  Using single crystal neutron diffraction, we present a systematic
investigation of the crystal structure and magnetism of van der Waals
topological insulators MnBi$_2$Te$_4$ and MnBi$_4$Te$_7$, where rich
topological quantum states have been recently predicted and observed.
Structural refinements reveal that considerable Bi atoms occupied on the Mn
sites in both materials, distinct from the previously reported antisite
disorder. We show unambiguously that MnBi$_{2}$Te$_{4}$ orders
antiferromagnetically below 24 K featured by a magnetic symmetry $R_I$-${3c}$
while MnBi$_{4}$Te$_{7}$ is antiferromagnetic below 13 K with a magnetic space
group $P_c$-${3c1}$. They both present antiferromagnetically coupled
ferromagnetic layers with spins along the $c$-axis. We put forward a stacking
rule for the crystal structure of an infinitely adaptive series
MnBi$_{2n}$Te$_{3n+1}$ (n$\geq$1) with the building unit of [Bi$_2$Te$_3$]. A
comparison of magnetic properties between MnBi$_{2}$Te$_{4}$ and
MnBi$_{4}$Te$_{7}$, together with the recent density-functional theory
calculations, enables us to draw that a two-dimensional magnetism limit might
be realized in the derivatives. Our work may promote the theoretical studies of
topological magnetic states in the series of MnBi$_{2n}$Te$_{3n+1}$.
