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Insulating moiré homobilayers lack a threefold symmetric second-harmonic generation

Atoms within moiré bilayers relax in plane to minimize elastic energy; such relaxation brings their space group symmetries down to P1. Here, the ab initio second harmonic generation (SHG) of twisted and atomistically optimized hBN bilayers was determined at four twist angles (θ = 38.21°, 60.00°, 73.17°, and 98.21°) and for three displacements τ measured away from the ground state AA' configuration. All moiré bilayers have a P1 space symmetry after structural optimization. This situation is quite different to monolayers with hexagonal lattices, which retain a threefold symmetry. We point out that the actual symmetries of the SHG reported for hBN bilayers on two experimental works do not coincide with the sixfold symmetric theoretical profiles they provide [either sin 2 ⁡(3⁢Φ) or cos 2 ⁡(3⁢Φ)], and show that the intrinsic low structural symmetry of (atomically optimized) hBN bilayer moirés can in fact be read out from experimental SHG intensity profiles—which are tunable by θ and by the frequency of light ω: The SHG is most definitely not sixfold symmetric because moirés do not retain a threefold symmetry. Furthermore, an extrinsic twofold symmetry of the SHG emission is realized by tilting the pump by an angle α away from the 2D material's normal, regardless of θ and ω. Furthermore, the design of in-plane and ultrathin sources of SHG with low symmetry could be useful for the eventual creation of entanglement sources from 2D materials.

2-dimensional systems↗

Sn-modified BaTiO 3 thin film with enhanced polarization

Hybrid molecular beam epitaxy (MBE) growth of Sn-modified BaTiO 3 films was realized with varying domain structures and crystal symmetries across the entire composition space. Macroscopic and microscopic structures and the crystal symmetry of these thin films were determined using a combination of optical second harmonic generation (SHG) polarimetry and scanning transmission electron microscopy (STEM). SHG polarimetry revealed a variation in the global crystal symmetry of the films from tetragonal (P4mm) to cubic (PM3¯m) across the composition range, x = 0 to 1 in BaTi 1–x Sn x O 3 (BTSO). STEM imaging shows that the long-range polar order observed when the Sn content is low (x = 0.09) transformed to a short-range polar order as the Sn content increased (x = 0.48). Consistent with atomic displacement measurements from STEM, the largest polarization was obtained at the lowest Sn content of x = 0.09 in Sn-modified BaTiO 3 as determined by SHG. Furthermore, these results agree with recent bulk ceramic reports and further identify this material system as a potential replacement for Pb-containing relaxor-based thin film devices.

36 MATERIALS SCIENCE↗

Extrinsic Nonlinear Kerr Rotation in Topological Materials under a Magnetic Field

Topological properties in quantum materials are often governed by symmetry and tuned by crystal structure and external fields, and hence, symmetry-sensitive nonlinear optical measurements in a magnetic field are a valuable probe. Here, we report nonlinear magneto-optical second harmonic generation (SHG) studies of nonmagnetic topological materials including bilayer WTe 2 , monolayer WSe 2 , and bulk TaAs. The polarization-resolved patterns of optical SHG under a magnetic field show nonlinear Kerr rotation in these time-reversal symmetric materials. For materials with 3-fold rotational symmetric lattice structure, the SHG polarization pattern rotates just slightly in a magnetic field, whereas in those with mirror or 2-fold rotational symmetry, the SHG polarization pattern rotates greatly and distorts. Further, these different magneto-SHG characters can be understood by considering the superposition of the magnetic field-induced time-noninvariant nonlinear optical tensor and the crystal-structure-based time-invariant counterpart. The situation is further clarified by scrutinizing the Faraday rotation, whose subtle interplay with crystal symmetry accounts for the diverse behavior of the extrinsic nonlinear Kerr rotation in different materials. Our work illustrates the application of magneto-SHG techniques to directly probe nontrivial topological properties, and underlines the importance of minimizing extrinsic nonlinear Kerr rotation in polarization-resolved magneto-optical studies.

