The unusual magnetic behaviour of helimagnet MnSi, noticed in recent years, prompted the suspicion that the magnetic states arising in such crystals are of topological nature. Recent experiments based on the topological Hall effect confirmed such topologically nontrivial states as the skyrmions, located on a plane perpendicular to the applied magnetic field. We present here a theoretical model for chiral magnets with competing exchange and Dzyaloshinskii-Moriya type interaction, which leads to an exact skyrmionic soliton with integer topological charge. Such topologically stable spin states with analytic solution on a two-dimensional plane show helical structures of partial order, without inversion and circular symmetry. These exact N-skyrmions, though represent higher excited states, correspond to the lowest energy stable configuration in each topological sector and are likely to appear in MnSi under suitable experimental conditions.

Instanton solutions in the anisotropic σ model

Exact non-circular symmetric N-skyrmions in helical magnets without inversion symmetry

Historically the common law allowed the prosecution to prove the defendant's guilt by adducing not only factual evidence, but also evidence of his bad character. The latter could take the form of evidence that the defendant had done the same thing on previous occasions as he was charged with today. This was known as similar fact evidence (SFE). Under the Criminal Justice Act 2003 the common law rules as to the admissibility of evidence of bad character were abolished and replaced with a statutory scheme which is capable of being used to admit some, but by no means all, of what was SFE at common law. This article considers alternative meanings of the two-word phrase ‘bad character’; whether SFE which is not admissible under the Act is nevertheless admissible at common law; the relationship between the statutory scheme and the common law; and crucially, the jury direction at common law.

Instanton solutions in the anisotropic σ model

Citations

Exact non-circular symmetric N-skyrmions in helical magnets without inversion symmetry

Mental Gymnastics and Intellectual Acrobatics: The Meanings of Statutory and Common Law ‘Bad Character’

References

Instanton solutions in the anisotropic σ-model

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