Abstract
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.
Highlights
Magnetic skyrmions are spin configurations with spherical topology[1,2,3,4,5], typically manifesting as circular domains with defect-free domain walls (DWs) in systems with otherwise uniform out-of-plane magnetization
In the Supplementary Information, we provide analytical expressions for both bulk and interface Dzyaloshinskii-Moriya interaction (DMI) terms; in the discussions below, we apply our model with a focus on systems with interface DMI only, but the model itself is more general
We have presented the first unified theory that describes both stray field and DMI skyrmions in one coherent model
Summary
The room temperature collapse diameter as a function of Di and film thickness is shown in Figs 2a,b for the wall-energy model and effective anisotropy model, respectively, using the most accurate available form of the former[41] These figures correspond to a 50kBTRT stability criterion; a 30kBTRT criterion (lifetime of order seconds) leads to similar results. The two types of skyrmions in the bi-stability region can have very different properties (Fig. 3b), confirmed by micromagnetic simulations: Their radii differ by more than one order of magnitude and their spin structure is Néel-like for the small (DMI) skyrmion and intermediate for the large (stray field) skyrmion. Moderate applied fields (Figs 4c,d) extend the stability range for large stray field skyrmions but do little to stabilize small skyrmions Since it is the domain wall energy whose minimum is responsible for zero-field skyrmions, stability can be enhanced by increasing film thickness since this energy scales with d. The ratio ΔID(ρ)/IA(ρ) derives from the Thiele effective force, with
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