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Results for “nonlinear x-ray optics”

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DOE OSTI2025

Linear and Nonlinear X-ray Spectra of Chiral Molecules: X-ray Circular Dichroism, Sum- and Difference-Frequency Generation of Fenchone and Cysteine

Recent advancements in X-ray light sources enable element-sensitive nonlinear spectroscopies for probing molecular chirality. We simulate X-ray absorption spectroscopy, X-ray circular dichroism (XCD), and nonlinear optical/X-ray SFG and DFG (OX SFG/DFG) signals for two prototypical chiral molecules, fenchone and cysteine. Furthermore, our multireference simulations reproduce experimental data and reveal how novel X-ray spectroscopies exploit the site- and element-sensitivity of X-rays to uncover molecular asymmetry. The XCD spectra show strong asymmetries at chiral centers, while distant atoms contribute weaker signals. The OX SFG/DFG signals, under fixed resonant optical excitation, strongly depend on the core and valence excitations. This allows us to introduce two-dimensional (2D) chirality-sensitive valence-core spectroscopy, which provides insight into the overlap between valence orbitals and local molecular asymmetry. Finally, our estimates using realistic laser and X-ray pulse parameters demonstrate that such nonlinear experiments are feasible at XFELs, offering a promising tool for investigating chiral molecules.

Circular dichroism spectroscopy↗

DOE OSTI2026

Nonlinear reversal of photoexcitation on the attosecond time scale improves ultrafast X-ray diffraction images

The complex refractive index of a material governs its light-matter interactions, with intense light fields enabling tailored nonlinear optical responses. In the X-ray regime, rapid photoionization limits the potential of nonlinear techniques by inducing irreversible electronic damage. Here we demonstrate that intense, sub-femtosecond X-ray pulses, shorter than typical Auger decay times, can partially reverse photoexcitation via stimulated emission near atomic resonances. By analyzing thousands of coherent diffraction patterns and ion spectra from neon nanoparticles exposed to sub-fs and 15-fs pulses, we observe enhanced X-ray diffraction alongside reduced energy absorption for sub-fs pulses. Theoretical modeling attributes this to dynamics akin to Rabi flopping that prolong the lifetime of resonant states and suppress electronic bleaching. These findings suggest that ultrashort, intense X-ray pulses enable active control of X-ray refractive index and damage pathways, opening avenues for improved high-resolution imaging and nonlinear spectroscopy in complex nanoscale systems.

Ulmer, Anatoli [Universität Hamburg (Germany)] (OR↗

DOE OSTI2026

Nanoscale ultrafast lattice modulation with a free-electron laser

Ultrafast optical laser-based techniques have enabled the probing of atomistic processes at their intrinsic temporal scales with femto- and attosecond resolution. However, the long wavelengths of optical lasers have prevented their interrogation and manipulation with nanoscale spatial specificity. Advances in hard X-ray free-electron lasers have enabled progress in developing X-ray transient-grating spectroscopy, a technique that aims to coherently control elementary excitations with nanoscale X-ray standing waves. Thus far, the realization of this technique at the nanoscale has been a challenge. Here we demonstrate X-ray transient-grating spectroscopy with spatial periods of the order of 10 nm via the subfemtosecond synchronization of two hard X-ray pump pulses at a precisely controlled crossing angle. This creates a thermal grating and preferentially excites coherent longitudinal acoustic phonon modes with the transient-grating wavevector. On probing with a third, variably delayed, X-ray pulse with the same photon energy, time-and-wavevector-resolved measurements of the modulation of the induced scattering intensity provide evidence of ballistic thermal transport at nanometre scales. Finally, these results highlight the potential of X-ray transient gratings as a powerful platform for studying nanoscale transport in condensed matter and the coherent control of nanoscale dynamics.

