Compared to a space group, a magnetic space group is much more complex, as both magnetic structure and magnetic moment direction can change the original symmetries of materials. The interplay between space symmetry and magnetism can generate versatile novel quantum states. However, detecting these topological phases experimentally, achieved through manipulating the magnetic configuration, has been restricted. It is mainly because the intrinsic link between the theory and the available experimental technique remains elusive. Here, we show that high harmonic generation (HHG) can identify these topological quantum states. We use rhombohedral ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ film as an example, and analyze the symmetry-dependent harmonic order and signal by combining first-principles calculations and time-dependent Liouville equation numerical computations. Our results provide a fundamental basis for using HHG to study the topological quantum phases mediated by various magnetic configurations that can be easily realized by applying an external magnetic field.

中文翻译：

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通过在MnBi2Te4中产生高谐波来探测磁性构型介导的拓扑相

与空间组相比，磁性空间组要复杂得多，因为磁性结构和磁矩方向都可以改变材料的原始对称性。空间对称性和磁性之间的相互作用可以产生通用的新型量子态。然而，通过操纵磁性结构来实验地检测这些拓扑阶段已经受到限制。主要是因为理论和可用的实验技术之间的内在联系仍然难以捉摸。在这里，我们表明高谐波产生（HHG）可以识别这些拓扑量子态。我们使用菱形${\mathrm{锰铋}}_2{\mathrm{特}}_4$以电影为例，并结合第一性原理计算和时间相关的Liouville方程数值计算，分析了对称性相关的谐波阶次和信号。我们的结果为使用HHG研究由各种磁性构型介导的拓扑量子相提供了基础，这些构型可以通过施加外部磁场轻松实现。