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The MnBi$_{2}$Te$_{4}$ family has attracted significant attention due to itsrich topological states such as the quantum anomalous Hall (QAH) insulatorstate, the axion insulator state, and the magnetic Weyl semimetal state.Nevertheless, the intrinsic antiferromagnetic (AFM) interlayer coupling inMnBi$_{2}$Te$_{4}$ partly hinders the realization of "high-temperature" QAHeffect. Here, by using first-principles electronic structure calculations, wedesign a new class of materials Mn\emph{X}$_{2}$\emph{B}$_{2}$\emph{T}$_{6}$(\emph{X}=Ge, Sn, or Pb; \emph{B}=Sb or Bi; \emph{T}=Se or Te) based on the\emph{X}$_{2}$\emph{B}$_{2}$\emph{T}$_{5}$ structures rather than theBi$_{2}$Te$_{3}$ family. We find that each septuple-layerMn\emph{B}$_{2}$\emph{T}$_{4}$ is sandwiched by two [\emph{X}\emph{T}] layers,which may turn the AFM interlayer coupling into a ferromagnetic (FM) coupling.The calculations specifically demonstrate that\emph{MnGe}$_{2}$\emph{Sb}$_{2}$\emph{Te}$_{6}$,\emph{MnGe}$_{2}$\emph{Bi}$_{2}$\emph{Te}$_{6}$, and\emph{MnPb}$_{2}$\emph{Bi}$_{2}$\emph{Te}$_{6}$ are FM axion insulators, whileMnGe$_{2}$Sb$_{2}$Se$_{6}$, MnGe$_{2}$Bi$_{2}$Se$_{6}$,MnSn$_{2}$Sb$_{2}$Te$_{6}$, and MnSn$_{2}$Bi$_{2}$Te$_{6}$ are A-type AFM axioninsulators. These seven materials all have an out-of-plane easy axis ofmagnetization. The Mn\emph{X}$_{2}$\emph{B}$_{2}$\emph{T}$_{6}$ family thusoffers a promising platform beyond the MnBi$_{2}$Te$_{4}$ family for therealization of quantized magnetoelectric effect and "high-temperature" QAHeffect in future experiments.

Intrinsic ferromagnetic and antiferromagnetic axion insulators in van der Waals materials Mn\emph{X}$_{2}$\emph{B}$_{2}$\emph{T}$_{6}$ family