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We report an infrared spectroscopy study of the axion topological insulator candidate EuIn$_2$As$_2$ for which the Eu moments exhibit an A-type antiferromagnetic (AFM) order below $T_N simeq 18 mathrm{K}$. The low energy response is composed of a weak Drude peak at the origin, a pronounced infrared-active phonon mode at 185 cm$^{-1}$ and a free carrier plasma edge around 600 cm$^{-1}$. The interband transitions start above 800 cm$^{-1}$ and give rise to a series of weak absorption bands at 5,000 and 12,000 cm$^{-1}$ and strong ones at 20,000, 27,500 and 32,000 cm$^{-1}$. The AFM transition gives rise to pronounced anomalies of the charge response in terms of a cusp-like maximum of the free carrier scattering rate around $T_N$ and large magnetic splittings of the interband transitions at 5,000 and 12,000 cm$^{-1}$. The phonon mode at 185 cm$^{-1}$ has also an anomalous temperature dependence around $T_N$ which suggests that it couples to the fluctuations of the Eu spins. The combined data provide evidence for a strong interaction amongst the charge, spin and lattice degrees of freedom.
Topological insulator with antiferromagnetic order can serve as an ideal platform for the realization of axion electrodynamics. In this paper, we report a systematic study of the axion topological insulator candidate EuIn$_2$As$_2$. A linear energy d
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