Novel magnetic topological insulator FeBi$_2$Te$_4$ with controllable topological quantum phase

Here, we report a new intrinsic magnetic topological insulator FeBi$_2$Te$_4$ based on first-principles calculations and it can achieve a rich topological phase under pressure modulation. Without pressure, we predict that both FeBi$_2$Te$_4$ ferromagnetic and antiferromagnetic orders are non-trivial topological insulators. Furthermore, FeBi$_2$Te$_4$ of FM-z order will undergo a series of phase transitions from topological insulator to semimetals and then to trivial insulator under pressure. Finally, we further clarify and verify topological phase transitions with low-energy effective model calculations. This topological phase transition process is attributed to the synergy of the magnetic moment and the spin-orbit coupling. The unique topological properties of FeBi$_2$Te$_4$ will be of great interest in driving the development of quantum effects.