中心对称磁性薄膜中的铋离子稳定性
Stability of Biskyrmions in Centrosymmetric Magnetic Films
摘要：
受中心对称磁性薄膜中双克尔米子的观察启发（Yu等人，Nature Communications 2014，Wang等人，Advanced Materials 2016），我们分析和数值研究了有限厚度薄膜中双克尔米子的稳定性，考虑了最近邻交换相互作用，垂直磁各向异性（PMA），偶极-偶极相互作用（DDI），和原子晶格的离散性。双克尔密子的特征在于拓扑电荷$Q=2$、空间尺度$λ$和另一个独立的长度$d$，其可以被解释为在均匀磁化的背景下$Q=2$拓扑缺陷内的两个$Q=1$ skyrmion的分离。我们发现，在一定的PMA/DDI比范围内，在具有足够数量的原子层$N_{z}$的薄膜中，磁场可以稳定具有$λ$级$d$的铋离子。通过对$1000\times1000\times N_{z}$原子晶格中相互作用自旋能量的数值极小化，得到了双原子的形状。当$d$小于磁畴壁宽度时，与Belavin-Polyakov模型的精确解接近。计算了双量子的磁矩，并讨论了在实验中产生双量子的方法。
英文摘要：
Motivated by the observation of biskyrmions in centrosymmetric magnetic films (Yu et al. Nature Communications 2014, Wang et al. Advanced Materials 2016), we investigate analytically and numerically the stability of biskyrmions in films of finite thickness, taking into account the nearest-neighbor exchange interaction, perpendicular magnetic anisotropy (PMA), dipole-dipole interaction (DDI), and the discreteness of the atomic lattice. The biskyrmion is characterized by the topological charge $Q=2$, the spatial scale $λ$, and another independent length $d$ that can be interpreted as a separation of two $Q=1$ skyrmions inside a $Q=2$ topological defect in the background of uniform magnetization. We find that biskyrmions with $d$ of order $λ$ can be stabilized by the magnetic field within a certain range of the ratio of PMA to DDI in a film having a sufficient number of atomic layers $N_{z}$. The shape of biskyrmions has been obtained by the numerical minimization of the energy of interacting spins in a $1000\times1000\times N_{z}$ atomic lattice. It is close to the exact solution of Belavin-Polyakov model when $d$ is below the width of the ferromagnetic domain wall. We compute the magnetic moment of a biskyrmion and discuss ways of creating biskyrmions in experiment.
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