ARTICLE https://doi.org/10.1038/s42005-022-00882-7 OPEN Terahertz displacive excitation of a coherent Raman-active phonon in V2O3 Flavio Giorgianni 1 ✉, Mattia Udina2, Tommaso Cea3, Eugenio Paris 4, Marco Caputo5, Milan Radovic 5, Larissa Boie 6, Joe Sakai7, Christof W. Schneider8 & Steven Lee Johnson 4,6 Nonlinear processes involving frequency-mixing of light fields set the basis for ultrafast coherent spectroscopy of collective modes in solids. In certain semimetals and semi- conductors, generation of coherent phonon modes can occur by a displacive force on the lattice at the difference-frequency mixing of a laser pulse excitation on the electronic system. 1234567890():,; Here, as a low-frequency counterpart of this process, we demonstrate that coherent phonon excitations can be induced by the sum-frequency components of an intense terahertz light field, coupled to intraband electronic transitions. This nonlinear process leads to charge- coupled coherent dynamics of Raman-active phonon modes in the strongly correlated metal V2O3. Our results show an alternative up-conversion pathway for the optical control of Raman-active modes in solids mediated by terahertz-driven electronic excitation. 1 Paul Scherrer Institute, 5232 Villigen-PSI, Switzerland. 2 ISC-CNR and Department of Physics, “Sapienza” University of Rome, P.le Aldo Moro 5, 00185 Rome, Italy. 3 IMDEA Nanoscience, C/Farady 9, 28049 Madrid, Spain. 4 SwissFel, Paul Scherrer Institute, 5232 Villigen-PSI, Switzerland. 5 Photon Science Division, Paul Scherrer Institute, 5232 Villigen-PSI, Switzerland. 6 Institute for Quantum Electronics, Physics Department, ETH Zurich, Auguste-Piccard-Hof 1, 8093 Zurich, Switzerland. 7 Institut Català de Nanociència i Nanotecnologia (ICN2), UAB Campus, ICN2 Building, 08193 Bellaterra, Spain. 8 Laboratory for Multiscale Materials Experiments, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland. ✉email: flavio.giorgianni@psi.ch COMMUNICATIONS PHYSICS | (2022)5:103 | https://doi.org/10.1038/s42005-022-00882-7 | www.nature.com/commsphys 1 ARTICLE COMMUNICATIONS PHYSICS | https://doi.org/10.1038/s42005-022-00882-7 P hononics has recently been proposed as a promising avenue corundum to monoclinic31,32. Recent experiments have shown that towards a new generation of faster and more efficient the coherent lattice displacement generated by perturbing the technologies1. Phenomena associated with lattice dynamics electronic distribution of strongly correlated metallic phase of V2O3 are often analogous to well-known effects involving electrons, for through ultrafast light excitation can drive both longitudinal example chirality and the phonon Hall effect2–4. Moreover, acoustic waves and optical phonons33–37. In these photoexcitation control over coherent phonons offers potential new pathways to processes, the electron-phonon coupling plays a central role in the drive transitions between phases in condensed matter and to transient atomic displacement of the structure38. coherently manipulate the ground state of magnetically ordered Figure 1a shows the schematic electronic energy levels for the phases5–11. While coherent acoustic phonon modes are com- metallic phase of V2O3. The Fermi energy crosses the partially filled monly generated by wide variety of mechanisms12, higher- a1g and eπg bands, enabling the direct optical absorption of THz light frequency coherent optical phonon modes are typically driven by intraband electronic transitions31,32. The Γ-point structural from interactions with intense sub-picosecond light pulses13. dynamics in this phase is largely dominated by a fully-symmetric In most cases, light pulses can drive optical phonons either A1g optical phonon mode at Ω/2π = 7.1 THz, which corresponds to directly via resonant electric-dipole interaction14,15, or indirectly the optical bending mode of the V2O2 unit cell [see displacement via interactions with electronic states or other phonon vectors in Fig. 1b35,39]. Other Raman-active optical phonons in this modes10,16–18. The latter case is a generalization of the stimulated frequency range, for example the Eg phonon mode at ~ 6 THz39, Raman mechanism, in which the ultrashort light pulse couples to have a comparatively lower Raman cross-section, as detailed in the the electronic system resulting in a nonlinear force on the lattice Supplementary