  Combinations of non-trivial band topology and long-range magnetic order hold
promise for realizations of novel spintronic phenomena, such as the quantum
anomalous Hall effect and the topological magnetoelectric effect. Following
theoretical advances material candidates are emerging. Yet, a compound with a
band-inverted electronic structure and an intrinsic net magnetization remains
unrealized. MnBi$_2$Te$_4$ is a candidate for the first antiferromagnetic
topological insulator and the progenitor of a modular
(Bi$_2$Te$_3$)$_n$(MnBi$_2$Te$_4$) series. For $n$ = 1, we confirm a
non-stoichiometric composition proximate to MnBi$_4$Te$_7$ and establish an
antiferromagnetic state below 13 K followed by a state with net magnetization
and ferromagnetic-like hysteresis below 5 K. Angle-resolved photoemission
experiments and density-functional calculations reveal a topological surface
state on the MnBi$_4$Te$_7$(0001) surface, analogous to the non-magnetic parent
compound Bi$_2$Te$_3$. Our results render MnBi$_4$Te$_7$ as a band-inverted
material with an intrinsic net magnetization and a complex magnetic phase
diagram providing a versatile platform for the realization of different
topological phases.
