Are Skyrmions and Magnetic Voretices the same? Else what is the fundamental difference between them?
A magnetic vortex is a very different object than the skyrmion. The vortex is just a field of vectors and the most important in magnetism are spin vortex formed by the intersection of two Neel walls. While the skyrmion is a topological quasiparticle formed with spins and therefore defined with a topological index.
Dear Mouad,
I magnetic vortex in Physics is a more general object than the topological spin vortice. For instance, the Abrikosov-Nielsen vortices in second type of superconductors are not topological objects as the ones of the Hall effect. But you are right that when you restrict to spin arrangements as the usual for skyrmions, you can compare (and clasify) both by their topological winding numbers n. They can take as topological excitations where a vortice (n=+1) has a half-integer skyrmion charge of q=|np/2|=1/2, being p (p=±1) the polarizability. For the antivortices n=-1.
Thus the concept of magnetic vortice is more general because it is not restricted to be a topological excitation as it can be done by a set of spins.
This link maybe help you: https://arxiv.org/ftp/arxiv/papers/1706/1706.08295.pdf
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