Polarization-Resolved Extreme-Ultraviolet Second-Harmonic Generation from ${\mathrm{LiNbO}}_3$

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.

Figure 1

Schematic overviews of the two experiments. In both experiments the $p$-polarized fundamental is incident on an $x$-cut ${\mathrm{LiNbO}}_3$ sample at 45° with respect to the crystal surface. The 45° incident angle is the Brewster’s angle for XUV energies. SHG is also detected at 45° with respect to the crystal surface. (a) Schematic illustration of the spectral measurement. The residual fundamental and the emitted second harmonic of the incident FEL are analyzed by dispersing with a grating and imaging with an MCP detector. The inset shows the crystal structure of ${\mathrm{LiNbO}}_3$ in its ferroelectric state where black lines mark the unit cell. (b) Schematic illustration of the second harmonic polarization measurement. The residual fundamental and the emitted second harmonic are reflected off of a multilayer mirror tuned to 66 eV. The polarization of the residual fundamental and the second harmonic are simultaneously measured. Crystal drawing is produced by VESTA [36].

Figure 2

Resonant transitions for ${\mathrm{LiNbO}}_3$ within the range of fundamental energies studied in the spectral experiment. (a) Schematic illustration of the possible transitions with respect to the electronic density of states. Two prominent transitions that involve the Li $1s$ and Nb $4p$ core states are labeled. For the Li $1s$ states (transitions 1 and 2), SHG occurs through a half-resonant scheme and it is facilitated by a virtual state, while the transition originating from Nb $4p$ (transition 3) is facilitated via the conduction band states of majority Nb $4d$ character. (b) Measured and theoretical values of the effective ${\chi }_{\mathrm{eff}}^{(2)}(\omega )$ spectrum for ${\mathrm{LiNbO}}_3$ showing three prominent features corresponding to the labeled transitions from panel (a).

Figure 3

Results of the polarization-resolved experiment on $x$-cut ${\mathrm{LiNbO}}_3$. Measured polarization of the incident FEL (blue squares) at 33 eV and the polarization of the SHG (red circles). $p$ polarization with respect to the optical table is 90° while $s$ polarization is 0°. The fitting error is shown for each point. The amplitude of the intensity is in arbitrary units and the scale is linear. The intensities of fundamental and second harmonic are individually normalized by their respective maximum.