Coupling of plasmons to the two-magnon continuum in antiferromagnets

TL;DR

The paper shows that plasmons in a two-dimensional electron gas can couple to the spin-zero two-magnon continuum in insulating antiferromagnets through exchange-striction polarization on bonds lacking inversion symmetry, without relying on spin–orbit coupling and at zero temperature. By deriving the magnon–plasmon coupling via Holstein–Primakoff and Bogoliubov transformations, it identifies a plasmon self-energy $\Sigma_{\bm q}(\epsilon)$ dominated by forward processes, which is intimately tied to the spin-zero two-magnon density of states and its Van Hove singularity. In Rutile-type and quasi-2D AFMs, the coupling leads to strong plasmon renormalization and decay when the plasmon energy enters the two-magnon continuum, achieving ultrastrong coupling with typical $|\Sigma_{\bm q}(\epsilon)|/\epsilon$ around 0.4; along certain directions, coupling is weaker due to polarization symmetry. These findings open pathways for robust, low-temperature magnon–plasmon hybrid quantum platforms and motivate exploration of materials with large bond-polarization amplitudes and engineered plasmon energies, including multiferroics or moiré plasmon systems.

Abstract

The coupling of magnons and plasmons offers a promising avenue for hybrid quantum systems, facilitating coherent energy and information transfer between magnetic and charge excitations. However, existing mechanisms often depend on spin-orbit coupling or temperature-activated processes, limiting their robustness for low-temperature quantum technologies. Here, we propose a coupling mechanism between plasmons and the two-magnon continuum in antiferromagnetic insulators, which operates at zero temperature and does not require spin-orbit coupling. Using a model system consisting of a two-dimensional electron gas on an insulating antiferromagnetic substrate, we show that the electric field of the plasmons interacts with the magnetically mediated electric polarization in the antiferromagnet, arising from bonds with broken inversion symmetry. This interaction enables a strong coupling to the spin-conserving two-magnon continuum, allowing for efficient hybridization and reaching the ultrastrong coupling regime.

Figures (7)

• Figure 1: (a) The setup considered, where a two-dimensional electron gas (2DEG) is placed on top of a semi-infinite insulating antiferromagnet. The 2DEG supports gapless plasmons, and their electric field extends into the antiferromagnet, where they couple to the two-magnon continuum. (b) A three-dimensional antiferromagnet inspired by the rutile-type antiferromagnets, such as MnF2, grown along [100]. The magnetic ions (red and blue) are antiferromagnetically ordered, and the anions (yellow) break the inversion symmetry along the nearest-neighbor bonds. This allows for a finite polarization vector $\bm P$, as indicated for one bond. (c) A quasi two-dimensional antiferromagnet. The magnetic ions are antiferromagnetically ordered and form a square lattice, and the non-magnetic ions (yellow) break the center of inversion symmetry located between neighbhoring magnetic ions.
• Figure 2: Feynmann diagrams contributing to the plasmon lifetime up to second order. Dashed and solid lines indicate plasmon and magnon propagators, respectively. (a) Forward, (b) backward, and (c) circle diagram. At zero temperature, only the forward and backward diagrams contribute.
• Figure 3: Coupling between plasmons and the magnon continuum in rutile-type antiferromagnets [Fig. \ref{['fig:setup']}]. (a) Magnon dispersion in the $k_x-k_y$ plane, with the white line indicating $\varepsilon_{\bm{k}}$. The dashed white line indicates the steep plasmon dispersion and the colorscale is the spin-zero two-magnon density of states. Shown on the right is a cut of the spin-zero two-magnon density of states along the plasmon energy, i.e., $D_{\bm q}(\mathcal{E}_{\bm q})$. (b) The plasmon spectral function $A_{\bm q}(\epsilon)$ along two propagation directions of the plasmon: $\bm q \parallel [0\bar{1}0] \parallel \hat{x}$ and $\bm q \parallel [001]\parallel \hat{y}$ (cf. Fig. \ref{['fig:setup']} for a real space geometry). The lower and upper edges of the spin-zero two-magnon continuum are indicated by the horizontal white lines. The bare plasmon dispersion is indicated by the white dotted line. We stress that the plasmon spectral function is shown on a logarithmic scale.
• Figure 4: Coupling between plasmons and the magnon continuum in a quasi two-dimensional antiferromagnet [Fig. \ref{['fig:setup']}]. (a) Magnon dispersion in the $k_x-k_y$ plane, with the white line indicating $\varepsilon_{\bm{k}}$. The dashed white line indicates the steep plasmon dispersion and the colorscale is the spin-zero two-magnon density of states. Shown on the right is a cut of the spin-zero two-magnon density of states along the plasmon energy, i.e., $D_{\bm q}(\mathcal{E}_{\bm q})$. (b) The plasmon spectral function $A_{\bm q}(\epsilon)$ along two propagation directions of the plasmon: $\bm q \parallel \hat{x}$ and $\bm q \parallel \hat{y}$ [see Fig. \ref{['fig:setup']}(a) for real space geometry]. The lower and upper edges of the spin-zero two-magnon continuum are indicated by the horizontal white lines. The bare plasmon dispersion is indicated by the white dotted line. We stress that the plasmon spectral function is shown on a logarithmic scale.
• Figure 5: For the quasi-2D AFM, the polarization operator illustrated between two magnetic sites $i$ and $j$, as mediated by a non-magnetic site $k$.