Recently reported with nontrivial topological properties and magnetic orders, ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ is an intrinsic, magnetic topological insulator which holds promise for exploring exotic quantum phenomena such as the quantum anomalous Hall effect. However, the layer-dependent magnetism of ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$, which is fundamental and crucial for further exploration of related quantum phenomena in this system, remains elusive. Here, by using polar reflective magnetic circular dichroism spectroscopy, we show that few-layered ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ exhibits an evident odd-even layer-number effect, i.e., the oscillations of the coercivity of the hysteresis loop (at ${\mu }_0{H}_c$) and the spin-flop transition (at ${\mu }_0{H}_1$), concerning the Zeeman energy and magnetic anisotropy energy. Noticeably, an anomalous magnetic hysteresis loop is observed in the even-number septuple-layered ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$, which might be attributed to the thickness-independent surface-related magnetization. A linear-chain model is applied to elucidate this odd-even layer-number effect of the spin-flop field and to determine the evolution of the magnetic states when subjected to an external magnetic field. A mean-field method further allows us to fully map the ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ flake’s magnetic phase diagrams in the parameter space of the magnetic field, layer number, and, especially, temperature. By harnessing the unusual layer-dependent magnetic properties, our work paves the way for further study of quantum phenomena of ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$.

中文翻译：

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MnBi2Te4中的奇偶层数效应和层相关的磁相图

最近报道的具有非平凡的拓扑特性和磁阶， ${\mathrm{锰铋}}_2{特}_4$是一种固有的磁性拓扑绝缘体，有望探索奇特的量子现象，例如量子反常霍尔效应。但是，层的磁性${\mathrm{锰铋}}_2{特}_4$对于进一步探索该系统中的相关量子现象而言，这是至关重要的，但仍然遥不可及。在这里，通过使用极性反射磁性圆二色性光谱，我们发现层数很少${\mathrm{锰铋}}_2{特}_4$ 表现出明显的奇偶层数效应，即，磁滞回线的矫顽力的振荡（在 ${\mu }_0{H}_C$）和旋转跳变（位于 ${\mu }_0{H}_{\mathrm{1个}}$），涉及塞曼能量和磁各向异性能量。值得注意的是，在偶数个七层结构中观察到了异常的磁滞回线${\mathrm{锰铋}}_2{特}_4$，这可能归因于与厚度无关的表面相关的磁化强度。应用线性链模型来阐明自旋触发器场的这种奇偶层数效应，并确定在受到外部磁场作用时磁态的演变。均值场方法还使我们能够完全映射${\mathrm{锰铋}}_2{特}_4$磁场，层数尤其是温度的参数空间中的薄片磁相图。通过利用不寻常的与层有关的磁特性，我们的工作为进一步研究量子点的现象铺平了道路。${\mathrm{锰铋}}_2{特}_4$。