In particle theory, the skyrmion is a topologically stable field configuration of a certain class of non-linear sigma models. Skyrmions, named after British physicist Tony Hilton Royle Skyrme, can be formed in magnetic materials in their 'bulk' such as in MnSi, or in magnetic thin films. They can be achiral, or chiral 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. See Magnetic skyrmion.
Questions tagged [skyrmion]
21 questions
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Non-chiral skyrmion v.s. Left/Right chiral skyrmion
A skyrmion in a 3-dimensional space (or a 3-dimensional spacetime) is detected by a topological index
$$n= {\tfrac{1}{4\pi}}\int\mathbf{M}\cdot\left(\frac{\partial \mathbf{M}}{\partial x}\times\frac{\partial \mathbf{M}}{\partial y}\right)dx dy
$$…
wonderich
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What is the modern status on the Skyrmion theory of baryons?
It was noticed in the 1960s that chiral perturbation theory, describing the goldstone-bosons (pions) of the breaking $SU(N_f)_L \times SU(N_f)_R \to SU(N_f)_V$ of the chiral symmetry, has solitonic solutions (skyrmions), so long as you include…
QCD_IS_GOOD
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Skyrmion number
The skyrmion number is defined as
$$n=\frac{1}{4\pi}\int\mathbf{M}\cdot\left(\frac{\partial\mathbf{M}}{\partial x}\times\frac{\partial\mathbf{M}}{\partial y}\right)dxdy$$
where $n$ is the topological index, $\mathbf {M}$ is the unit vector in the…
Eric Z
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Number of baryons in the Skyrme model
In QCD, the Eightfold Way organizes the number of baryons with respect to their flavor and color quantum numbers: for three light $(u,d,s)$ quark constituents, a spin-(1/2) baryon octet and a spin-(3/2) baryon decouplet emerge, because the…
Thomas
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What is the difference between a skyrmion and a magnetic vortex?
Skyrmions and magnetic vortices are spin structures occurring in magnets.
What are the differences between them? More specifically, I would like to understand their origin and how to distinguish them.
B. Brekke
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half Skyrmion vs Meron
Is there a difference between a half skyrmion and a meron? I'm asking this in regard to half skyrmion theories of High Tc Superconductors. It would be interresting to know if the proposed half skyrmions which emerge in the disturbed…
P3trus
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Skyrmion's Hall Effect
I found an interesting phenomenon: as this Physical Review B on arXiv said,
The Sk moves faster in $+\hat x$ direction and then saturates when the amplitude
exceeds $V = 0.8$. The motion along the $\hat y$ direction is always
slower than that in…
myhsia
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Hopfion with only in-plane vortex rather than skyrmion along the torus?
A simple torus-like hopfion with hopf charge $Q_H=1$ will typically exhibit a skyrmion at each slice cutting the toroidal circle. What if the skyrmion is replaced by an in-plane 2D vortex, i.e., we set the vector component $S_3=0$ for all such slice…
xiaohuamao
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How "hedgehog" or instanton event changes the configuration of neel vector in 2D antiferromagnet?
The definition of "hedgehog" or instanton event here is "a space-time event where the skyrmion number Q changes by $\pm1$ is called a hedgehog" (ref.1 & 2).
A nice figure illustrates such an instanton event is found in ref.3, where the initial…
ZJX
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1 answer
What does topologically stable mean?
I am working on an article about skyrmion manipulation and it is written that those particles are "topologically stable particle-like spin configurations that carry a characteristic topological charge S". I am struggling with the word…
mm-robert
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No global monopoles in QCD
If a global symmetry gets both spontaneously and explicitly broken, the explicit symmetry breaking pattern is crucial for understanding the formation of topological defects.
For example, in the axion solution to the strong CP problem, the explicit…
Thomas
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Skyrmion of pseudo-scalar mesons and vector mesons
I had heard statements that Skyrmion of pions (pseudo-scalar mesons) cannot be an object like baryon, however, Skyrmion of vectors mesons may indeed form an object like baryon. For example, see this Ref and the work of this author and Ref 2.
For…
wonderich
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vote
1 answer
A primer on topological solitons in scalar field theories
As the title suggests I want to learn more about topological solitons in scalar field theories. I am searching for a resource which is self-contained, in the sense that it also explains the mathematics needed, at least to some extent. It should be a…
AlmostClueless
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1
vote
1 answer
How does the Mermin-Ho theorem handle singularities arising from the hairy ball theorem?
I am reading about the derivation of the Mermin-Ho relation in chapter III. B of (Kamien, 2002) and trying to understand how it fits with the hairy ball theorem.
Assuming you have a unit vector $\hat{n}(\vec{r})$ which covers the entire unit sphere…
Ben
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How to derive the Einstein-Skyrme equations?
I would like to derive the Einstein-Skyrme equations. The action can be read as
\begin{equation}
S[g,U] = \int d^{4}x\sqrt{-g}\biggl[R + \frac{K}{4}Tr\bigg(A^{\mu}A_{\mu} + \frac{\lambda}{8}F_{\mu\nu}F^{\mu\nu}\bigg)\biggr]
\end{equation}
where the…
Hello
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