36 MATERIALS SCIENCE↗

Tunable Second Harmonic Generation in Twisted Bilayer Graphene

Twisted stacking of van der Waals (vdW) materials introduces a new way in bandstructure engineering and has given rise to numerous extraordinary physical phenomena. Despite the absence of second harmonic generation (SHG) in non-gated monolayer graphene, artificially twisted bilayer graphene (tBLG) possesses more possible point-group symmetries including those with broken inversion-symmetry. Here, we report twist-angle-dependent SHG from tBLG, which is the first demonstration of an elemental material with intrinsically tunable nonlinearity. We show that depending on the twist angle, the susceptibility of the dominant chiral tensor component of tBLGs can vary from 0 to 28×10 4 pm 2 /V, which is at the same order of magnitude as on-resonance susceptibility of monolayer MoS 2 . These results shed light on the underlying symmetry of tBLG systems and electronic band-structure near van Hove singularities (vHs). More importantly, they introduce a new degree of freedom, the twisting, in creating efficient second-order nonlinear material form centrosymmetric constituents

36 MATERIALS SCIENCE↗

MgSiP 2 : An Infrared Nonlinear Optical Crystal with a Large Non‐Resonant Phase‐Matchable Second Harmonic Coefficient and High Laser Damage Threshold

Superior infrared nonlinear optical (NLO) crystals are in urgent demand in the development of lasers and optical technologies for communications and computing. The critical challenge is to find a crystal with large non‐resonant phase‐matchable NLO coefficients and high laser damage threshold (LDTs) simultaneously, which however scale inversely. This work reports such a material, MgSiP 2, that exhibits a large second harmonic generation (SHG) coefficient of d 14 ≈ d 36 = 89 ± 5 pm V −1 at 1550 nm fundamental wavelength, surpassing the commercial NLO crystals AgGaS 2 , AgGaSe 2 , and ZnGeP 2 . First principles theory reveals the polarizability and geometric arrangement of the [SiP 4 ] tetrahedral units as the origin of this large nonlinear response. Remarkably, it also exhibits a high LDT value of 684 GW cm −2 , which is six times larger than ZnGeP 2 and three times larger than CdSiP 2 . It has a wide transparency window of 0.53–10.35 µm, allowing broadband tunability. Further, it is Type I and Type II phase‐matchable with large effective SHG coefficients of d eff,I ≈80.2 pm V −1 and d eff,II ≈73.4 pm V −1 . The outstanding properties of MgSiP 2 make it a highly attractive candidate for optical frequency conversion in the infrared.

36 MATERIALS SCIENCE↗

Large second harmonic generation in a penta-CdO 2 sheet exfoliated from its bulk phase

Two-dimensional (2D) materials composed solely of pentagonal motifs are of particular interest due to their unique geometries and novel properties. Especially, the broken centrosymmetry and in-plane mirror symmetry in penta-graphene-like materials result in both in-plane and out-of-plane second harmonic generation (SHG). Transition metal cations with a filled d 10 shell (d 10 -TM) can significantly enhance the SHG response as found in many previously studied bulk materials. Here, in this study, based on first-principles calculations combined with independent particle approximation, we show that large SHG can also exist in some 2D d 10 -TM oxides, such as penta-CdO 2 , which can be chemically exfoliated from its bulk phase with its dynamical, thermal, and mechanical stability intact. We further find that penta-CdO 2 possesses extraordinary in-plane and out-of-plane SHG responses with large static SHG susceptibilities of χ sheet 14 (0) = χ sheet 25 (0) = χ sheet 36 (0) = 8.86 pm 2 V -1 due to the phase-matching between fundamental and second-harmonic light. In addition, the low thermal expansion and a large optical band gap of 3.24 eV endow the penta-CdO 2 sheet with a high laser-induced damage threshold. Discussions are also made on the penta-ZnO 2 sheet. This study expands the family of 2D materials with outstanding SHG performance.