Note 3 and Supplementary Fig. 4. that resonantly drives coherent phonon modes at the difference To study the possibilities for driving coherent structural frequency mixing Ω = ω1 − ω2, with ω1 and ω2 taken for the dynamics in V2O3, we performed ultrafast THz pump-optical pulse spectrum. This is commonly referred to in the literature as probe spectroscopy (scheme shown in Fig. 1c). Intense quasi either Impulsive Stimulated Raman Scattering (ISRS), when the single-cycle THz pulses were focused onto the sample. The THz- light field is non-resonantly coupled to the electric system (in induced response was monitored by measuring the optical optically transparent solids), or Displacive Excitation of Coherent transmission modulation ΔT/T of a near-infrared (NIR) laser Phonons (DECP), when the light pulse is resonant with intraband probe at 1.55 eV as a function of the time delay tpp with respect to or interband electronic transitions (in opaque solids)19–23. Unlike the pump25,40. The ΔT/T response is able to detect the coherent ISRS, which involves non-resonant coupling to electronic states to lattice oscillations from the fully-symmetric A1g via time- produce impulsive excitation, in the DECP regime, coherent dependent modulation of the diagonal elements of the linear phonons are generated by a displacive force associated with a optical susceptibility tensor, while it is insensitive to the Eg modes, sudden change in carrier density or electronic temperature which effect the probe polarization state through the modulation induced by the intense light pulse. A third generation mechanism of the off-diagonal elements of the susceptibility tensor (see is called Ionic Raman scattering (IRS) and involves a higher detailed discussion in Supplementary Note 4). frequency phonon mode that serves as the intermediate18. In all The temporal waveform of the THz pump electric field E(t) (see these processes, the driving mechanism involves difference- Fig. 1d) was measured at the sample position using electro-optic frequency mixing, and requires the bandwidth of the driving light sampling from a GaP crystal (see Supplementary Methods). The pulse to be comparable to or larger than the frequency of the center frequency of the pump is νp ≃ 3.5 THz. The sample is a high- optical phonon mode that is to be excited24. quality, 84 nm thick V2O3 thin film epitaxially grown on an R-plane As an alternative to these well-established routes for coherent (1 -1 0 2) − Al2O3 substrate (see Methods). Figure 1e shows the phonon generation using stimulated Raman schemes, it is also temporal evolution of the THz-induced transmission modulation possible to drive coherent Raman-active vibrational modes using ΔT/T. The time origin (tpp = 0) is set to the delay where the optical sum-frequency excitation (SFE)25,26. Recent experiments, indeed, probe interacts with the sample at the same time as does the peak of have demonstrated both photonic and phononic SFE the square of the pump electric field ∣E(t)∣2. The observed THz- mechanisms25,27–30, which involve the absorption of two photons induced dynamics are dominated by coherent oscillations super- or two phonons with frequencies ω1 and ω2 to create one phonon imposed to a gradually increasing slowly-varying background. This in a Raman-active mode at frequency Ω = ω1 + ω2, as up- long-lived step-like evolution of ΔT/T is attributed to incoherent conversion counterparts of ISRS and IRS, respectively. dynamics of the electronic thermalization through electron-phonon Here, we demonstrate an alternative scheme for coherent scattering, as described in refs. 33,35. Strikingly, the oscillating generation of Raman-active phonon modes based on terahertz- component of ΔT/T clearly displays oscillations with a period driven dispacive excitation as up-conversion counterpart of the shorter than the one of the THz driving field. To better show this DECP mechanism. An intense THz pulse, inducing strong tran- feature, in Fig. 1f we compare the oscillatory component, obtained sient electronic excitation, is found to generate large-amplitude by subtracting the step-like background from ΔT/T, with the coherent oscillations of Raman-active phonon modes in the intensity profile of the THz field ∣E(t)∣2. The fitting procedure for the metallic phase of V2O3 at twice the frequency of the driving