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Concept
Magnetic skyrmion
Summary
In physics, magnetic skyrmions (occasionally described as 'vortices,' or 'vortex-like'
configurations) are statically stable soliton which have been predicted theoretically and observed experimentally in condensed matter systems. Magnetic skyrmions can be formed in magnetic materials in their 'bulk' such as in manganese monosilicide (MnSi), or in magnetic thin films. They can be achiral, or chiral (Fig. 1 a and b are both chiral skyrmions) in nature, and may exist both as dynamic excitations or stable or metastable states. Although the broad lines defining magnetic skyrmions have been established de facto, there exist a variety of interpretations with subtle differences.
Most descriptions include the notion of topology – a categorization of shapes and the way in which an object is laid out in space – using a continuous-field approximation as defined in micromagnetics. Descriptions generally specify a non-zero, integer value of the topological index, (not to be confused with the chemistry meaning of 'topological index'). This value is sometimes also referred to as the winding number, the topological charge (although it is unrelated to 'charge' in the electrical sense), the topological quantum number (although it is unrelated to quantum mechanics or quantum mechanical phenomena, notwithstanding the quantization of the index values), or more loosely as the “skyrmion number.” The topological index of the field can be described mathematically as
where is the topological index, is the unit vector in the direction of the local magnetization within the magnetic thin, ultra-thin or bulk film, and the integral is taken over a two dimensional space. (A generalization to a three-dimensional space is possible)..
Passing to spherical coordinates for the space ( ) and for the magnetisation ( ), one can understand the meaning of the skyrmion number. In skyrmion configurations the spatial dependence of the magnetisation can be simplified by setting the perpendicular magnetic variable independent of the in-plane angle () and the in-plane magnetic variable independent of the radius ( ).
Official source
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