Topological hybridisation of plasmons with ferrimagnetic magnons

TL;DR

The paper addresses the realization and topological classification of hybrid plasmon–magnon modes at the interface between a Rashba Janus TMD monolayer and an insulating ferrimagnet. It develops a combined microscopic-macroscopic framework and derives an effective Hamiltonian $\hat{\mathcal{H}}_{\mathbf{q}}^{\mathrm{out}}$ that yields a three-band dispersion $\Omega_{\mathbf{q}}^{\pm}$ with coupling $M^{\alpha}_{\mathbf{q}}$, revealing a nontrivial topology $\mathcal{C}=\{1,-2,1\}$. For out-of-plane order, the hybrid spectrum is fully gapped and isotropic, while in-plane order induces strong anisotropy and Dirac-type crossings; edge states and a finite Berry curvature lead to an anomalous thermal Hall response. The results, supported by realistic parameter estimates, indicate strong, room-temperature–accessible THz plasmon–magnon hybridization in ferrimagnet–Janus-TMD heterostructures, offering a pathway to topological magnon–plasmon devices and novel transport phenomena.

Abstract

We study the formation of hybrid plasmon-magnon modes in a heterostructure comprising a monolayer semiconductor with strong Rashba spin-orbit coupling -- specifically, Janus transition-metal dichalcogenides (TMDs) -- and an insulating ferrimagnet, such as yttrium iron garnet-based compounds. Using a combined microscopic-macroscopic framework for plasmon-magnon coupling, we show that plasmons and magnons strongly hybridize over both GHz and THz frequency ranges, enabling experimental access well above cryogenic temperatures. Moreover, the developed approach provides an efficient and natural classification of the topology of the hybrid modes, rooted in the phase winding of the plasmon-magnon coupling induced by spin-momentum locking and the associated chiral winding of the electronic spin along the Fermi contours. Finally, we identify experimentally accessible manifestations of the hybridization, such as topological interface modes and an anomalous thermal Hall response.

Figures (3)

• Figure 1: Illustration of a Janus TMD interfaced with an insulating ferrimagnet for (a) out-of-plane and (b) in-plane magnetization, together with sketches of the corresponding hybrid plasmon--magnon spectra. Black (red) arrows denote electron current (spin) oscillations, while precessing green arrows indicate magnetization fluctuations. For out-of-plane magnetization, the spectrum is gapped and isotropic, exhibiting nonzero topological Chern numbers. For in-plane magnetization, the spectrum exhibits a pair of Dirac branch-crossing nodes and is strongly anisotropic.
• Figure 2: Dispersion of hybrid plasmon--magnon modes (red or blue), shown together with the corresponding bare plasmon and magnon branches (dashed). (a) For out-of-plane magnetic ordering, the hybrid modes acquire a nontrivial topological character, with each branch carrying a nonzero Chern number (see insets). For in-plane magnetic ordering, the hybridization depends on the relative angle between the propagation direction and the magnetization axis, $\phi_{\mathbf{q}}$, and vanishes for perpendicular orientation, $\phi_{\mathbf{q}}=\pi/2$, leading to Dirac-like branch crossings. In all panels, $\mathrm{L}$ ($\mathrm{R}$) denotes left- (right-) handed magnon modes.
• Figure 3: Feynmann diagrams of the response functions in Eq. (\ref{['ResponseFunc']}). The solid arrowed lines represent the non-interacting retarded electron Greens function $G^{(0)}_{\sigma}(\mathbf{q},\omega)=(\omega - \epsilon_{\mathbf{p}}^{\sigma}+i\delta)^{-1}$, the dashed line represents the complex free magnon propagator $\mathcal{D}^{(0)}(\mathbf{q},\omega)=-2\varepsilon_{\mathbf{q}}/((\omega+i\delta)^{2}+\varepsilon_{\mathbf{q}}^{2})$, and the wiggly line represents the free plasmon field. Counter-clockwise from the top left: $\hat{\sigma}(\omega)$ is the AC conductivity given by the electron current-current correlation function. $\hat{\chi}(\omega)$ is the response function which encodes the current response from the magnetic spin fluctuation, given by the electron current-spin correlation function. $\hat{\kappa}(\omega)$ is the response function which encodes the electron spin-density response to the magnetic spin fluctuation, given by the spin-spin correlation function. $\hat{\Lambda}(\omega)$ is the response function which encodes the spin-density response to the internal self consistent electric field from the electron density fluctuations, given by the spin-current correlation function.