nonlinear optics↗

DOE OSTI2025

Attosecond inner-shell lasing at ångström wavelengths

Since the invention of the laser, nonlinear effects such as filamentation, Rabi cycling and collective emission have been explored in the optical regime, leading to a wide range of scientific and industrial applications. X-ray free-electron lasers (XFELs) have extended many optical techniques to X-rays for their advantages of ångström-scale spatial resolution and elemental specificity. An example is XFEL-driven inner-shell Kα 1 (2p 3/2 → 1s 1/2 ) X-ray lasing in elements ranging from neon to copper, which has been used for nonlinear spectroscopy and development of new X-ray laser sources. Here, in this study, we show that strong lasing effects similar to those in the optical regime can occur at 1.5–2.1 Å wavelengths during high-intensity (>10 19 W cm −2 ) XFEL-driven Kα 1 lasing of copper and manganese. Depending on the temporal XFEL pump pulse substructure, the resulting X-ray pulses (about 10 6 −10 8 photons) can exhibit strong spatial inhomogeneities and spectral splitting, inhomogeneities and broadening. Three-dimensional Maxwell–Bloch calculations show that the observed spatial inhomogeneities result from X-ray filamentation and that the broad spectral features are driven by sub-femtosecond Rabi cycling. Our simulations indicate that these X-ray pulses can have pulse lengths of less than 100 attoseconds and coherence properties that provide opportunities for quantum X-ray optics applications.

47 OTHER INSTRUMENTATION↗

DOE OSTI2025

Soft x-ray high-harmonic generation in an anti-resonant hollow core fiber driven by a 3 μ m ultrafast laser

High-harmonic upconversion driven by a mid-infrared femtosecond laser can generate coherent soft x-ray beams in a tabletop-scale setup. Here, we report on a compact ytterbium-pumped optical parametric chirped pulse amplifier (OPCPA) laser system seeded by an all-fiber front-end and employing periodically poled lithium niobate (PPLN) nonlinear media operated near the pulse fluence limits of current commercially available PPLN crystals. The OPCPA delivers 3 µm wavelength pulses with 775 µJ energy at 1 kHz repetition rate, with transform-limited 120 fs pulse duration, diffraction-limited beam quality, and ultrahigh 0.33% rms energy stability over >18 h. Using this laser, we generate soft x-ray high harmonics (HHG) in argon gas by focusing into a low-loss, high-pressure gas-filled anti-resonant hollow core fiber (ARHCF), generating coherent light at photon energies up to the argon L-edge (250 eV) and carbon K-edge (284 eV), with high beam quality and ∼1% rms energy stability. This work demonstrates soft x-ray HHG in a high-efficiency guided-wave phase matched geometry, overcoming the high losses inherent to mid-IR propagation in unstructured waveguides, or the short interaction lengths of gas cells or jets. The ARHCF can operate in the long term without damage and with the repetition rate, stability, and robustness required for demanding applications in spectromicroscopy and imaging. Finally, we discuss routes for further optimizing the soft x-ray HHG flux by driving He at higher laser intensities using either the signal (1.5 μm) or idler wavelengths (3 μm).

Femtosecond lasers↗

DOE OSTI2025

Tunable Semiconducting Behavior and Linear-Nonlinear Optical Properties of Ag–Sn Dual-Doped Nanocrystalline CdO Thin Films for Optoelectronics

Semiconductor-based thin films have a great impact on determining the anticipated optoelectronic device construction and the advancement of cutting-edge applications. Herein, Ag and Sn dual-doped nanocrystalline transparent conducting CdO thin films were prepared on glass substrates using a cost-effective spray coating method, and their structural, morphological, optical, and semiconducting behaviors were investigated. The successful incorporation of Ag and Sn resulted in the polycrystalline nature of the deposited films without the additional peaks, as verified by X-ray diffraction (XRD) analysis. The XRD report also revealed the enhanced crystallinity (65%) at the higher doping level (3 wt % Ag and Sn-doped CdO film). All the deposited CdO films exhibited homogeneous, spherical, or round-shaped grains, with agglomeration revealed by scanning electron microscopy analysis. UV–visible spectroscopy was utilized to determine the linear and nonlinear optical properties of the deposited CdO thin films, and a reduction in the band gap from 3.891 to 3.772 eV was observed. A significant enhancement in the first- and third-order nonlinear susceptibility and nonlinear refractive index of the doped CdO films was also observed with increasing doping concentration. Hall effect data were collected at room temperature to investigate the electrical properties of all of the CdO films. The charge carrier concentration of CdO thin films was increased from 142.08 × 10 18 to 169.10 × 10 18 cm –3 , and the highest conductivity was found to be 192 s/cm on doping 3 wt % Ag–Sn. All the CdO thin films exhibited n-type conductivity, while an incredible n-type to p-type charge carrier transition was noticed at a higher doping level (3 wt % Ag–Sn). The findings of the current work are expected to advance the synthesis of semiconductor thin films through cost-effective spray coating methods for optoelectronic device applications.

