The Heusler compound Co$_2$MnSi provides a crystallographic transition from B2 to L2$_1$ structure with increasing annealing temperature $T_a$, being a model system for investigating the influence of crystallographic ordering on structural, magnetic, optic, and magnetooptic (MO) properties. Here, we present quadratic magnetooptic Kerr effect (QMOKE) spectra depending on $M^2$ in addition to the linear magnetooptic Kerr effect (LinMOKE) spectra being proportional to $M$, both in the extended visible spectral range of light from 0.8\,eV to 5.5\,eV. We investigated a set of Co$_2$MnSi thin films deposited on MgO(001) substrates and annealed from 300$^\circ$C to 500$^\circ$C. The amplitude of LinMOKE and QMOKE spectra scales linearly with $T_a$, and this effect is well pronounced at the resonant peaks below 2.0\,eV of the QMOKE spectra. Furthermore, the spectra of the MO parameters, which fully describe the MO response of Co$_2$MnSi up to the second order in $M$, are obtained dependend on $T_a$. Finally, the spectra are compared to ab-initio calculations of a purely L2$_1$ ordered Co$_2$MnSi Heusler compound.

中文翻译：

---

使用 Co2MnSi Heusler 化合物的 L21 排序的二次和线性磁光克尔效应光谱的标度

Heusler 化合物 Co$_2$MnSi 提供了从 B2 到 L2$_1$ 结构的晶体学转变，随着退火温度 $T_a$ 的增加，是研究晶体学排序对结构、磁性、光学和磁光 (MO) 影响的模型系统） 特性。在这里，除了线性磁光克尔效应（LinMOKE）光谱与 $M$ 成正比之外，我们还提出了取决于 $M^2$ 的二次磁光克尔效应（QMOKE）光谱，两者都在从 0.8\ ,eV 到 5.5\,eV。我们研究了一组沉积在 MgO(001) 衬底上并从 300$^\circ$C 退火到 500$^\circ$C 的 Co$_2$MnSi 薄膜。LinMOKE 和 QMOKE 光谱的振幅与 $T_a$ 成线性比例，并且这种效应在 QMOKE 光谱的 2.0\,eV 以下的共振峰非常明显。此外，MO 参数的光谱完全描述了 Co$_2$MnSi 的 MO 响应直到 $M$ 中的二阶，依赖于 $T_a$ 获得。最后，将光谱与纯 L2$_1$ 有序 Co$_2$MnSi Heusler 化合物的 ab-initio 计算进行比较。