Picosecond Ultrasonics in Magnetic Topological Insulator\nMnBi<sub>2</sub>Te<sub>4</sub>

MnBi<sub>2</sub>Te<sub>4</sub> is a magnetic topological insulator\nwith layered A-type antiferromagnetic order. It exhibits a rich layer-\nand magnetic-state dependent topological phase diagram; however, much\nabout the coupling between spin, charge, and lattice remains to be\nexplored. In this work, we report that MnBi<sub>2</sub>Te<sub>4</sub> is an excellent acoustic phonon cavity by realizing phonon frequency\ncombs using picosecond ultrasonics. With the generated acoustic phonon\nwavepackets, we demonstrate that the timing and phase of acoustic\nechoes can be used to detect the presence of stacking faults between\nvan der Waals layers buried deep within the crystal. Furthermore,\nby implementing this nondestructive ultrafast optical measurement\nin conjunction with time-resolved magneto-optical Kerr effect experiments,\nwe uncover that out-of-plane vibrations in MnBi<sub>2</sub>Te<sub>4</sub> do not couple to the magnetic order, i.e. there is no appreciable\nmagnetostriction. Our work points out how a well-developed technique\ncan probe the structural defects and phonon pulse engineering in layered\ntopological insulators.