Abstract
Magnetic skyrmions and bubbles, observed in ferromagnetic thin films with perpendicular magnetic anisotropy, are topological solitons which differ by their characteristic size and the balance in the energies at the origin of their stabilisation. However, these two spin textures have the same topology and a continuous transformation between them is allowed. In the present work, we derive an analytical model to explore the skyrmion-bubble transition. We evidence a region in the parameter space where both topological soliton solutions coexist and close to which transformations between skyrmion and bubbles are observed as a function of the magnetic field. Above a critical point, at which the energy barrier separating both solutions vanishes, only one topological soliton solution remains, which size can be continuously tuned from micrometer to nanometer with applied magnetic field.
Highlights
As both spin textures have the same topology, we will use the more general name topological soliton to discuss the model solutions in the first place and later specify what type of topological soliton solution presents the characteristic of a magnetic skyrmion or bubble
We present the relaxed topological soliton radius as function of applied magnetic field (Figure 4a) and for comparison the equilibrium topological soliton radius obtained analytically using the same parameters except the D values, ranging from 3.40 to 3.60 mJ/m2 (Figure 4b)
We have developed an analytical topological soliton model containing expressions of the long range demagnetising and exchange curvature energies, two key ingredients to stabilize bubbles and skyrmions in ferromagnetic thin films
Summary
Skyrmions, are topological solitons which present particle-like properties: they have quantized topological charges, interact via attractive and repulsive forces, and can condense into ordered phases. The case of intermediate-size solitons is more favorable, as stable RT topological solitons with sizes of a few hundred to a few tens of nanometers have been reported in multilayers [32] and even in a single ferromagnetic layer [33,34] These topological solitons are sometimes called skyrmion bubbles when the demagnetising energy plays a role in their stabilization. As minimising the total energy of the soliton is numerically expensive, we derive in the present work an analytical topological soliton model in order to build a skyrmion-bubble phase diagram and obtain a better physical insight of the differences between skyrmions and bubbles This allows us to calculate skyrmions and bubbles equilibrium solutions out of a single model from nanometer to micrometer radius and demonstrate the existence of transitions between them as a function of magnetic field
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