account the effects of finite domain wall width and variable domain wall angle. By minimizing the total energy, we predict the domain width, the domain wall width, and the domain wall angle for given material parameters. We show how the domain wall width depends on the film thickness and the domain size. We explore the domain wall angle as a function of Dzyaloshinskii-Moriya interaction (DMI) and derive a threshold value $D_{\text{thr}}$ beyond which the system is in a Néel state. We find that thicker films require larger values of DMI to stabilize the Néel state. Finally, we test the effective medium theory, which allows treating multilayers as effective single layer films, and provide criteria for the applicability of the model in the presence of both surface and volume stray fields. Our results are supported by micromagnetic simulations, which indicate that the predictions are still precise even if the system is in a labyrinthine domain state. Using our model, otherwise inaccessible magnetic parameters, such as the DMI constant or the exchange constant, can now be obtained straightforwardly from static measurements of the stripe domain width in such films.