Exploring Intrinsic Magnetic Topological Insulators: The Case of EuIn$_2$As$_2$

In this study, ultrafast optical spectroscopy was employed to elucidate the intricate topological features of EuIn$_2$As$_2$, a promising candidate for a magnetic topological-crystalline axion insulator. Our investigation, focusing on the real-time evolution of topological states, unveiled a narrow surface magnetic gap (2$\Delta_0$ $\simeq$ 8.2 meV)) emerging at the antiferromagnetic transition temperature ($T_N$ $\approx$ 16 K). Below $T_N$, two extremely low-energy collective modes, $\omega_1$ and $\omega_2$, with frequencies of $\sim$9.9 and 21.6 GHz at $T$ = 4 K, respectively, were observed, exhibiting strong temperature dependence. $\omega_1$ correlates with an acoustic phonon, while $\omega_2$ is associated with a magnon. The results suggest that EuIn$_2$As$_2$ has the potential to manifest a magnetic topological-crystalline axion insulator, presenting a small magnetic energy gap on the (001) surface. The findings further our understanding of the interplay between magnetism and topology in this material, showcasing its potential for applications in quantum information processing and spintronics.