deposition↗

DOE OSTI2025

Laser-Modulation-Driven X-Ray Pulse Shaping in Regenerative Amplifier Free-Electron Lasers

In this Letter, we present a robust method for generating custom-shaped, coherent hard x-ray pulses in regenerative amplifier free-electron lasers (RAFELs) using laser-induced energy modulation of the electron beam. A temporally shaped optical modulation imprints an optical-wavelength energy pattern on the beam, which interacts with the recirculated seed in the x-ray cavity to generate spectral sidebands. These sidebands lie outside the Bragg reflection bandwidth and are extracted as out-coupled radiation, while the seed is retained for continued amplification, enabling a novel mechanism for both output coupling and pulse shaping. Furthermore, this approach allows deterministic control over the spectral and temporal properties of the emitted x-rays, including multicolor generation, twin-pulse structures, pulse duration tuning, and complex temporal waveforms. Importantly, it does not require modification of the RAFEL cavity or optics and is fully compatible with high-repetition-rate operation, offering a practical pathway to deliver coherent, shaped, and on-demand x-ray pulses for advanced time-resolved and nonlinear x-ray science.

Free-electron lasers↗

DOE OSTI2025

Vibrational sum frequency generation spectroscopy reveals the inertness of chromium oxide (001) surfaces

Nanoengineered metal oxides such as Cr(III)-oxide (chromia) films have diverse potential applications in corrosion inhibition, remediation, energy generation, catalysis, data storage, and biological and environmental systems. Concerns about material degradation or oxidation to toxic chromate necessitate an understanding of chromia/aqueous interfaces, beginning with their hydroxylation and hydration behavior. Vibrational sum-frequency generation spectroscopy (vSFG) provides specific molecular-level information about water at the oxide/aqueous junction with high surface selectivity. To overcome the strong absorber problem typical of certain metal oxides in the UV–visible range during nonlinear optical studies, we employed molecular beam epitaxy to deposit transparent, epitaxial nanofilms of Cr 2 O 3 with (001) crystalline orientation on sapphire (Al 2 O 3 (001)) substrates, as confirmed by atomic force microscopy and X-ray diffraction. vSFG spectra of the air and water interfaces of the Cr 2 O 3 (001) films reveal hydroxyl features corresponding to both dissociated and molecular water on the surface. In contrast to the dangling hydroxyls found on the bare Al 2 O 3 (001) substrate, the hydroxyl groups on the deposited Cr 2 O 3 (001) nanofilm do not readily undergo isotopic H/D exchange when exposed to varying forms of D 2 O under ambient conditions. When considering the chemistries of the corresponding trivalent cations in aqueous solution, the finding is at variance with their similar acidities and proton exchange dynamics but consistent with markedly slower inner-sphere water ligand exchange of hexaquo Cr 3+ . This finding challenges the idea that proton and water exchange at the water/Cr₂O₃(001) interface are solely correlated, driven by the strength of metal-bridging oxygen bonds and surface hydroxyl distribution, without direct causation.

Boamah-Agyemang, Mavis D. [Pacific Northwest Natio↗

DOE OSTI2025

High gas-pressure apparatus for nonlinear X-ray propagation and reshaping via stimulated X-ray Raman scattering

Abstract We describe an experimental setup for non-linear interaction and propagation of ultrashort and intense x-ray free-electron laser (XFEL) pulses in a dense gas. It allows one to provide high, but adjustable, target-gas pressures of up to 6 bar within a vacuum environment of 3∙10 − 3 mbar or better. The setup enables investigation of intense x-ray propagation in an optically thick medium with minimal absorption loss of the unfocused beam outside of the target. As an application, we demonstrate the amplification of spectrally-resolved stimulated x-ray Raman scattering (SXRS) in dense neon gas, where the most intense inner part of the beam is almost completely absorbed. As a result, in the inner part of the beam, the SXRS signal exceeds the residual XFEL pulse by a factor of around two. In principle, this reshaping effect allows for a spatial separation of the two spectral components, i.e., the driving pulse and the SXRS signal.

