# Foreword: Ultrafast Phenomena in condensed matter physics

Eric Collet, S. Ravy

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## To cite this version:

Eric Collet, S. Ravy. Foreword: Ultrafast Phenomena in condensed matter physics. Comptes Rendus. Physique, 2021, 22 (S2), pp.3-14. 10.5802/crphys.88 . hal-03556788

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# Comptes Rendus
Physique

Eric Collet and Sylvain Ravy

## Foreword: Ultrafast Phenomena in condensed matter physics

Volume 22, issue S2 (2021), p. 3-14

<https://doi.org/10.5802/crphys.88>

## Part of the Special Issue: Physics of ultra-fast phenomena

Guest editors: Éric Collet (Université Rennes 1, CNRS, France) and Sylvain Ravy (Université Paris-Saclay, CNRS, France)

© Académie des sciences, Paris and the authors, 2021.

Some rights reserved.

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This article is licensed under the

CREATIVE COMMONS ATTRIBUTION 4.0 INTERNATIONAL LICENSE.

http://creativecommons.org/licenses/by/4.0/
Foreword / Avant-propos

# Foreword: Ultrafast Phenomena in condensed matter physics

## Avant-propos : Phénomènes ultra-rapides en physique de la matière condensée

Eric Collet<sup>●*</sup>,<sup>a</sup> and Sylvain Ravy<sup>●*, b</sup>

<sup>a</sup> Univ Rennes, CNRS, IPR (Institut de Physique de Rennes) - UMR 6251, F-35000 Rennes, France

URL: https://ipr.univ-rennes1.fr/interlocuteurs/eric-collet

<sup>b</sup> Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405, Orsay, France

URL: https://www.lps.u-psud.fr/spip.php?article531

E-mails: eric.collet@univ-rennes1.fr (E. Collet), sylvain.ravy@universite-paris-saclay.fr (S. Ravy)

**Abstract.** Matter is dynamic and changes under the effect of various external constraints, in particular light. The development of ultra-fast techniques now makes it possible to study the elementary mechanisms of ultrafast photoinduced phenomena, in particular by following the dynamics of electronic and structural degrees of freedom of matter. These studies provide a better understanding of these non-equilibrium processes in order to control the physical properties of molecules and materials by light. In this introductory article we discuss different aspects of studying ultra-fast condensed matter phenomena.

**Résumé.** La matière est dynamique et se transforme sous l'effet de différentes contraintes extérieures, en particulier la lumière. Le développement de techniques ultra-rapides permet à présent d'étudier les mécanismes élémentaires de phénomènes photoinduits ultra-rapides, en particulier en suivant les dynamiques des degrés de libertés électroniques et structuraux de la matière. Ces études permettent de mieux comprendre ces processus hors équilibre pour envisager un contrôle des propriétés physiques de molécules et matériaux par la lumière. Dans cet article d'introduction nous abordons différents aspects de l'étude de phénomènes ultra-rapide en matière condensée.

**Keywords.** Condensed matter, Molecules, Materials, Ultra-fast phenomena, Out-of-equilibrium, Spectroscopies, Diffraction.

**Mots-clés.** Matière Condensée, Molécules, Matériaux, Phénomènes ultra-rapides, Hors équilibre, Spectroscopies, Diffraction.

<footnote>* Corresponding authors.</footnote>
For understanding the physical properties of molecules or materials, it is necessary to investigate how the constituting degrees of freedom (spin, charge, orbital, molecular structure or crystalline packing, Figure 1) equilibrate and get ordered at microscopic scales. At thermal equilibrium, these orders may change under the effect of external parameters such as pressure and temperature, which may transform molecules or drive phase transitions. More recently, new challenges have emerged to direct the functionality of condensed matter, as excitation with an ultrashort laser pulse allows for driving ultrafast photoinduced molecular transformations or phase transitions. Advances in sophisticated technologies and instrumentation in ultrafast science make it now possible to drive ultrafast transformations by stimulating selectively a responsive degree of freedom [1, 2]. In addition, various time-resolved techniques allow for probing selectively the ultrafast and out-of-equilibrium dynamics, the equilibration and the coupling of different degrees of freedom coming into play [3–8]. Directing the functionality of materials towards a desired outcome at the relevant length, time and energy scales is a current challenge in materials' science.

