We investigate rare-earth magnetic Weyl semimetals through first-principles simulations, analyzing the connection between incommensurate magnetic order and the presence of Weyl nodes in the electronic band structure. Focusing on PrAlSi, NdAlSi, and SmAlSi, we demonstrate that the reported helical ordering does not originate from the nesting of topological features at the Fermi surface or the Dzyaloshinskii-Moriya interaction. Instead, the helical order arises from frustrated isotropic short-range superexchange between the $4f$ moments facilitated by $pd$ hybridization with the main group elements. Employing a spin Hamiltonian with isotropic exchange and single-ion anisotropy we replicate the experimentally observed helical modulation.

中文翻译：

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RAlSi 磁性外尔半金属 (R=Pr、Nd、Sm) 中不相称磁序的起源

我们通过第一原理模拟研究稀土磁性韦尔半金属，分析不相称的磁序与电子能带结构中韦尔节点的存在之间的联系。重点关注 PrAlSi、NdAlSi 和 SmAlSi，我们证明所报道的螺旋排序并非源自费米表面拓扑特征的嵌套或 Dzyaloshinskii-Moriya 相互作用。相反，螺旋顺序是由受挫的各向同性短程超交换产生的$4F$促进的时刻$pd$与主族元素的杂交。采用具有各向同性交换和单离子各向异性的自旋哈密顿量，我们复制了实验观察到的螺旋调制。