Giant electric field-induced second harmonic generation in polar skyrmions

Second-harmonic generation (SHG) is a second-order nonlinear optical process in which two photons at frequency ω combine to form a photon at 2ω. SHG underpins many laser, optoelectronic, materials, and biomedical applications and, with integrated photonics, enables on-chip devices such as switches, frequency combs, and quantum light sources. Electrically tunable SHG, achievable via electric field-induced second-harmonic generation (EFISH, a χ(3)-mediated process without symmetry constraints), has been explored in optical crystals, polymers, silicon, layered chalcogenides, and photonic structures. However, typical EFISH platforms exhibit weak effective χ(2) and small modulation depths, limiting device utility. Alternatively, tuning SHG in χ(2)-active polar materials via domain reconfiguration or polar–nonpolar phase transitions can yield large modulation but often suffers from hysteresis, sluggish response, and fatigue. Recent discoveries of topological polar structures (vortices, skyrmions, merons) in PbTiO3/SrTiO3 superlattices introduce new opportunities: their nanoscale swirling dipole configurations, frustrated polarization regions, and long-range in-plane ordering give rise to emergent properties and high responsiveness to external stimuli. Motivated by these prospects, this work demonstrates a polar-skyrmionic EFISH effect in PbTiO3/SrTiO3 superlattices, enabling strong, reversible, and fast SHG modulation by bias-induced symmetry breaking without domain-wall nucleation or motion, advancing materials for on-chip optoelectronics.

Prior EFISH studies span optical crystals, polymers, strain-free silicon, layered transition metal dichalcogenides, and artificial photonic structures. While broadly applicable due to χ(3) symmetry freedom, these approaches typically deliver weak effective χ(2) (χ(3)E) and low modulation depths (a few %/V). In χ(2)-active polar materials, SHG can be tuned via ferroelectric domain switching (interference between 180° domains) or bias-driven polar–nonpolar phase transitions (e.g., BiFeO3/TbScO3 superlattices; MoTe2 monolayers). Yet such mesoscopic processes are governed by domain-wall/phase-front kinetics, producing hysteresis, slow dynamics, and fatigue. Topological polar structures (vortices, skyrmions, merons) in PbTiO3/SrTiO3 superlattices exhibit nanoscale periodic units with swirling dipoles and frustrated polarization akin to Néel/Bloch walls, yielding emergent phenomena such as negative permittivity, SHG circular dichroism, and sub-THz collective dynamics. In situ studies indicate large polarization reconfiguration under external stimuli, suggesting potential for agile SHG modulation using topological phases.

Materials and device fabrication: ~96 nm [(PbTiO3)14/(SrTiO3)16] superlattices were epitaxially grown on (001) LSAT substrates with a 5 nm SrRuO3 (SRO) bottom electrode by pulsed laser deposition (KrF 248 nm). Laser fluences/repetition rates: PTO 1.3 J cm^-2/5 Hz; STO 1.7 J cm^-2/3 Hz; SRO 1.5 J cm^-2/10 Hz. Growth temperature 650 °C; oxygen pressures: SRO 25 Pa, superlattice 10 Pa. Post-anneal 650 °C for 10 min, cool in 20 kPa O2. A ~20 nm SRO top electrode was deposited; 100 μm diameter SRO/Superlattice/SRO capacitors were patterned by UV lithography and chemical etching (NaIO3 solution) to form semi-transparent top electrodes for SHG. Structural characterization: 3D X-ray reciprocal space mapping (RSM) around LSAT 002 and in-plane reflections (10 keV) confirmed excellent crystallinity, designed periodicity (~12 nm per bilayer), and in-plane skyrmion ordering with ~7.6 nm periodicity (satellites at ~0.083 Å^-1). Cross-sectional STEM (HAADF and differential phase contrast, 300 kV) provided cation-column contrast, elemental maps (no interdiffusion), local polar displacements, and electric fields. DPC vectors yielded semi-quantitative local E-field maps; unit-cell polarization was inferred from B-site displacements. Nonlinear optical measurements: A Ti:sapphire femtosecond laser (800 nm, 35 fs, 50–200 mW) was used for SHG. Normal incidence and 45° incidence geometries were employed; the latter couples to out-of-plane polarization components more effectively. SHG polarimetry (input/output polarization control) and laser-scanned imaging were performed while biasing capacitors in situ via tungsten probes using a function generator/sourcemeter. Temperature dependence measured up to 450 K; AC frequency response up to 10^7 Hz; cycling fatigue with 10 MHz square waves. In situ diffraction under bias: Synchrotron-based 3D RSM with a large beam footprint covered entire capacitors; bias-dependent superlattice OOL peaks and skyrmion satellite intensities were tracked. Phase-field simulations: Time-dependent Ginzburg–Landau framework for PTO/STO superlattices on LSAT solved polarization evolution considering Landau, elastic, electrostatic, and gradient energies on a 192×192×350 grid with periodic in-plane boundary conditions. Elastic inhomogeneity treated via iterative perturbation. Simulations analyzed Pontryagin density maps, autocorrelation functions, and Fourier spectra to identify intra- and inter-skyrmion correlations relevant to EFISH.