Watching the elementary processes driving the transformation of matter, including electronic and structural dynamics, requires the use of techniques with a temporal resolution approaching the femtosecond range (1 fs = $10^{-15}$ s) with sub-Ångström spatial resolution. In this way, A. H. Zewail pioneered femtochemistry by developing fs pump-probe spectroscopy to study photochemical processes [9]. Pump-probe techniques use a pump laser pulse to trigger the transformation of molecules or materials and a probe pulse to measure the state of the system at a given time $t$ after photo-excitation (Figure 1).

The last decades witnessed unprecedented controls of Photo-Induced Phase Transitions (PIPT) [1] through the use of femtosecond (1 fs = $10^{-15}$ s) UV or visible laser pulses, which excite and reorganize electronic structure and modify the equilibrium atomic coordinates in the crystalline structure. The pumping energy determines the excited degrees of freedom: optical (≈1 eV) photons mainly cause inter-band electronic transitions, whereas mid-IR or THz excitations (≈1–100 meV) can resonantly activate phonon modes. These two kinds of excitations are fundamentally different: the first one promotes the system to an electronically excited state, whereas the second modifies the system within its electronic ground state. Pump-probe experiments spread over a growing community of scientists studying ultrafast phenomena, as new technological developments allow for generating not only ultrashort electromagnetic pulses in the THz, infrared (IR), visible (VIS), ultraviolet (UV) and X-ray range but also pulses of electrons [1, 4, 10–14]. Optical pump-probe spectroscopies, using IR, VIS or UV pulses are home-based experiments that can now routinely operate on a daily basis. However, radiation in the IR–VIS–UV domain does not provide information about the evolution of the atomic structure of matter, except in rare cases of simple systems for which the dependence of potential energy curves on the structural dynamics is known. It was therefore necessary to develop ultra-short pulses of X-ray or electron to perform measurements allowing for watching directly structural dynamics [4, 5, 15–19]. This broad spectrum of techniques allows now for monitoring the temporal evolution of the probed degrees of freedom on their intrinsic timescales, including spin, charge, molecular, lattice and crystalline structure.

Delocalized optical electronic excitation has been studied in hard-condensed matter, with insulators and semi-metals for example. This process modifies the relative electronic population of bonding and anti-bonding bands and the fraction of excited electrons $n_e$ is the control parameter that can continuously reshape the potential energy surface (PES, Figure 2a) because the ultrafast thermalisation of electrons modifies the Fermi-Dirac distribution. This drives collective degrees of freedom of the lattice, such as an optical lattice phonon mode $Q_L$, moving the system over long-range order to a new equilibrium structure. The study of the excitation of the coherent phonon in Bismuth was an important step in the development of ultrafast science [14,20–22]. The crystalline
<figure><img src="image_4.png" /><figcaption>**Figure 1.** Schematic representation of different degrees of freedom involved in photoin- duced processes. Pump-probe techniques allow for monitoring in time the evolution of a degree of freedom.</figcaption></figure>

