Bi-isotropic effects on hybrid surface polaritons in bilayer configurations

TL;DR

This work addresses the tuning of bi-isotropic effects on hybrid Dirac plasmon–phonon–magnon polaritons in TI/AFM bilayers. A semiclassical Maxwell framework with constitutive relations $D=ε_0 ε E+ μ_0 α H$ and $B= μ_0 μ H+ μ_0 α E$ is combined with transfer-matrix methods to derive general dispersion relations that include the bi-isotropic parameter $α$ and quantify TI–magnon hybridization. Application to Bi2Se3/Cr2O3 and Bi2Se3/FeF2 shows that increasing $α$ redshifts the upper branch and suppresses anticrossings, while increasing the Fermi energy $E_F$ blueshifts modes and enhances coupling, with partial compensation between these effects. The results establish independent and complementary control of light–magnon coupling via $α$ and $E_F$, informing reconfigurable THz spintronic and photonic devices and motivating future work on tensor magnetoelectric responses $α_{ij}$.

Abstract

In this work, we investigate the bi-isotropic effects in the formation and tunability of hybrid surface polaritons in bilayer configurations. We consider a heterostructure composed of a medium with bi-isotropic constitutive relations and an AFM layer. Using the transfer matrix formalism, we derive general expressions for the dispersion relations of surface polaritonic modes, including the dependence on the bi-isotropic parameter, and analyze their coupling to bulk magnon-polaritons. As an illustration of application, we consider a heterostructure formed with Bi$_{2}$Se$_{3}$ interfaced with antiferromagnetic (AFM) materials that support terahertz-frequency magnons, specifically Cr$_{2}$O$_{3}$ and FeF$_{2}$. In the strong bi-isotropic coupling regime, the surface Dirac plasmon--phonon--magnon polariton (DPPMP) dispersion undergoes a pronounced redshift, accompanied by suppression of the characteristic anticrossing between the Dirac plasmon and the phonon. This effect, observed in all AFM materials considered, suggests a weakening of the hybrid interaction, possibly due to saturation or detuning mechanisms induced by increased $α$. Furthermore, increasing the Fermi energy of the topological insulator enhances the surface plasmon and phonon contributions, inducing a blueshift of the DPPP branches and bringing them closer to resonance with the magnon mode, thereby increasing the hybridization strength. Intriguingly, this redshift partially compensates the blueshift induced by a higher Fermi level, restoring the system to a weak-coupling regime analogous to that observed at lower Fermi energies. Our findings reveal that both the Fermi level and the bi-isotropic response offer independent and complementary control parameters for tuning the strength of light--magnon coupling in TI/AFM heterostructures, with potential implications for reconfigurable THz spintronic and photonic devices.

Figures (10)

• Figure 1: Schematic of a multilayer structure consisting of $N$ constituent layers that have the same width $w$ along the $x$-direction. The $z$-axis is chosen as the growth direction of the structure. The thickness, premittivity, permeability, bi-isotropic parameter in the $m$th layer, and optical conductivity of the carrier sheet at the $m$th surface/interface are denoted by $d_{m}$, $\epsilon_{m}$, $\mu_{m}$, $\alpha_{m}$ and $\sigma_{m}$, respectively, whereas $I_{m}$ indicates the interface matrix at the $m$th interface.
• Figure 2: Schematic of a multilayer structure consisting of $N$ layers. Electric and magnetic field components. The $z$-axis is chosen as the growth direction of the structure. The propagation of the electromagnetic wave is confined in $x$-$z$ plane.
• Figure 3: Schematic of the amplitudes of incoming and outgoing EM waves used in the scattering matrix approach. The EM wave is incident on the left of the surface in the figure.
• Figure 4: (a) The structure consisting of a topological insulator (TI) and an antiferromagnet (AFM) with an arbitrary magnetization direction. An electromagnetic (EM) wave, generally containing both TE and TM polarizations, impinges on the surface of the TI material to induce electric excitations in the TI film, which can couple to magnetic modes in the AFM layer. (b) A finite TI film of thickness $d_{\mathrm{TI}}$ is placed on a semi-infinite AFM substrate. Here, $A_{i,j}$ and $B_{i,j}$, with $i = x, y$ and $j = 0, 2$, denote the amplitudes of the forward- and backward-propagating electromagnetic waves in air ($j = 0$) and in the AFM medium ($j = 2$).
• Figure 5: Frequency-dependent dielectric function of Bi$_{2}$Se$_{3}$ given in Eq. (\ref{['eq-application-17']}). The solid (dashed) line indicates the real (imaginary) parts of $\epsilon(\omega)$. Here, we have used the values of Tab. \ref{['table1']}.