Magnon-plasmon coupling mediated by linear magnetoelectric effect in two-dimensional crystals with Dzyaloshinskii-Moriya interaction

TL;DR

The paper addresses magnon-plasmon coupling in two-dimensional crystals that exhibit a linear magnetoelectric effect and Dzyaloshinskii-Moriya interaction, focusing on a VSe$_2$ monolayer on NbSe$_2$. It develops a three-term Hamiltonian $\mathcal{H}_{\rm m}+\mathcal{H}_{\rm pl}+\mathcal{H}_{\rm m-pl}$ and derives the coupling parameter $C_{\bf k}$, which scales with the magnetoelectric constant $\alpha_{me}$, then diagonalizes the system using a Bogoliubov transformation to obtain hybrid magnon-plasmon modes. The study shows that the magnon spectrum can be tuned by a vertical gate field $E_z$ that modifies the DMI and anisotropy, and the plasmon energy can be adjusted via the effective electron mass, enabling resonant hybridization at various $\mathbf{k}$; DMI-based coupling is discussed but remains experimentally constrained. Numerically, the coupling can reach a few meV at the Brillouin zone boundary, producing observable anticrossings, and the results highlightgate-tunability and mass-tunability as practical levers to control magnon-plasmon hybridization in 2D heterostructures. The findings pave a path to integrate plasmonics and magnonics in 2D materials, with potential for gate-controlled hybrid excitations and spectroscopic extraction of $\alpha_{me}$ and related parameters.

Abstract

Recently, one can observe a renewed interest in coupling of spin waves (magnons) and collective charge oscillations (plasmons), especially in two-dimensional systems. Several mechanisms of the magnon-plasmon hybridization in ferromagnetic and antiferromagnetic systems have been proposed. Here, we consider another mechanism of magnon-plasmon hybridization, which is based on the linear magnetoelectric interaction. As a specific system we consider a monolayer of vanadium-based diselenide with perpendicular easy-axis magnetic anisotropy and Dzialoshinskii-Moriya interaction. The derived parameter of magnon-plasmon coupling is proportional to the magnetoelectric constant. Assuming for this constant an adequate experimental value, we calculate dispersion relations of the hybridized magnon-plasmon mods. Moreover, we also show that an external electric field normal to the layer (due to a gate voltage) can be used as a tool to tune the magnon modes and this way also hybridized magnon-plasmon coupling. A specific case of magnon-plasmon coupling based on tuning Dzialoshinskii-Moriya interaction is also considered.

Figures (7)

• Figure 1: Atomic structure of the VSe$_2$ monolayer deposited on a NbSe$_2$ monolayer. Top view (a) and side view (b).
• Figure 2: Energy of spin waves in the monolayer of VSe$_2$ with perpendicular ground-state spin configuration. (a,b) Energy maps of spin waves in the whole Brillouin zone in the presence of DMI (a), and in the absence of DMI ($d_\perp = d^\prime_\perp =0$) (b). (c) Dispersion curves of spin waves in the presence of DMI (red curves) and in the absence of DMI (black curves). The inset shows the low-energy part of the spectrum. In (a-c) the results are for the absence of external gating. (d) The low-energy part of the spin wave spectrum for the gate fields, $E_z^\perp$, as indicated, while $E_z^D=0$. For all figures, the other parameters are as described in the main text.
• Figure 3: Variation of the magnon-plasmon coupling parameter with $k_xa$ in the range from the Brillouin zone center (point $\Gamma$) to the Brillouin zone boundary (point K$_1$) along the $k_x$ direction. In the part (a) different curves correspond to the indicated values of parameter $\alpha_{me}$ and for the effective electron mass $m = m_0$. In turn, different curves in (b) correspond to indicated values of the effective mass $m$ and constant value of $\alpha_{me} =4/3$. All other parameters assumed in (a) and (b) are described in the text.
• Figure 4: Dispersion relations of the uncoupled magnon and plasmon modes for the indicated values of the magnetic anisotropy constant $D_z$ and effective electron mass $m$. All other parameters are as in the main text. Behavior of the uncoupled modes is shown in the whole Brillouin zone (a) and in the area near the Brillouin zone center (b). In the latter case the magnon curve for $D_z=1$ meV is also added to emphasize the role of magnetic anisotropy in tuning positions of the crossing points.
• Figure 5: Dispersion relations of the coupled magnon-plasmon states (black and red solid lines), and of the uncoupled magnon and plasmon modes (dashed green and blue lines). The upper panel (a-c) corresponds to the high energy crossings, while the lower panel (d-f) to the the crossings at low energy. The mode repulsion is clearly visible, especially for the crossing points at high energy. The parameters assumed in calculations are $\alpha_{me}=1$, $m=m_0$, while the other parameters are as described as in the main text.