There is growing interest in revealing exotic properties of collective spin excitations in kagome-lattice ferromagnets such as magnon Hall effects, topological magnon insulators, and flat magnon bands. Using the well-established nearest-neighbor Heisenberg ferromagnet model with Dzyaloshinskii-Moriya interaction (DMI), in this study we uncover intriguing new aspects in the selectivity and topology of flat magnon bands. Among the three magnon bands (except for the top one, which is flat in the absence of DMI), we observe that each of the three bands can be selectively flattened at the critical DMI of \(D=\pm\sqrt{3}J/3\) and \(D=\pm\sqrt{3}J\). With a general DMI, the magnon bands become non-flat; however, there are nested lines that create a David star pattern for all three magnon bands whose flatness is robust during changing exchange coupling or DMIs. Contrary to prevailing belief, we show that each of the three flat bands is actually topologically trivial at critical DMIs. Furthermore, we show that while the middle band remains topologically trivial, for the other two bands, D = 0 corresponds to the topological phase transition where their Chern numbers get interchanged; when \(D=\pm\sqrt{3}J\), the system undergoes a phase transition to the nonferromagnetic state. These central findings increase our understanding of spin excitations for future magnonics applications.

中文翻译：

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具有Dzyaloshinskii-Moriya相互作用的kagome-晶格铁磁体中的磁振子带的选择性平坦化

人们越来越感兴趣地揭示kagome-lattice铁磁体中集体自旋激发的奇异特性，例如，马农霍尔效应，拓扑马农绝缘子和平坦马农带。使用建立良好的最近邻海森堡铁磁体模型和Dzyaloshinskii-Moriya相互作用（DMI），在这项研究中，我们发现了扁平磁振子带的选择性和拓扑结构方面有趣的新方面。在三个磁振子频带中（除了顶部的一个，在没有DMI的情况下是平坦的），我们观察到三个频带中的每个都可以在\（D = \ pm \ sqrt {3} J / 3 \）和\（D = \ pm \ sqrt {3} J \）。对于一般的DMI，磁振子频带变得不平坦；但是，有些嵌套线会为所有三个磁振子带创建一个大卫星型图案，在改变交换耦合或DMI时其平坦度很强。与普遍的看法相反，我们表明三个平坦带中的每个实际上在关键DMI上在拓扑上都是微不足道的。此外，我们表明，尽管中带在拓扑上仍然是微不足道的，但对于其他两个带，D = 0对应于其Chern数互换的拓扑相变；当\（D = \ pm \ sqrt {3} J \）时，系统经历相变至非铁磁状态。这些主要发现加深了我们对未来磁电机应用中自旋激发的理解。