Abstract
Small fluctuations of the ordered moments in magnets are known as magnons. For a single skyrmion, geometrically confined spin excitations arise corresponding to various deformations of the ground-state skyrmion texture.
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- 1.
Alternatively, spin waves. The two terms are used interchangeably in this chapter.
- 2.
Another way to introduce HP bosons in terms of the local triad \((\mathbf{n}_0, \hat{\theta }, \hat{\phi })\) is to write \(S^+ = \mathbf{S} \cdot (\hat{\theta } + i \hat{\phi } ) = \sqrt{2S} b\), \(S^- = \mathbf{S} \cdot (\hat{\theta } - i \hat{\phi } ) = \sqrt{2S} b^\dag \), and \(\mathbf{S} \cdot \mathbf{n}_0 = S - b^\dag b\).
- 3.
The singular part \(\cos \theta (\varvec{\nabla }\times \varvec{\nabla }\phi )_\lambda \) has been dropped from the curl.
- 4.
The geometric action is basically a collection of actions for each spin. With each spin, the action measures the amount of solid angle traced by that spin over time, which must obviously be the same no matter which coordinate frame is used to compute it.
- 5.
The three-dimensional generalization gives \(L_{int.} = -2\pi \mathbf{q} \cdot (\mathbf{j}^e \times \mathbf{u} ) \).
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Han, J.H. (2017). Magnon Dynamics. In: Skyrmions in Condensed Matter. Springer Tracts in Modern Physics, vol 278. Springer, Cham. https://doi.org/10.1007/978-3-319-69246-3_6
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