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Recently,natural van der Waals heterostructures of (MnBi2Te4)m(Bi2Te3)n have been theoretically predicted and experimentally shown to host tunable magnetic properties and topologically nontrivial surface states.We systematically investigate both the structural and electronic responses of MnBi2 Te4 and MnBi4 Te7 to exteal pressure.In addition to the suppression of antiferromagnetic order,MnBi2 Te4 is found to undergo a metalsemiconductor-metal transition upon compression.The resistivity of MnBi4 Te7 changes dramatically under high pressure and a non-monotonic evolution of ρ(T) is observed.The nontrivial topology is proved to persist before the structural phase transition observed in the high-pressure regime.We find that the bulk and surface states respond differently to pressure,which is consistent with the non-monotonic change of the resistivity.Interestingly,a pressure-induced amorphous state is observed in MnBi2Te4,while two high-pressure phase transitions are revealed in MnBh Te7.Our combined theoretical and experimental research establishes MnBi2 Te4 and MnBi4 Te7 as highly tunable magnetic topological insulators,in which phase transitions and new ground states emerge upon compression.