In this work, we investigate the bi-isotropic effects in the formation and tunability of hybrid surface polaritons in bilayer configurations. To do that, we consider a heterostructure constituted with layers formed by a TI medium endowed with bi-isotropic constitutive relations and an AFM medium. Using transfer matrix formalism, we derive general dispersion relations for surface polaritonic modes including the bi-isotropic coupling parameter, and analyze their coupling to bulk magnon-polaritons in the AFM layer. As an illustration, we consider a heterostructure formed with ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ interfaced with antiferromagnetic (AFM) materials that support terahertz-frequency magnons. In the non-null bi-isotropic coupling regime, the surface Dirac plasmon-phonon-magnon polariton (DPPMP) dispersion undergoes a pronounced redshift, accompanied by the suppression of the characteristic anticrossing between the Dirac plasmon and the phonon. This effect, observed for all AFM materials considered, suggests a weakening of the hybrid interaction, possibly due to saturation or detuning mechanisms induced by the increased $\alpha$ parameter. The latter yields a redshift that 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.

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• Dielectric properties
• Light propagation, transmission & absorption
• Permittivity
• Surface plasmon polariton
• Electromagnetic wave theory