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arXiv · 1912.05085

Magnetic Skyrmions are Quasi-Magnetic Monopoles in Two-Dimensional Magnetic Materials

Ji-Rong Ren·Zhi Wang·Fei Qu·Hao Wang
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Abstract

Using $su(N)$ Cartan subalgebra local bases parametrization of density operator $\rho$, we prove that the Wu-Yang potentials of a general $N$-level quantum system are completely expressed by $SU(N)$ gauge transformation. By taking the $SU(2)$ Cartan subalgebra local basis as a local normalized magnetization vector, we find that magnetic skyrmion and Wu-Yang magnetic monopole have the same algebraic structure. Moreover, by taking the adiabatic unitary evolution of magnetization as local gauge transformation, we verify that the Wu-Yang potential of magnetic skyrmions is proportional to the Berry connection, this means that magnetic skyrmion is quasi-magnetic monopole. The exact relation between Wu-Yang potentials and Berry connection is discussed in detail for the general $SU(N)$ case, i.e. the Berry connection for the pure or mixed state is the weighted average of the $(N-1)$ Wu-Yang potentials.

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Ji-Rong Ren, Zhi Wang, Fei Qu, Hao Wang. 2019-12-11. Magnetic Skyrmions are Quasi-Magnetic Monopoles in Two-Dimensional Magnetic Materials. https://arxiv.org/abs/1912.05085

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