field. This nonlinear process can be described as a displacive excitation background subtraction is reported in the Supplementary Note 4 that involves the sum-frequency mixing component of the THz and consists of Gaussian function to describe the THz excitation and pulse coupled to the electronic system. The temperature depen- a step-like function for the electronic relaxation dynamics as dence of the generated coherent phonons supports the scenario in observed in refs. 33,35. To demonstrate that coherent oscillations which the excitation process is strongly enhanced by intra-band originate from the V2O3 thin film, we conducted the same electronic transitions driven by the intense THz field. experiment on the bare R-plane Al2O3 substrate showing that there are neither oscillations nor a long-lived signal in the ΔT/T dynamics, see Fig. 1f and Supplementary Note 2 for details. Furthermore, from Results Fig. 1f we note that the envelope function of the oscillatory response Coherent phonon oscillations detected by THz pump – near- does not merely follow that of ∣E(t)∣2, but instead persists well infrared probe spectroscopy. In V2O3, strong electronic correla- beyond the times when the THz pulse intensity is negligible. This tions cause a metal-insulator transition (MIT) at TMIT ≃ 150 K, strongly suggests that the oscillations are indeed due to a coherent which is accompanied by a first-order structural transition from excitation of the A1g mode in V2O3 at its resonance frequency39. 2 COMMUNICATIONS PHYSICS | (2022)5:103 | https://doi.org/10.1038/s42005-022-00882-7 | www.nature.com/commsphys COMMUNICATIONS PHYSICS | https://doi.org/10.1038/s42005-022-00882-7 ARTICLE Fig. 1 Coherent phonon generation by terahertz electronic excitations in V2O3. a Energy level diagram for the paramagnetic metallic phase of V2O3 showing vanadium and oxygen energy levels. The Fermi energy EF crosses the partially filled a1g and eπg bands formed by vanadium 3d orbitals. O2p bands lie between 3.5 and 8.5 eV below EF while eσg is centered at ~ 3 eV above EF. Level diagrams adapted from ref. 32. b Phonon displacement vectors of the A1g phonon mode in V2O3. c Schematic of the setup for the THz pump-NIR probe experiment on V2O3 thin film on R-plane Al2O3 substrate to investigate the THz driven coherent lattice dynamics: intense THz pulse (green) excites the A1g phonon mode, whose coherent dynamics are probed by a temporally delayed ultrashort optical pulse (red). d Waveform of THz pump electric field. The peak electric field is 6.5 MV/cm. e Probe transmission modulation signal ΔT/T as a function of the pump-probe delay tpp. The THz pump pulse induces coherent lattice oscillations related to the fully-symmetric A1g phonon at approximately twice the frequency of the driving electric field. The red curve represents the experimental data. Gray curve represents the slowly-varying background as determined by double-exponential relaxation fitting procedure (see Supplementary Note 4). f Light-blue curve shows the oscillatory component of ΔT/T time-trace of V2O3 on R-plane Al2O3 after subtracting the background. Orange curve is the ΔT/T dynamics of the bare R-plane Al2O3 substrate measured in the same experimental conditions. The purple curve shows the intensity profile ∣E(t)∣2 of the THz pump. Sample is at 300 K. Such effect is clearly visible in the frequency domain where driven electronic excitation. We propose that the interaction of Fourier amplitude of the observed optical transmission oscilla- the THz-frequency pulse with the metallic phase of V2O3 first tions show a narrow response where the pump spectrum has a leads to the excitation of a time-dependent electronic distribution negligible amplitude (Fig. 2a, b). The spectrum of the oscillatory η(t) in the conduction bands. The time-domain dynamics of η(t) component peaks at the A1g phonon frequency measured by by THz excitation are described by: Raman spectroscopy, which matches the double of the frequency Z 1   of the driving field (Fig. 2c). As one can see, the spectrum of the ηðtÞ ¼ κ E2 ðt  τÞ eβτ þ c dτ; ð1Þ A1g Raman spectrum shows a narrower line shape than the 0 frequency response of the oscillations of the transmission where E(t) is the electric field temporal waveform of the THz modulation (Fig. 2b), because its spectral contents also depend pump pulse, 1/β