36 MATERIALS SCIENCE↗

Domain wall dynamics in tungsten trioxide: Evidence for polar domain walls

Domain walls have distinct properties from the bulk, and tailoring them to suit the needs for device applications is critical. Tungsten trioxide, WO 3 , is of great interest for device applications that make use of domain wall properties; it exhibits a phenomenologically rich sequence of phase transitions, virtually all of which are ferroelastic in character, resulting in many sets of domain walls at low temperatures, each with their own unique properties. Domain wall motion and its contribution to the piezoelectric response have been investigated in WO 3 from 300 to 180 K using resonant ultrasound spectroscopy (RUS) and resonant piezoelectric spectroscopy (RPS), which showed that the P 2 1 / n , P 1 ¯ , and P 2 1 / c phases give a piezoelectric response despite the bulk being nominally centrosymmetric. Second harmonic generation (SHG) confirmed that polarity was strongest within the domain walls, and additional weak signals were found in the domains. Domain wall mobility was investigated in the P b c n , P 2 1 / n , and P 2 1 / c phases from 685 to 5 K. Domain walls in the P 2 1 / n and P 1 ¯ were more mobile than those in the P b c n and P 2 1 / c structures, and soon after the P 1 ¯ → P 2 1 / c transition the walls become pinned at ∼ 140 K . Published by the American Physical Society 2024

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Stabilization of the Polar Structure and Giant Second-Order Nonlinear Response of Single Crystal γ-NaAs 0.95 Sb 0.05 Se 2

The dearth of suitable materials significantly restricts the practical development of infrared (IR) laser systems with highly efficient and broadband tuning. Recently, γ-NaAsSe 2 is reported, and it exhibits a large nonlinear second-harmonic generation (SHG) coefficient of 590 pm V —1 at 2 µm. However, the crystal growth of γ-NaAsSe 2 is challenging because it undergoes a phase transition to centrosymmetric δ-NaAsSe 2 . Herein, the stabilization of non-centrosymmetric γ-NaAsSe 2 by doping the As site with Sb, which results in γ-NaAs 0.95 Sb 0.05 Se 2 is reported. The congruent melting behavior is confirmed by differential thermal analysis with a melting temperature of 450 °C and crystallization temperature of 415 °C. Single crystals with dimensions of 3 mm × 2 mm are successfully obtained via zone refining and the Bridgman method. The purification of the material plays a significant role in crystal growth and results in a bandgap of 1.78 eV and thermal conductivity of 0.79 Wm —1 K —1 . The single-crystal SHG coefficient of γ-NaAs 0.95 Sb 0.05 Se 2 exhibits an enormous value of |d 11 | = 648 ± 74 pm V —1 , which is comparable to that of γ-NaAsSe 2 and ≈20× larger than that of AgGaSe 2 . Importantly, the bandgap of γ-NaAs 0.95 Sb 0.05 Se 2 (1.78 eV) is similar to that of AgGaSe 2 , thus rendering it highly attractive as a high-performing nonlinear optical material.

36 MATERIALS SCIENCE↗

Direct visualization and control of antiferromagnetic domains and spin reorientation in a parent cuprate

Here, we report magnetic optical second-harmonic generation (SHG) polarimetry and imaging on Sr 2 Cu 3 O 4 Cl 2 , which allows direct visualization of the mesoscopic antiferromagnetic (AFM) structure of a parent cuprate. Temperature- and magnetic-field-dependent SHG reveals large domains with 90° relative orientations that are stabilized by a combination of uniaxial magnetic anisotropy and the Earth's magnetic field. Below a temperature T R ~ 97 K, we observe an unusual 90° spin reorientation transition, possibly driven by competing magnetic anisotropies of the two copper sublattices, which swaps the AFM domain states while preserving the domain structure. This allows deterministic switching of the AFM states by thermal or laser heating. Near T R , the domain walls become exceptionally responsive to an applied magnetic field, with the Earth's field sufficient to completely expel them from the crystal. Our findings unlock opportunities to study the mesoscopic AFM behavior of parent cuprates and explore their potential for AFM technologies.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Optical second harmonic generation in anisotropic multilayers with complete multireflection of linear and nonlinear waves using ♯SHAARP.ml package

