Interacting topological Dirac magnons

Abstract

In this work, we study the magnon-magnon interaction effect in typical honeycomb ferromagnets consisting of van der Waals-bonded stacks of honeycomb layers, e.g., chromium trihalides CrX 3 (X = F, Cl, Br, and I), that display two spin-wave modes (Dirac magnon). Using Green's function formalism with the presence of the Dzyaloshinskii-Moriya interaction, we obtain a spinor Dyson equation up to the second-order approximation by the cluster expansion method. Numerical calculations show prominent renormalizations of the single-particle spectrum. Furthermore, we propose a tunable renormalization effect using a parametric magnon amplification scheme. By amplifying the magnon population at different k points, the enabled renormalization effect not only reshapes the band structure but also modifies the Berry curvature distribution. Our work demonstrates the interplay between band geometry, interactions, and the external light field in the bosonic system and can potentially lead to new insights into the properties of magnon-based spintronic devices.

Interacting topological magnons in a checkerboard ferromagnet

“…Using a similar approach, Lu et al [22] obtained the renormalized energy bands of honeycomb ferromagnets. Here, we first write the first-order Dyson equation for interacting magnons, [23] which reads…”

“…To properly consider the role of the magnon-magnon interaction, we employ the perturbation technique developed by Sun et al [23] to obtain the form of the first-order (Hartree-037503-3 type) self-energy that will yield a renormalized magnon energy spectrum. Using a similar approach, Lu et al [22] obtained the renormalized energy bands of honeycomb ferromagnets.…”

“…They showed that the magnon-magnon interactions can induce a topological phase transition of Dirac magnons, which is depicted via the sign transformation of the thermal Hall conductivity. Very recently, Sun et al [23] have shown that the honeycomb ferromagnetic spin system with a nontrivial DMI can reveal very interesting physics after considering the effect of magnon-magnon interaction. More importantly, they have realized flat bands with nontrivial topology, which can provide one realistic platform to investigate those strongly correlated bosonic systems.…”

Effect of interlayer exchange coupling interaction on topological phase of a bilayer honeycomb Heisenberg ferromagnet

“…些点达到峰值，即该系统的磁子贝里曲率主要由狄拉克点贡献 [70] 。 狄拉克点是晶体能带结构中的关键节点，其能量色散关系呈现出线性特征，类似于 无质量的狄拉克粒子，使得磁子在这些点附近的行为表现出特殊性质 [71][72][73] 。在双层蜂窝 状铁磁体系统中，狄拉克点对于磁子贝里曲率的贡献尤为显著。在狄拉克点附近，能带 的线性色散关系导致磁子在传播过程中受到的有效磁场力发生显著变化。这种变化直接 反映在磁子贝里曲率的分布上，使得狄拉克点成为磁子贝里曲率的主要贡献者。狄拉克 点的存在为磁子的传播提供了特定的通道，使磁子在这些点附近的行为与传统材料中的 磁子有很大不同。这种特殊性质不仅会影响磁子的传播行为，还可能对材料的磁性、热 导率等物理性质产生深远影响 [74] 对于玻色子系统，计算能带对应的陈数也是研究磁子拓扑性质的一种可靠方法。陈 数作为一种拓扑不变量，是描述磁子系统中磁子拓扑性质的关键参数，其被定义为贝里 曲率的积分，贝里曲率反映了波函数在参数空间中的几何性质，而陈数则是这一几何性 质的量化表现 [75,76] ，可以写成如下形式：  …”