is the fast electronic relaxation rate after the THz on the frequency of the pump stimulus, which give rise to further excitation and c accounts for long-lived thermalization dynamics broadening. This effect is also observed in V2O3 with conven- that last longer than 2 ps as also observed in V2O3 by optical tional pump-probe optical spectroscopy36. Furthermore, to pump-probe spectroscopy36,39. The excited electronic states exclude the contribution of other modes to the observed interact with the A1g lattice mode via electron-phonon coupling dynamics, we repeated the experiment on a V2O3 thin film and, in a semi-classical picture, they exert an effective force on the deposited on a C-plane (0001) Al2O3 substrate, whose orientation A1g mode that has a time-dependence given by the intensity of results in a diagonal susceptibility tensor allowing only for the the THz light field. According to general theory of DECP (see fully-symmetric A1g modes to be detected (see Supplementary ref. 22), the effective force acting on the lattice associated with the Note 3). The pump-probe dynamics of this sample also shows electronic perturbation due to the intense time-varying electric coherent oscillations peaked at the frequency of the A1g phonon field E(t) leads to the following equation of motion for the pho- mode (see Supplementary Fig. 5), further demonstrating that the non displacement field: phonon generated by the THz excitation is the A1g mode. € þ 2γQ_ þ Ω2 Q ¼ αηðtÞ; Q ð2Þ Figure 2d shows the dependence of the oscillation amplitude A on the electric field amplitude E0 of the incident THz field. The where Q is the normal coordinate of the A1g phonon, Ω/2π the 2 dependence is well described by a quadratic trend A ¼ aðE0 Þ phonon eigenfrequency, γ/2π the phonon damping rate36,39 and proving that the mode is nonlinearly coupled to the driving α the coupling constant. We model the THz-induced transmis- electric field. Moreover, as the spectral content of the pump pulse sion modulation as the sum of the lattice and electronic con- contains negligible intensity above 5 THz, we exclude a linear tributions [Eqs. (1) and (2)], as described in ref. 22: (dipolar) coupling of light to the lattice mode, which is in any case symmetry-forbidden since the mode is purely Raman active. ΔT=Tðt pp Þ ¼ AQðt pp Þ þ Bηðt pp Þ; ð3Þ with A and B multiplying constants. THz displacive excitation of phonons. Next, we discuss the Under this assumption, from Eq. (3) we calculated numerically nonlinear excitation mechanism of the vibrational modes by THz the time-evolution of the transmission modulation dynamics COMMUNICATIONS PHYSICS | (2022)5:103 | https://doi.org/10.1038/s42005-022-00882-7 | www.nature.com/commsphys 3 ARTICLE COMMUNICATIONS PHYSICS | https://doi.org/10.1038/s42005-022-00882-7 Fig. 2 THz field-driven lattice phonon oscillations in frequency domain. a Normalized spectral amplitude (Norm. sp. ampl.) of the THz pump pulse in Fig. 1d (green solid curve) and same spectrum with 2x frequency (green dashed curve). b Fourier transform of the oscillatory component of ΔT/T for tpp > 0.4 ps (blue curve). c Raman spectroscopy of V2O3 thin film at 300 K. Light blue dots are experimental data and light solid curve is the fit curve, which contains different spectral components: two Eg modes and the A1g. The red curve is lineshape of the A1g phonon, which is peaked at 7.1 THz. Vertical offset of -0.5 has been added to the experimental data for the overlap with the A1g phonon lineshape. Data without offset is shown in Supplementary Fig. 4 and discussed in Supplementary Note 3. d Normalized oscillations amplitude (Norm. osc. ampl.) vs the normalized (Norm.) THz field strength, E0/Epeak, with Epeak = 6.5 MV/cm. The amplitude scales quadratically with the pump electric field (the light blue solid line represents a quadratic fit). Error bars indicate the standard deviations of the mean determined from pump-probe scan measurements with 15 acquisitions per point. Fig. 3 Modelling of terahertz displacive excitation of phonons. a Experimental data at 300 K and b, numerical calculation using Eq. (3) using phononic and electronic parameters of V2O3 at 300 K. c Comparison of the time derivative of the dynamics: experimental data (red curve) and numerical calculation (light blue curve), both normalized to the value at tpp = 0. d