Interaction induced topological magnon in electron-magnon coupled systems

Abstract

We theoretically study the emergence of topological magnons in electron-magnon coupled systems. The magnon dispersion in a ferromagnet usually possesses an effective time reversal symmetry in the absence of Dzyaloshinskii-Moriya (DM) interaction, preventing the appearance of topological magnons. When a spin system is coupled to itinerant electrons, we find that the magnon band structure of the spin system experiences time-reversal symmetry breaking with the electron-magnon interaction via the exchange coupling, where topological magnons arise without requiring strong DM. Specifically, we consider a heterostructure consisting of a ferromagnetic insulator and a transition metal dichalcogenide (TMD) monolayer and investigate topological gap opening in magnon bands. Our findings reveal that even trivial ferromagnets can host topological magnons via coupling to itinerant electronic systems.

Figures (8)

• Figure 1: Schematic of a spin system coupled to an electronic system. Yellow balls indicate a flow of electrons. Geometrical properties of the electron system with broken time-reversal symmetry are imprinted on the magnon system via electron-magnon interactions, resulting in the emergence of topological magnons.
• Figure 2: Schematic of the TMD monolayer and its band structure. (a) Schematic of the TMD monolayer. The band structure is gapped due to the large staggered potential $\Delta$. Blue and red cones denote spin-up and spin-down bands, respectively. (b) Band structure of the TMD monolayer. Blue solid and red dashed lines denote spin-up and spin-down bands, respectively. Vertical lines indicate the position of the Fermi energy $\varepsilon_F$. We use the following parameters: $t_2/t_1=0.12$, $\Delta/t_1=0.75$, $\phi=0.3\pi$, $J/t_1=1.0\times10^{-3}$, $\Delta_z/t_1=1.0\times10^{-4}$, $J_{ex}/t_1=0.07$, and $S=1$.
• Figure 3: Band structure and Berry curvature of the effective Hamiltonian coupled to TMDs. (a) Band structure and Chern number of the effective Hamiltonian. (b) Berry curvature of the lowest band in log-scale $\Gamma(\Omega)=\text{sign}(\Omega)\log(1+|\Omega|)$. (c) Band structure of the TMD monolayer around the Fermi level. Blue solid and red dashed lines represent spin-up and spin-down bands, respectively. Black and gray arrows depict transitions that make dominant contributions to magnons at the $K^\prime$ and $K$ points, respectively. $\vb{k_m}$ and $\vb{k_d}$ denote the momenta of the magnon and the spin-down electron, respectively, which correspond to $\vb*{k}$ and $\vb*{q}$ in Eq. \ref{['eq:Heff']}. We use the following parameters: $t_2/t_1=0.12$, $\Delta/t_1=0.75$, $\phi=0.3\pi$, $J/t_1=1.0\times10^{-3}$, $\Delta_z/t_1=1.0\times10^{-4}$, $J_{ex}/t_1=0.07$, $S=1$ and $\varepsilon_F/t_1=0.5$
• Figure 4: Topological phase diagram with the Fermi energy dependence. (a) Chern number of the lowest magnon band as a function of the Fermi energy. (b) Integrated Berry curvature of occupied bands of the electron system as a function of the Fermi energy. We use the following parameters: $t_2/t_1=0.12$, $\Delta/t_1=0.75$, $\phi=0.3\pi$, $J/t_1=1.0\times10^{-3}$, $\Delta_z/t_1=1.0\times10^{-4}$, $J_{ex}/t_1=0.07$, and $S=1$.
• Figure 5: The magnon spectral function along the high-symmetry lines in the Brillouin zone. The parameters are the same as those in Fig. 2(b) in the main text: $t_2/t_1=0.12$, $\Delta/t_1=0.75$, $\phi=0.3\pi$, $J/t_1=1.0\times10^{-3}$, $\Delta_z/t_1=1.0\times10^{-4}$, $J_{ex}/t_1=0.07$, $S=1$, and $\varepsilon_F/t_1=0.5$.