  Magnetic defects play an important, but poorly understood, role in magnetic
topological insulators (TIs). For example, topological surface transport and
bulk magnetic properties are controlled by magnetic defects in
Bi$_2$Se$_3$-based dilute ferromagnetic (FM) TIs and MnBi$_2$Te$_4$ (MBT)-based
antiferromagnetic (AFM) TIs. Despite its nascent ferromagnetism, our inelastic
neutron scattering data show that a fraction of the Mn defects in Sb$_2$Te$_3$
form strong AFM dimer singlets within a quintuple block. The AFM superexchange
coupling occurs via Mn-Te-Mn linear bonds and is identical to the AFM coupling
between antisite defects and the FM Mn layer in MBT, establishing common
interactions in the two materials classes. We also find that the FM
correlations in (Sb$_{1-x}$Mn$_x$)$_2$Te$_3$ are likely driven by magnetic
defects in adjacent quintuple blocks across the van der Waals gap. In addition
to providing answers to long-standing questions about the evolution of FM order
in dilute TI, these results also show that the evolution of global magnetic
order from AFM to FM in Sb-substituted MBT is controlled by defect engineering
of the intrablock and interblock coupling.