Magunia, Alexander↗

DOE OSTI2026

Cs X Si 15 P 21 ( X = Sn or Pb): Polar Noncentrosymmetric Si–P Frameworks Stabilized by Covalent X –P Bonding

Metal silicon phosphides composed of earth-abundant Si and P tend to exhibit semiconducting properties and adopt diverse crystal structures with relatively small additions of structure-directing elements. The potential of silicon phosphide materials in nonlinear optical applications has been hindered by the inability to systematically produce noncentrosymmetric structures with such a flexible framework. Here, in this work, two isostructural compounds with a novel noncentrosymmetric structure were made possible by the inclusion of elements with stereochemically active lone pairs (Sn 2+ and Pb 2+ ). The structures were determined through single-crystal and synchrotron powder X-ray diffraction. Analysis of chemical bonding in real space through the electron localization function revealed stereochemically active Pb 2+ and Sn 2+ species in a trigonal pyramidal coordination with {Pb/Sn}–P bonds. Such covalent bonding between Pb and P is quite uncommon in extended solids and has been reported in a few rare instances. Band structure calculations and linear optical measurements confirm the semiconducting nature of Cs X Si 15 P 21 ( X = Sn or Pb). The synthesis was optimized to yield high-purity polycrystalline samples. The nonlinear optical properties show promising second-harmonic generation (SHG) coefficients from the Kurtz–Perry method. First-principles calculations of the nonlinear optical properties support the experimentally determined SHG values and provide moderate values of birefringence, suggesting Cs X Si 15 P 21 could be phase-matchable and practical nonlinear optical materials in the mid-IR region.

crystal structure↗

DOE OSTI2025

Impact of dynamic Jahn-Teller effect on magnetic excitations, lattice vibration, and thermal conductivity in U 𝑥 ⁢T⁢h 1−𝑥 ⁡O 2 system

Vibrational and magnetic properties of single-crystal uranium-thorium dioxide (U 𝑥 ⁢T⁢h 1−𝑥⁡ O 2 ) with a full range of 0 < 𝑥 < 1 are investigated. Thorium dioxide is a diamagnet whose thermal properties are governed by lattice vibration. The addition of paramagnetic uranium ions leads to the emergence of magnetic effects that alter the thermophysical properties noticeably even at room temperature. The interaction of phonons with magnetic moments of uranium 5⁢𝑓 electrons mediated by magnetoelastic coupling results in an anomalous low-temperature thermal conductivity profile. Analysis of the magnetic susceptibility measurements indicates a departure from the Curie-Weiss relationship characteristic of noninteracting paramagnetic ions, previously associated with the dynamic Jahn-Teller (DJT) effect characterized by coupling between spin and the oxygen sublattice. The T 2⁢g Raman peak position follows a nonlinear trend as a function of uranium concentration and hints that these Raman active optical modes play a role in either DJT or in mediating quadrupole-quadrupole interactions. A first-principle-based thermal transport model is implemented to explain the low-temperature transport measurements, where the anomalous reduction is attributed to phonon-spin resonant scattering. The interplay between spins and phonons is also captured using high-resolution inelastic x-ray scattering (IXS) measurements of phonon linewidths. Our results provide insights into the phonon interactions with the magnetic excitations governing DJT effect and impacting the low-temperature thermal transport processes in this material system. Furthermore, these findings have implications for understanding low-temperature thermal transport and magnetic properties in advanced materials for information processing and energy applications.

36 - MATERIALS SCIENCE↗

DOE OSTI2026

Shock compression of diamond single crystals to 120 GPa: Refractive index and nonlinear photoelasticity

The optical response of transparent solids at extreme conditions is important for both fundamental science and many applications. Strong transparent solids are of particular interest for use as optical windows in dynamic compression experiments. Due to diamond’s exceptional strength and optical properties, laser-driven shock experiments and plate impact experiments were carried out to examine the diamond optical response for shock wave compression along two different crystal orientations. Using laser interferometry at 532 nm and 1550 nm wavelengths, optical transparency was observed and refractive indices were determined for [100] diamond at stresses up to 119 GPa and for [111] diamond at stresses up to 87 GPa. From these results, the nonlinear photoelastic response for [100] and [111] diamond was determined, revealing significant dependence on both crystal orientation and laser wavelength. To enable [100] diamond as an interferometry window in dynamic compression experiments, the requisite window corrections were determined for 532 nm and 1550 nm wavelengths. Because of diamond’s excellent x-ray transparency, the present findings will be particularly useful for incorporating [100] diamonds as windows in dynamic compression experiments involving x-ray diffraction or other x-ray diagnostics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Shock-induced bubble jets: a dual perspective of bubble collapse and interfacial instability theory