Abstract Optical second harmonic generation (SHG) is a nonlinear optical effect widely used for nonlinear optical microscopy and laser frequency conversion. Closed-form analytical solution of the nonlinear optical responses is essential for evaluating materials whose optical properties are unknown a priori. A recent open-source code, ♯SHAARP. si , can provide such closed form solutions for crystals with arbitrary symmetries, orientations, and anisotropic properties at a single interface. However, optical components are often in the form of slabs, thin films on substrates, and multilayer heterostructures with multiple reflections of both the fundamental and up to ten different SHG waves at each interface, adding significant complexity. Many approximations have therefore been employed in the existing analytical approaches, such as slowly varying approximation, weak reflection of the nonlinear polarization, transparent medium, high crystallographic symmetry, Kleinman symmetry, easy crystal orientation along a high-symmetry direction, phase matching conditions and negligible interference among nonlinear waves, which may lead to large errors in the reported material properties. To avoid these approximations, we have developed an open-source package named Second Harmonic Analysis of Anisotropic Rotational Polarimetry in Multilayers (♯SHAARP. ml ). The reliability and accuracy are established by experimentally benchmarking with both the SHG polarimetry and Maker fringes using standard and commonly used nonlinear optical materials as well as twisted 2-dimensional heterostructures.

36 MATERIALS SCIENCE↗

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↗

Second-harmonic and linear spectroscopy of $\textit{α}$-In 2 Se 3

We report spectroscopic measurements of optical transmission, ellipsometry, and second-harmonic generation (SHG) from as-grown vapor-deposited $\textit{α}$-In 2 Se 3 nanoflakes ranging in thickness from a single quintuple layer (QL) to bulk material. In this work, we compare these measurements with ab initio calculations of structural and optical properties. Linear optical measurements yield thickness-dependent band gaps and dielectric functions, while SHG diagnoses microscopic film structure and ferroelectric polarization. The rotational anisotropy of SHG for s-polarized incident photons of energy 1.4 eV reveals crystalline symmetry and orientation of individual QLs. Peak SHG intensity increases from one to three QLs, then decreases for larger numbers, tracking thickness-dependent trends in the second-order susceptibility components $χ^{xxx}$ and $χ^{zxx}$. Comparison of measured and calculated SHG spectra for s-polarized photons of energies between 1.2 and 1.7 eV incident upon two QL samples discriminates among candidate stacking arrangements, and favors an arrangement with electric polarization vectors of the two QLs pointing outward in opposite directions.

36 MATERIALS SCIENCE↗

Multifunctional Cu 2 TSiS 4 (T = Mn and Fe): Polar Semiconducting Antiferromagnets with Nonlinear Optical Properties

In this work, Cu 2 TSiS 4 (T = Mn and Fe) polycrystalline and single-crystal materials were prepared with high-temperature solid-state and chemical vapor transport methods, respectively. The polar crystal structure (space group Pmn2 1 ) consists of chains of corner-sharing and distorted CuS 4 , Mn/FeS 4 , and SiS 4 tetrahedra, which is confirmed by Rietveld refinement using neutron powder diffraction data, X-ray single-crystal refinement, electron diffraction, energy-dispersive X-ray spectroscopy, and second harmonic generation (SHG) techniques. Magnetic measurements indicate that both compounds order antiferromagnetically at 8 and 14 K, respectively, which is supported by the temperature-dependent (100–2 K) neutron powder diffraction data. Additional magnetic reflections observed at 2 K can be modeled by magnetic propagation vectors k = (1/2,0,1/2) and k = (1/2,1/2,1/2) for Cu 2 MnSiS 4 and Cu 2 FeSiS 4 , respectively. The refined antiferromagnetic structure reveals that the Mn/Fe spins are canted away from the ac plane by about 14°, with the total magnetic moments of Mn and Fe being 4.1(1) and 2.9(1) μ B , respectively. Both compounds exhibit an SHG response with relatively modest second-order nonlinear susceptibilities. Density functional theory calculations are used to describe the electronic band structures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Large Non‐Resonant Infrared Optical Second Harmonic Generation in Bulk Crystals of Van der Waals Semiconductor, SnP 2 Se 6

