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arXiv 2008.08681cond-mat.mes-hall
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手征磁性的几何透视

Chiral magnetism: a geometric perspective

Daniel Hill, Valeriy Slastikov, Oleg Tchernyshyov

摘要:

我们讨论了手征铁磁性的几何观点。就像引力成为相对论中时空曲率的影响一样,Dzyaloshinski-Moriya相互作用出现在具有非平凡自旋平行输运的海森堡模型中。Dzyaloshinskiii-Moriya矢量作为背景SO(3)规范场。在2维空间中,当外加磁场与规范曲率相匹配时,该模型部分可解。在这个特殊点上,Bogomolny方程的解是模型的精确激发态。我们构建了一个变分基态的形式的skyrmion晶体,并证实其可行性的蒙特卡罗模拟。几何的角度提供了重要的问题,在磁性的见解,例如,在手性相互作用存在下的自旋电流守恒。

英文摘要:

We discuss a geometric perspective on chiral ferromagnetism. Much like gravity becomes the effect of spacetime curvature in theory of relativity, the Dzyaloshinski-Moriya interaction arises in a Heisenberg model with nontrivial spin parallel transport. The Dzyaloshinskii-Moriya vectors serve as a background SO(3) gauge field. In 2 spatial dimensions, the model is partly solvable when an applied magnetic field matches the gauge curvature. At this special point, solutions to the Bogomolny equation are exact excited states of the model. We construct a variational ground state in the form of a skyrmion crystal and confirm its viability by Monte Carlo simulations. The geometric perspective offers insights into important problems in magnetism, e.g., conservation of spin current in the presence of chiral interactions.

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