Van der Waals antiferromagnetic and topological insulator materials provide powerful platforms for modern optical, electronic, and spintronic devices applications. The interaction between an antiferromagnet (AFM) and a topological insulator (TI), if sufficiently strong, could offer emergent hybrid material properties that enable new functionality exceeding what is possible in any individual material constituent. In this work, we study strong coupling between THz excitations in a three dimensional (3D) topological insulator and a quasi-two dimensional (2D) antiferromagnetic material resulting in a new hybridized mode, namely a surface Dirac plasmon-phonon-magnon polariton. We find that the interaction between a surface Dirac plasmon polariton in the 3D TI and a magnon polariton in the 2D AFM is mediated by the phonon coupling in the 3D TI material. The coupling of phonons with an electromagnetic wave propagating in the 3D TI enhances the permittivity of the TI thin film in a way that results in a strong correlation between the dispersion of Dirac plasmon polaritons on the surfaces of the TI with the thickness of the TI. As a result, the dispersion of surface Dirac plasmon polaritons in the TI can be tuned toward resonance with the magnon polariton in the AFM material by varying the TI's thickness, thereby enhancing the strength of the coupling between the excitations in the two materials. The strength of this coupling, which results in the surface Dirac plasmon-phonon-magnon polariton, can be parameterized by the amplitude of the avoided-crossing splitting between the two polariton branches at the magnon resonance frequency...