2D van der Waals (vdW) materials have emerged as a highly promising candidates for nonlinear optical (NLO) applications. This study presents the synthesis, comprehensive linear optical, and optical second harmonic generation (SHG) characterization of a novel 2D vdW semiconductor SnP2Se6 in its bulk single crystal form. It exhibits an indirect bandgap of ≈1.47 eV and an exceptional non-resonant SHG coefficient of d 33 ∼ −222 ± 30 pm V −1 at a fundamental wavelength of 2 µm, which is ≈7 times larger than that of the commercial AgGaSe 2 with a comparable bandgap. Density functional theory (DFT) calculations of the linear and nonlinear optical properties exhibit reasonable agreement with the experimental measurements, revealing the chemical origin of the enhanced properties. Moreover, SnP 2 Se 6 can exhibit both type-I and type-II phase matching over a wide spectral range, fulfilling one of the key criteria for an ideal NLO crystal. These exceptional properties position SnP 2 Se 6 as a highly promising candidate for NLO applications.

36 MATERIALS SCIENCE↗

Multiresolution Quantum Chemistry: Nonlinear Response Properties at the Basis Set Limit

We benchmark the accuracy of Dunning correlation-consistent Gaussian basis sets for computing frequencydependent second-order hyperpolarizabilities relevant to second-harmonic generation (SHG), using multiresolution analysis (MRA) as a reference. Basis set errors are analyzed using a unit-sphere representation of the effective hyperpolarizability vector, enabling direct assessment of directional error structure. We introduce a relative RMS total error metric that integrates directional deviations over the unit sphere and complement it with signed projection errors that distinguish over- and underestimation. Unsupervised clustering based on these signed directional metrics reveals four distinct convergence behaviors across a set of 68 molecules. Unitsphere visualizations of representative systems show that basis set errors are often highly anisotropic and localized along specific bond directions, even when global error measures appear small. Doubly augmented basis sets consistently outperform singly augmented ones, and core-polarization functions are required for uniform convergence in second-row systems. Overall, this work demonstrates that directional analysis combined with clustering provides a robust framework for understanding basis set convergence in nonlinear optical response properties.

Basis sets↗

Large Enhancements in Optical and Piezoelectric Properties in Ferroelectric Zn 1- x Mg x O Thin Films through Engineering Electronic and Ionic Anharmonicities

Multifunctionality as a paradigm requires materials exhibiting multiple superior properties. Integrating second-order optical nonlinearity and large bandgap with piezoelectricity can, for example, enable broadband, strain-tunable photonics. Though very different phenomena at distinct frequencies, both second-order optical nonlinearity and piezoelectricity are third-rank polar tensors present only in acentric crystal structures. However, simultaneously enhancing both phenomena is highly challenging since it involves competing effects with tradeoffs. Recently, a large switchable ferroelectric polarization of ≈80 μC cm –2 was reported in Zn 1-x Mg x O films. Here, ferroelectric Zn 1-x Mg x O is demonstrated to be a platform that hosts simultaneously a 30% increase in the electronic bandgap, a 50% enhancement in the second harmonic generation (SHG) coefficients, and a near 200% improvement in the piezoelectric coefficients over pure ZnO. These enhancements are shown to be due to a 400% increase in the electronic anharmonicity and a ≈200% decrease in the ionic anharmonicity with Mg substitution. Precisely controllable periodic ferroelectric domain gratings are demonstrated down to 800 nm domain width, enabling ultraviolet quasi-phase-matched optical harmonic generation as well as domain-engineered piezoelectric devices.