Interactions between shock waves and gas bubbles in a liquid can lead to bubble collapse and high-speed liquid jet formation, relevant to biomedical applications such as shock wave lithotripsy and targeted drug delivery. This study reveals a complex interplay between acceleration-induced instabilities that drive jet formation and radial accelerations causing overall bubble collapse under shock wave pressure. Using high-speed synchrotron X-ray phase contrast imaging, the dynamics of micrometre-sized air bubbles interacting with laser-induced underwater shock waves are visualised. These images offer full optical access to phase discontinuities along the X-ray path, including jet formation, its propagation inside the bubble, and penetration through the distal side. Jet formation from laser-induced shock waves is suggested to be an acceleration-driven process. A model predicting jet speed based on the perturbation growth rate of a single-mode Richtmyer–Meshkov instability shows good agreement with experimental data, despite uncertainties in the jet-driving mechanisms. The jet initially follows a linear growth phase, transitioning into a nonlinear regime as it evolves. To capture this transition, a heuristic model bridging the linear and nonlinear growth phases is introduced, also approximating jet shape as a single-mode instability, again matching experimental observations. Upon piercing the distal bubble surface, jets can entrain gas and form a toroidal secondary bubble. Linear scaling laws are identified for the pinch-off time and volume of the ejected bubble relative to the jet’s Weber number, characterising the balance of inertia and surface tension. At low speeds, jets destabilise due to capillary effects, resulting in ligament pinch-off.

Drops and Bubbles: Bubble dynamics↗

DOE OSTI2025

Tandem neural network-based controller for x-ray bimorph mirrors

Nanometer-scale shape control of x-ray mirrors is crucial for coherent x-ray beam experiments at low-emittance synchrotron beamline instruments. Piezoelectric bimorph mirrors offer adaptive control but are hindered by nonlinearities such as cross talk, creep, and hysteresis. To overcome these limitations, we present a novel feedback-free control solution, inspired by the proportional–integral–derivative (PID) scheme, driven by tandem neural networks (TNNs). Using task-specific datasets, the TNN-based system predicts actuator voltages with greater speed, accuracy, and stability than a single NN-based model. This approach is ideal for real-time applications, such as adapting beam focus to dynamic sample sizes while maintaining precise wavefront quality. Our findings highlight the potential of artificial intelligence in rapidly optimizing adaptive optics and managing nonlinear control systems.

Zhang, Runyu↗

DOE OSTI2025

Single-shot measurements of shaped XUV FEL pulses with frequency-resolved optical gating

The ability to control the amplitude and phase of extreme ultraviolet (XUV) and X-ray free-electron laser (FEL) pulses can allow for the extension of optical techniques, such as multidimensional spectroscopy or coherent control, to higher photon energies, for probing and controlling core electronic transitions. However, this requires the ability to make single-shot, and complete, electric field measurements of potentially complex FEL pulses, in order to develop, and verify, pulse shaping strategies. Here, we present direct, single-shot measurements of XUV pulses generated under special operating configurations for producing specific pulse shapes from a laser-seeded XUV FEL. To do this, we built upon our past work using transient grating (TG) cross correlation frequency-resolved optical gating (FROG), where an optical reference pulse is diffracted from an XUV TG produced by a pair of interfering FEL pulses. The resulting nonlinear signal versus frequency and delay, i.e., the FROG trace, contains the electric field of the FEL pulse. The FEL pulse electric field is reconstructed from the FROG trace using a phase retrieval algorithm. Here we confirmed three different pulse shaping strategies for generating chirped, double and multiple FEL pulses by tuning the seed laser and FEL parameters and measuring the resulting shaped FEL pulses with TG XFROG. This work paves the way for generating on-demand pulse shapes with a seeded FEL by improving the characterization of FEL pulses, for transform-limited to more complex shapes.

