Second harmonic generation (SHG) spectroscopy ubiquitously enables the investigation of surface chemistry, interfacial chemistry, as well as symmetry properties in solids. Polarization-resolved SHG spectroscopy in the visible to infrared regime is regularly used to investigate electronic and magnetic order through their angular anisotropies within the crystal structure. However, the increasing complexity of novel materials and emerging phenomena hampers the interpretation of experiments solely based on the investigation of hybridized valence states. Here, polarization-resolved SHG in the extreme ultraviolet (XUV-SHG) is demonstrated for the first time, enabling element-resolved angular anisotropy investigations. In noncentrosymmetric ${\mathrm{LiNbO}}_3$, elemental contributions by lithium and niobium are clearly distinguished by energy dependent XUV-SHG measurements. This element-resolved and symmetry-sensitive experiment suggests that the displacement of Li ions in ${\mathrm{LiNbO}}_3$, which is known to lead to ferroelectricity, is accompanied by distortions to the Nb ion environment that breaks the inversion symmetry of the ${\mathrm{NbO}}_6$ octahedron as well. Our simulations show that the measured second harmonic spectrum is consistent with Li ion displacements from the centrosymmetric position while the $\mathrm{Nb}─\mathrm{O}$ bonds are elongated and contracted by displacements of the O atoms. In addition, the polarization-resolved measurement of XUV-SHG shows excellent agreement with numerical predictions based on dipole-induced SHG commonly used in the optical wavelengths. Our result constitutes the first verification of the dipole-based SHG model in the XUV regime. The findings of this work pave the way for future angle and time-resolved XUV-SHG studies with elemental specificity in condensed matter systems.

中文翻译：

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来自 LiNbO3 的偏振分辨极紫外二次谐波产生

二次谐波发生 (SHG) 光谱无处不在，可以研究表面化学、界面化学以及固体的对称性。可见光至红外范围内的偏振分辨 SHG 光谱通常用于通过晶体结构内的角各向异性来研究电子和磁序。然而，新材料和新兴现象的日益复杂阻碍了仅基于杂化价态研究的实验解释。在这里，首次展示了极紫外 (XUV-SHG) 中的偏振分辨 SHG，从而能够进行元素分辨的角度各向异性研究。在非中心对称${\mathrm{铌酸锂}}_3$，通过能量相关的 XUV-SHG 测量可以清楚地区分锂和铌的元素贡献。这个元素分辨和对称敏感的实验表明锂离子在${\mathrm{铌酸锂}}_3$已知会导致铁电性，伴随着 Nb 离子环境的扭曲，破坏了铁电的反转对称性 ${\mathrm{氧化铌}}_6$八面体也是如此。我们的模拟表明，测量的二次谐波谱与中心对称位置的锂离子位移一致，而$铌─\mathrm{哦}$键通过 O 原子的位移被拉长和收缩。此外，XUV-SHG 的偏振分辨测量与基于通常用于光波长的偶极子诱导 SHG 的数值预测非常吻合。我们的结果构成了 XUV 体系中基于偶极子的 SHG 模型的首次验证。这项工作的发现为未来在凝聚态系统中具有元素特异性的角度和时间分辨 XUV-SHG 研究铺平了道路。