36 MATERIALS SCIENCE↗

Harnessing complexity: Nonlinear optical phenomena in L-shapes, nanocrescents, and split-ring resonators

Here, we conduct systematic studies of the optical characteristics of plasmonic nanoparticles that exhibit C 2v symmetry. In particular, we analyze three distinct geometric configurations: an L-type shape, a crescent, and a split-ring resonator shaped like the Greek letter π. Optical properties are examined using the finite-difference time-domain method. It is demonstrated that all three shapes exhibit two prominent plasmon modes associated with the two axes of symmetry. This is in addition to a wide range of resonances observed at high frequencies corresponding to quadrupole modes and peaks due to sharp corners. Next, to facilitate nonlinear analysis, we employ a semiclassical hydrodynamic model, where the electron pressure term is explicitly accounted for. This model goes beyond the standard Drude description and enables capturing nonlocal and nonlinear effects. Employing this model enables us to rigorously examine the second-order angular resolved nonlinear optical response of these nanoparticles in each of the three configurations. Two pumping regimes are considered, namely, continuous wave (CW) and pulsed excitations. For CW pumping, we explore the properties of the second harmonic generation (SHG). Polarization and angle-resolved SHG spectra are obtained, revealing strong dependence on the nanoparticle geometry and incident wave polarization. The C 2v symmetry is shown to play a key role in determining the polarization states and selection rules of the SHG signal. For pulsed excitations, we discuss the phenomenon of broadband terahertz (THz) generation induced by the difference-frequency generation . It is shown that the THz emission spectra exhibit unique features attributed to the plasmonic resonances and symmetry of the nanoparticles. The polarization of the generated THz waves is also examined, revealing interesting patterns tied to the nanoparticle geometry. To gain deeper insight, we propose an analytical theory that agrees very well with the numerical experiments. The theory shows that the physical origin of the THz radiation is the mixing of various frequency components of the fundamental pulse by the second-order nonlinear susceptibility. An expression for the far-field THz intensity is derived in terms of the incident pulse parameters and the nonlinear response tensor of the nanoparticle. The results presented in this work offer new insights into the linear and nonlinear optical properties of nanoparticles with C 2v symmetry. The demonstrated strong SHG response and efficient broadband THz generation hold great promise for applications in nonlinear spectroscopy, nanophotonics, and optoelectronics. The proposed theoretical framework also provides a valuable tool for understanding and predicting the nonlinear behavior of other related nanostructures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Optomechanical Tuning of Second Harmonic Generation Anisotropy in Janus MoSSe/MoS 2 Heterostructures

Symmetry breaking in van der Waals materials enables the realization of quantum states and advanced device functionalities. Janus transition-metal dichalcogenides (TMDs) exhibit distinctive nonlinear optical properties due to their broken out-of-plane mirror symmetry. However, the dynamic control of second harmonic generation (SHG) anisotropy and resonance behavior via optical excitation remains elusive. Here, in this work, we investigate the SHG response of Janus MoSSe/MoS 2 heterostructures with 2H and 3R stackings. We can tune the SHG response by varying the incident photon wavelength from 800 to 1000 nm, which shows a resonance-dependent enhancement in intensity and a deviation from 6-fold symmetry, indicating wavelength-dependent anisotropy. The ratio between maximum and minimum intensity in the armchair directions, associated with the SHG anisotropy, reaches a value of 1.73 at the excitation wavelength of 1000 nm. Group theory analysis and first-principles calculations reveal that the observed anisotropy arises from optically induced strain. Our findings highlight the role of symmetry breaking and optical resonance contributing to the optomechanical tuning of SHG anisotropy, offering opportunities for developing Janus TMD-based photonic devices for frequency conversion, light generation, and optical switching.

Janus transition metal dichalcogenides↗