Elverson, Francesca↗

DOE OSTI2025

Magnetic Properties and Large Second-Harmonic Generation Response of a Chiral Ternary Chalcogenide: Eu 2 SiSe 4

Eu(II)-containing chalcogenides are an emerging class of materials that are of great interest due to their high optical activity and intriguing magnetism. Here, we synthesized Eu 2 SiSe 4 as red-colored single crystals and characterized its structure with single-crystal X-ray diffraction, confirming the reported chiral monoclinic P2 1 symmetry at room temperature. The crystal structure of Eu 2 SiSe 4 comprises distorted SiSe 4 tetrahedral units and charge-balancing Eu(II) cations. Here, we develop a two-step solid-state synthesis method for Eu 2 SiSe 4 and compare it to the known boron chalcogenide method. We find the second-harmonic generation (SHG) activity of polycrystalline Eu 2 SiSe 4 to be ∼7 × AgGaS 2 , placing it among the highest-known SHG-active chalcogenides. No symmetry lowering is observed down to 100 K in single-crystal X-ray diffraction, although an anomalous expansion in the b-axis lattice parameter occurs and may be correlated to lattice modes of the SiSe 4 tetrahedra. We investigate the physical properties of Eu 2 SiSe 4 using magnetometry and heat capacity measurements and find a transition to an antiferromagnetic ground state at T N ≈ 5.5 K. The low-temperature transition releases less entropy than expected, which may be due to the complex crystal electric field effects of Eu(II).

36 MATERIALS SCIENCE↗

DOE OSTI2025

The Kangaroo’s First Hop: The Early Fast Cooling Phase of EP250108a/SN 2025kg

Fast X-ray transients are a rare and poorly understood population of events. Previously difficult to detect in real time, the launch of the Einstein Probe with its Wide-field X-ray Telescope has led to a rapid expansionof the sample and allowed the exploration of these transients across the electromagnetic spectrum. EP250108a is a recently detected example linked to an optical counterpart, SN 2025kg, or “the kangaroo.” Together with a companion Letter we present our observing campaign and analysis of this event. In this letter, we focus on the early evolution of the optical counterpart over the first 6 days, including our measurement of the redshift of z = 0.17641. We compare to other supernovae and fast transients showing similar features, finding significant similarities with SN 2006aj and SN 2020bvc, and show that the source is well modelled by a rapidly expanding cooling blackbody. We show the observed X-ray and radio properties are consistent with a collapsar-powered jet that is low energy (≲10 51 erg) and/or fails to break out of the dense material surrounding it. While we examine the possibility that the optical emission emerges from the shock produced as the supernova ejecta expand into a dense shell of circumstellar material, due to our X-ray and radio inferences, we favour a model where it arises from a shocked cocoon resulting from a trapped jet. This makes SN 2025 one of the few examples of this currently observationally rare event.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

Crystal Structures, Optical Behavior, and Magnetic Properties in Hydrated Lanthanide Iron Sulfates

Single crystals of LnFe(SO 4 ) 3 (H 2 O) 2 (Ln = La, Ce, Pr, Nd, Sm, Eu, Gd, Dy, Ho, Er, Tm; compounds 1–11) and LnFe(SO 4 ) 3 (H 2 O) (Ln = Tm, Yb, Lu; compounds 12–14) were synthesized under hydrothermal conditions. Single-crystal X-ray diffraction (SCXRD) analysis revealed that the dihydrated compounds (1–11) crystallize in centrosymmetric (CS) structures, with the lanthanide ions adopting eight-coordinate geometries. In contrast, the monohydrated compounds (12–14) exhibit noncentrosymmetric (NCS) structures, where the lanthanide ions are seven-coordinated. Vibrating sample magnetometry (VSM) confirmed that compounds 2, 4, and 7–11 are paramagnetic below 400 K, with compound 8 displaying the highest magnetic susceptibility. Compounds 1, 5, 6, 13, and 14 show a sharp increase in magnetic susceptibility at Néel temperatures ( T N ) of approximately 72, 76, 70, 58, and 56 K, respectively, indicating antiferromagnetic ordering. High-temperature magnetic susceptibility measurements further support the presence of antiferromagnetic transitions in these compounds. Second harmonic generation (SHG) measurements showed that the noncentrosymmetric Yb (compound 13) and Lu (compound 14) compounds exhibit SHG intensities of 0.3× and 1.6× that of potassium dihydrogen phosphate (KDP), respectively.

anions↗