Calculated electronic (blue curve) and lattice (red curve) contributions to the ΔT/T dynamics from Eq. (3). The electron dynamics show no signature of long lived oscillatory components. e Time-derivative of the lattice dynamics Q(t) in frequency domain calculated by displacive excitation of coherent phonons (DECP) model [Eq. (2)] as a function of the center frequency ω0/2π of the driving THz field. Temporal derivative is shown to emphasize the oscillatory component over the slowly-varying background. The phonon amplitude is maximum when Ω = 2ω0. The black curve is the A1g phonon lineshape as a function of the lattice frequency ωQ/2π. ΔT/T(tpp) by using the experimental THz driving field shown in Furthermore, we compute the lattice dynamics Q(t) by DECP Fig. 1c and the following A1g phonon parameters Ω/(2π) = 7.1 THz, model (Eq. (2)) as a function the driving frequency of THz pump. γ/(2π) = 0.5 THz obtained by Raman spectroscopy (see Supple- The numerical calculation of Q(t) is performed for multiple mentary Note 3 and Supplementary Table 2). For the fast electronic Gaussian THz pulses with a full width half maximum of 0.5 THz relaxation dynamics after the THz excitation we set 1/β = 80 fs in and center frequency ω0/2π, spanning from 1 to 10 THz with a agreement with ref. 35; For the electron-phonon relaxation dynamics frequency step of 0.125 THz. In Fig. 3e, we show the temporal we set c = 0.2 and B/A = 0.002 to fit the amplitude of the derivative of Q(t) in frequency domain, which shows a maximum experimental data. As expected from the numerical result of Eq. (3), when THz driving frequency ω0/2π is half of the phonon the calculated dynamics by DECP model exhibits coherent lattice frequency ωQ/2π as described by SFE, while no excitation is oscillations at twice the frequency of the electric field (Fig. 3a, b) observed in resonant condition ωQ = ω0/2π. and a step-like dynamics in agreement with the experiment, as also shown by the comparison of the corresponding time derivatives, see Fig. 3c. Figure 3d shows both the calculated electronic and lattice THz-induced dynamics across the temperature driven components of the dynamics from Eq. (3). As observed, the insulator-to-metal transition. We now consider the temperature electronic dynamics has no long-lasting oscillating features. dependence of the oscillatory response. Figure 4a shows the phase 4 COMMUNICATIONS PHYSICS | (2022)5:103 | https://doi.org/10.1038/s42005-022-00882-7 | www.nature.com/commsphys COMMUNICATIONS PHYSICS | https://doi.org/10.1038/s42005-022-00882-7 ARTICLE Fig. 4 Temperature evolution of the sum-frequency excitation across the insulator to metal transition. a Temperature vs doping phase diagram of V2O3 according to ref. 44. The empty circles denote the values of the temperature measured in the present work. b Temperature dependence of the THz pump induced optical transmission modulation in V2O3. When the THz pulse interacts with the insulating Mott phase, no prominent signatures of lattice oscillation are observed. TMIT indicates the metal-isulator transition temperature, while Tch is the quasiparticle coherence temperature. c Pump-probe traces at selected temperatures. d, e Temperature dependence of the maximum oscillations amplitude (Max. osc. ampl.) d, and the real part of THz optical conductivity σ1 e of V2O3. THz optical conductivity of the V2O3 film as a function of temperature was measured using Fourier-transform infrared spectroscopy in the THz range (see Supplementary Note 1). The color shading of d, e divides insulating phase and metallic phase. Error bars indicate the standard deviations of the mean determined from pump-probe scan measurements with 15 acquisitions per point. diagram of ðV1x Mx Þ2 O3 , where the dopant M is either Cr or Ti. structure across the different phases. We can, however, qualita- We drive the temperature across the metal-to-insulator transition tively understand the data shown in Fig. 4d, e by noting that the at x = 0. The temperature evolution of ΔT/T(tpp) across the MIT THz generated displacive force on the lattice coordinate (see Eq. is shown in Fig. 4b for various temperatures between 77 K and (1) and ref. 22) is proportional to the deposited THz energy which 500 K. In the insulating phase (T < TMIT) the transmission is, in turn, proportional to the real part of the optical