Two-dimensional van der Waals MnBi_2n Te_3n+1 (n = 1, 2, 3, 4) compounds have been recently found to be intrinsic magnetic topological insulators rendering quantum anomalous Hall effect and diverse topological states. Here, we summarize and compare the crystal and magnetic structures of this family, and discuss the effects of chemical composition on their magnetism. We found that a considerable fraction of Bi occupies at the Mn sites in MnBi_2n Te_3n+1 (n = 1, 2, 3, 4) while there is no detectable Mn at the non-magnetic atomic sites within the resolution of neutron diffraction experiments. The occupancy of Mn monotonically decreases with the increase of n. The polarized neutron diffraction on the representative MnBi₄Te₇ reveals that its magnetization density is exclusively accumulated at the Mn site, in good agreement with the results from the unpolarized neutron diffraction. The defects of Bi at the Mn site naturally explain the continuously reduced saturated magnetic moments from n = 1 to n = 4. The experimentally estimated critical exponents of all the compounds generally suggest a three-dimensional character of magnetism. Our work provides material-specified structural parameters that may be useful for band structure calculations to understand the observed topological surface states and for designing quantum magnetic materials through chemical doping.

最近发现二维范德华MnBi _{2 n} Te _{3 n +1}（n = 1、2、3、4）化合物是本征磁性拓扑绝缘体，具有量子异常霍尔效应和多种拓扑状态。在这里，我们总结并比较了该家族的晶体和磁性结构，并讨论了化学成分对其磁性的影响。我们发现Bi的相当一部分占据了MnBi _{2 n} Te _{3 n +1}（n= 1、2、3、4），而在中子衍射实验的分辨率范围内，在非磁性原子位点没有可检测到的Mn。Mn的占有率随n的增加而单调减少。在代表性的MnBi ₄ Te ₇上的极化中子衍射表明，其磁化密度完全聚集在Mn处，这与非极化中子衍射的结果十分吻合。Mn处Bi的缺陷自然可以解释饱和磁矩从n = 1到n的连续减小＝ 4。所有化合物的实验估计的临界指数通常表明磁性的三维特征。我们的工作提供了特定于材料的结构参数，这些参数对于能带结构计算以了解观察到的拓扑表面状态以及通过化学掺杂设计量子磁性材料可能有用。