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arXiv · 0809.2100

On topological spin excitations on a rigid torus

V. L. Carvalho-Santos·A. R. Moura·W. A. Moura-Melo·A. R. Pereira
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Abstract

We study Heisenberg model of classical spins lying on the toroidal support, whose internal and external radii are $r$ and $R$, respectively. The isotropic regime is characterized by a fractional soliton solution. Whenever the torus size is very large, $R\to\infty$, its charge equals unity and the soliton effectively lies on an infinite cylinder. However, for R=0 the spherical geometry is recovered and we obtain that configuration and energy of a soliton lying on a sphere. Vortex-like configurations are also supported: in a ring torus ($R>r$) such excitations present no core where energy could blow up. At the limit $R\to\infty$ we are effectively describing it on an infinite cylinder, where the spins appear to be practically parallel to each other, yielding no net energy. On the other hand, in a horn torus ($R=r$) a singular core takes place, while for $R<r$ (spindle torus) two such singularities appear. If $R$ is further diminished until vanish we recover vortex configuration on a sphere.

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V. L. Carvalho-Santos, A. R. Moura, W. A. Moura-Melo, A. R. Pereira. 2008-09-11. On topological spin excitations on a rigid torus. https://doi.org/10.1103/physrevb.77.134450

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