• Demonstration of polar-skyrmionic EFISH in PTO/STO superlattices with giant performance metrics under non-resonant 800 nm excitation: maximum induced χ(2) component χxxx ≈ −54.2 pm V^-1; EFISH modulation depth Δα2/α2 ≈ −664% V^-1 (peak at ~7 V).
• SHG intensity–bias characteristics: rapid increase from near-zero at 0 V to saturation near −10 to −15 V (p-in/p-out), reversible and nearly hysteresis-free within ±10 V. Positive bias yields stronger p-in/p-out response than negative bias.
• Anisotropy and χ(2) tensors from SHG polarimetry: distinct tensor ratios for positive vs negative biases. For V<0, χxxx:χxzz:χzzz ratios close to bulk PbTiO3 (4mm). For V>0, markedly enhanced χxxx and diminished χzzz, implying additional SHG contributions beyond simple c-domains (coherent skyrmion-wall contributions).
• Quantified global SHG efficiency ~9.3 × 10^-9 W^-1 at −14 V (referenced to LiNbO3 standard), exceeding bulk PTO (−17 pm V^-1) and underpinning the large modulation depth.
• Structural mechanism: In situ RSM shows superlattice peak splitting and ~0.25% out-of-plane lattice expansion at high bias, consistent with rotation toward single c-domains; skyrmion satellite intensities decrease with bias without shifting wavevectors (macroscopic 4mm symmetry retained). Phase-field simulations reveal asymmetric transition paths: under negative bias skyrmions expand and coalesce into elongated stripes; under positive bias skyrmions shrink individually, maintaining number until higher voltages. EFISH arises from bias-driven displacement of skyrmion walls that breaks pseudo-centrosymmetry (initially near-zero net Pz), activating SHG.
• Order parameter: Fourier amplitudes of the Pontryagin-density autocorrelation show an inter-skyrmion correlation peak whose bias dependence mirrors the EFISH trend, identifying a hidden structural order parameter governing EFISH.
• Device-relevant characteristics: Broad operating temperature range with reversible suppression above ~450 K and recovery on cooling; high-speed response with minimal roll-off up to 10^7 Hz (≥50 ns processes; inferred potential GHz bandwidth); excellent fatigue resistance with <±10% SHG variation over ~10^10 cycles at 10 MHz, 0–20 V.
• Comparative advantage: Among thin-film materials, PTO/STO skyrmion superlattices combine high χ(2) and the largest EFISH modulation depths, surpassing platforms like LNOI and many 2D/photonic systems (which often rely on narrowband resonances).
• Application concept: Fresnel-lens-type electrode design using alternate biases focuses SHG with ~4× enhancement at ~60 μm focal length compared to a single capacitor; tunable focusing and potential quasi-phase-matching via periodic electrodes/metasurfaces are envisioned.

The study addresses the challenge of achieving large, fast, and reversible electric control of nonlinear optical responses for integrated photonics. Leveraging the topological polar skyrmion phase in PTO/STO superlattices, bias-induced symmetry breaking occurs via continuous skyrmion-wall displacement rather than nucleation/propagation of conventional domain walls, avoiding hysteresis and slow kinetics. This topological protection allows agile, fatigue-resistant modulation with strong χ(2) contributions from coherently ordered skyrmion walls under appropriate bias polarity. Combined in situ diffraction and phase-field modeling link macroscopic EFISH to microscopic polarization evolution and identify inter-skyrmion correlation as an order parameter. Compared to existing EFISH materials, the demonstrated system delivers superior modulation depth with competitive χ(2) and bandwidth, promising broadband operation (mid-IR to near-bandgap) and integrability via oxide thin-film platforms. The approach suggests a general strategy to manipulate nonlinear optics by tuning topological polar textures through strain, layer design, and growth conditions, enabling device concepts such as tunable SHG modulators, lenses, and potentially waveguide-based quasi-phase-matched converters.

Electric-field-induced SHG was realized in polar skyrmions of (PbTiO3)14/(SrTiO3)16 superlattices, with microscopic mechanisms elucidated by in situ X-ray diffraction and phase-field simulations. Capacitor devices exhibit a giant EFISH modulation depth (~664% V^-1), induced χ(2) ~54.2 pm V^-1, and strong SHG efficiency (~9.3 × 10^-9 W^-1) at 800 nm, along with wide operating temperature range, high-speed response, and excellent cycling endurance. The thin-film superlattice platform offers multiple tunable degrees of freedom (strain, layer thicknesses, composition) for further performance enhancement and on-chip integration. These findings position polar skyrmions as a competitive and versatile material system for nonlinear photonics and optoelectronics, and motivate exploration of other topological polar phases for electrically tunable SHG.

• The in situ X-ray measurements used a large beam footprint covering biased and unbiased regions, introducing uncertainty in quantitative analysis of bias-induced changes, though providing good statistical averaging.
• High-frequency (≫10 MHz) response could not be directly measured; GHz bandwidth is inferred from flat trends up to 10^7 Hz rather than demonstrated.
• The EFISH response may include contributions from extrinsic optical effects (e.g., interference/reflection at skyrmion walls, interfacial effects) for which current effective models are lacking due to subwavelength feature sizes.
• Built-in asymmetry from growth conditions sets the initial skyrmion core polarization (upward Pz), leading to bias-asymmetric transition paths; generality across different growth conditions requires further verification.
• Thermal stability: SHG under bias diminishes approaching ~450 K (reversible), setting an upper practical operating temperature near this range.
• Reported SHG efficiency values and tensor components depend on calibration against reference materials and specific device geometry; resonance-free broadband claims remain to be fully mapped spectrally.