Delicate Ferromagnetism in MnBi$_6$Te$_{10}$

Tailoring magnetic orders in topological insulators is critical to the realization of topological quantum phenomena. An outstanding challenge is to find a material where atomic defects lead to tunable magnetic orders while maintaining a nontrivial topology. Here, by combining magnetization measurements, angle-resolved photoemission spectroscopy, and transmission electron microscopy, we reveal disorder-enabled, tunable magnetic ground states in MnBi$_6$Te$_{10}$. In the ferromagnetic phase, an energy gap of 15 meV is resolved at the Dirac point on the MnBi$_2$Te$_4$ termination. In contrast, antiferromagnetic MnBi$_6$Te$_{10}$ exhibits gapless topological surface states on all terminations. Transmission electron microscopy and magnetization measurements reveal substantial Mn vacancies and Mn migration in ferromagnetic MnBi$_6$Te$_{10}$. We provide a conceptual framework where a cooperative interplay of these defects drives a delicate change of overall magnetic ground state energies, and leads to tunable magnetic topological orders. Our work provides a clear pathway for nanoscale defect-engineering towards the realization of topological quantum phases.