  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.
