We show that a suitable combination of flat-band ferromagnetism, geometry and nontrivial electronic band topology can give rise to itinerant topological magnons. An SU(2) symmetric topological Hubbard model with nearly flat electronic bands, on a Kagome lattice, is considered as the prototype. This model exhibits ferromagnetic order when the lowest electronic band is half-filled. Using the numerical exact diagonalization method with a projection onto this nearly flat band, we can obtain the magnonic spectra. In the flat-band limit, the spectra exhibit distinct dispersions with Dirac points, similar to those of free electrons with isotropic hoppings, or a local spin magnet with pure ferromagnetic Heisenberg exchanges on the same geometry. Significantly, the non-flatness of the electronic band may induce a topological gap at the Dirac points, leading to a magnonic band with a nonzero Chern number. More intriguingly, this magnonic Chern number changes its sign when the topological index of the electronic band is reversed, suggesting that the nontrivial topology of the magnonic band is related to its underlying electronic band. Our work suggests interesting directions for the further exploration of, and searches for, itinerant topological magnons.

我们表明，平带铁磁性、几何和非平凡电子带拓扑的适当组合可以产生巡回拓扑磁振子。一个SU(2) 在 Kagome 晶格上具有近乎平坦电子带的对称拓扑哈伯德模型被认为是原型。当最低电子带被半填充时，该模型表现出铁磁有序。使用数值精确对角化方法并投影到这个近乎平坦的带上，我们可以获得磁波谱。在平带极限中，光谱表现出不同的狄拉克点色散，类似于具有各向同性跳跃的自由电子，或在相同几何形状上具有纯铁磁海森堡交换的局部自旋磁铁。值得注意的是，电子能带的非平坦性可能会在狄拉克点处引起拓扑间隙，从而导致具有非零陈数的磁能带。更有意思的是，当电子能带的拓扑指数反转时，这个磁陈数会改变其符号，这表明磁能带的非平凡拓扑与其潜在的电子能带有关。我们的工作为进一步探索和搜索巡回拓扑磁子提供了有趣的方向。