${\mathrm{TbMn}}_6{\mathrm{Sn}}_6$ is a metallic ferrimagnet displaying signatures of both topological electrons and topological magnons arising from ferromagnetism and spin-orbit coupling within its Mn kagome layers. Inelastic neutron scattering measurements find strong ferromagnetic (FM) interactions within the Mn kagome layer and reveal a magnetic bandwidth of $\sim 230\mathrm{meV}$. The low-energy magnetic excitations are characterized by strong FM Mn-Mn and antiferromagnetic (AFM) Mn-Tb interlayer magnetic couplings. We observe weaker, competing long-range FM and AFM Mn-Mn interlayer interactions similar to those driving helical magnetism in the ${\mathrm{YMn}}_6{\mathrm{Sn}}_6$ system. Combined with density-functional theory calculations, we find that competing Mn-Mn interlayer magnetic interactions occur in all $R{\mathrm{Mn}}_6{\mathrm{Sn}}_6$ compounds with $R=\mathrm{Y}$, Gd-Lu, resulting in magnetic instabilities and tunability when Mn-$R$ interactions are weak. In the case of ${\mathrm{TbMn}}_6{\mathrm{Sn}}_6$, strong AFM Mn-Tb coupling ensures a highly stable three-dimensional ferrimagnetic network.

中文翻译：

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拓扑FerrimagnetTbMn6Sn6中的低温竞争磁能标度

${锰}_6{锡}_6$是一种金属铁磁体，显示出拓扑电子和拓扑磁子的特征，这些特征是由其 Mn kagome 层内的铁磁性和自旋轨道耦合产生的。非弹性中子散射测量发现 Mn kagome 层内有强铁磁 (FM) 相互作用，并揭示了磁带宽$～230\mathrm{毫伏特}$. 低能磁激发的特点是强 FM Mn-Mn 和反铁磁 (AFM) Mn-Tb 层间磁耦合。我们观察到较弱的、相互竞争的长程 FM 和 AFM Mn-Mn 层间相互作用，类似于在${锰}_6{锡}_6$系统。结合密度泛函理论计算，我们发现竞争的 Mn-Mn 层间磁相互作用发生在所有$R{锰}_6{锡}_6$化合物与$R=\mathrm{是}$, Gd-Lu，当 Mn- 时导致磁不稳定性和可调性$R$相互作用很弱。如果是${锰}_6{锡}_6$，强大的 AFM Mn-Tb 耦合确保了高度稳定的三维亚铁磁网络。