conductivity modulation displays a negative step-like component (see Fig. 4c) σ1 according to the Joule heating model: ∫σ1E2(t)dt, being the due to a partial formation of the metallic phase by the intense imaginary part σ2 of metallic phase negligible in the THz range45. THz field41,42. However, the amplitude of coherent lattice Therefore the temperature trend of the phonon amplitude and of vibrations is strongly reduced in the insulating phase (see Fig. 4d σ1 further supports the interpretation that the underlying gen- and Supplementary Fig. 7). In contrast, as the temperature eration mechanism is displacive rather than impulsive in nature. approaches the MIT, we observe an emerging oscillatory signal at 2ωp/2π, which denotes that the phonon excitation mechanism becomes efficient when the THz pump is resonant with the Discussion conduction states. By further increasing the temperature, the We propose the following scenario to describe the mechanism for transmission modulation response rapidly decreases above the the nonlinear generation of a coherent A1g phonon mode in V2O3. coherence temperature (Tch ~ 400 K), see Fig. 4d. This may be due First, the incident THz field drives primarily intraband transitions in to the suppression of the optical conductivity by means of the the a1g electronic band of 3d vanadium orbitals having the dominant enhanced scattering rate of the electrons in the correlated elec- contribution in the Drude spectral weight compared to the ones tronic phase of V2O3 at TMIT < T < Tch43,44. The amplitude of the from the eπg band32. These newly populated states exert an effective oscillations versus the temperature strongly recalls the THz force on the ions, driving a coherent A1g symmetry mode. Okamoto optical conductivity, as shown in the Fig. 4d, e. At present, an et al.39 have shown that Raman intensity of A1g phonon modes are accurate model describing the transmission modulation response dominated by the electronic occupancy of a1g band mediated by as a function of the temperature is still lacking, as it must account electron-phonon coupling39,46,47. Phenomenologically, the sum fre- for the evolution of both the electronic phase and the lattice quency excitation of the phonon mode in metallic V2O3 can be COMMUNICATIONS PHYSICS | (2022)5:103 | https://doi.org/10.1038/s42005-022-00882-7 | www.nature.com/commsphys 5 ARTICLE COMMUNICATIONS PHYSICS | https://doi.org/10.1038/s42005-022-00882-7 explained because the intense THz transient can temporally control 4. Moya, X. & Mathur, N. D. Caloric materials near ferroic phase transitions. the electronic distribution by intraband transitions in the a1g bands, Nat. Mater. 13, 439 (2014). proportional to the THz intensity, leading to the coherent up- 5. Rini, M. et al. 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Transport properties and c/a ratio of V2O3 thin films grown on C- and R-plane sapphire substrates by pulsed laser Open Access This article is licensed under a Creative Commons deposition. Appl. Phys. Lett. 107, 241901 (2015). Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party Acknowledgements material in this article are included in the article’s Creative Commons license, unless We thank Lara Benfatto for the fruitful discussion and for critical reading of the indicated otherwise in a credit line to the material. If material is not included in the manuscript. We are grateful to Hans-Heinrich Braun, Carlo Vicario and the PSI-LNO article’s Creative Commons license and your intended use is not permitted by statutory group for support. We acknowledge financial support by Swiss National Science Foun- regulation or exceeds the permitted use, you will need to obtain permission directly from dation project no. IZLRZ2_164051, by MAECI under the Italian-India collaborative the copyright holder. To view a copy of this license, visit http://creativecommons.org/ project SUPERTOP-PGR04879 and by EC FP7 Graphene Flagship Project No. licenses/by/4.0/. CNECTICT-604391. The research was supported by the NCCR MUST, founded by the Swiss National Science Foundation, and by ERC Grant Hyper Quantum Criticality (HyperQC). MR and MC acknowledges the support of SNF Project No. 200021_182695. © The Author(s) 2022 COMMUNICATIONS PHYSICS | (2022)5:103 | https://doi.org/10.1038/s42005-022-00882-7 | www.nature.com/commsphys 7