structure of Bismuth is rhombohedral, with two Bi atoms per unit cell, packed along the large di- agonal of the cell with alternating short (X) and long (1 − X) Bi–Bi interatomic distances. This equilibrium crystalline structure is governed by the electronic population of more or less bond- ing states (Figure 2a). The optical excitation of Bi populates less bonding electronic states, which modifies the equilibrium distance X. The inter-atomic potential is mainly governed by the ther- malization of the electrons, which occurs on a fast timescale. Therefore, after photoexcitation, the potential is changed on a timescale much shorter than the phonon period and the atoms move coherently towards the new equilibrium position. The activation and damping of this co- herent phonon QL were investigated by various techniques sensitive to the change of electronic state and/or structure [14, 20, 21, 23]. A thermodynamical model based on the two-temperature approach, the one of the electrons and the one of the lattice, evidenced that the coherent atomic motion is and entropy-driven process [24]. In addition, a lattice instability may appear above the critical value ne > nc as the PES changes from double to single well, i.e. towards a higher symme- try. However, such processes require a lot of energy: the initial electronic temperature can reach 1000 K. In addition, only a small amount of the optical energy is coherently transferred to QL because of energy transfers through electron–phonon and phonon–phonon couplings towards many other degrees of freedom. For some systems, structural reorganization along QL can switch physical properties from insulating to metallic state for example [25] and even towards hidden phases [26].

Similar coherent structural dynamics was reported in molecular crystals. The family of (EDOTTF)₂XF₆ systems, where X stands for counter anions As, Sb or P, corresponds to 1/4 filled
<figure><img src="image_5.png" /><figcaption>**Figure 2.** (a) PIPT driven by electronic excitation for delocalized electronic population of antibonding bands modifies the equilibrium of the lattice along $Q_L$. (b) Electronic excitation localized at the molecular level results in another PES for the new electronic state with different equilibrium structure of the molecule along $Q_M$.</figcaption></figure>

molecular conductors (in terms of holes), which exhibit charge order in the insulating low temperature phase [27, 28] and the associated symmetry breaking corresponds to a doubling of the unit cell as neutral-bent and ionic-flat (EDOTTF)₂ dimers alternate. Those materials display a gigantic response to femtosecond laser excitation in the insulating phase, modulating so optical reflectivity up to 120%. The dynamics is associated with coherent structural reorganization and time-resolved electron diffraction evidenced the molecular motions involved in the process [29]. This is also the case for the molecular crystal $Me_4P[Pt(dmit)_2]_2$ [6], which exhibits a photoinduced charge transfer. Femtosecond electron diffraction studies allowed one to directly observe the coherent molecular motions involved in the process, and clearly identified them as due to a dimer expansion and a librational mode.

PIPTs driven by optical excitation were studied in molecular materials. Some initial processes are local and can be described at the molecular scale. The molecular entity is here the relevant building block: different and discrete PES correspond to discrete molecular electronic states (Figure 2b). The excitation from a ground state (black) to an electronic excited state (blue) may decay and be trapped in a less bonding and metastable state (red) by the structural reorganisation along a molecular mode $Q_M$. The coupling between electronic excitation and structural reorganisations is also an important aspect responsible for the appearance of light-induced excited spin state trapping (LIESST) in many transition metal complexes with electronic configuration $d^4-d^7$ and capable of spin crossover [12, 30, 31]. In these bistable molecular materials, the metal bonded to the ligand (L) may have two spin states in the case of a $d^6$ configuration: the LS state of electronic configuration ($S = 0, t_{2g}^6 e_g^0 L^0$) and the HS state ($S = 2, t_{2g}^4 e_g^2 L^0$). The LIESST effect consists in exciting by light a system in the LS state in order to switch it to the HS state. The structural trapping of the photoinduced HS state occurs at the time scale of elementary atomic movements and involves a reorganization of the molecular structure, linked to the variation of the iron-ligand (Fe–L) bond length, which accompanies the population of anti-bonding $e_g$ states. X-ray absorption spectroscopy is a powerful technique for monitoring such local transformation occurring around the metal ion. A recent XANES study performed at the LCLS X-ray free electron laser
<figure><img src="image_6.png" /><figcaption>**Figure 3.** Evolution of the X-ray absorption signal (left) of a spin transition system after fs optical laser excitation, reprinted with permission from [12]. The signal decomposes in terms of electronic state change and structural dynamics with the evolution of the Fe–L distance *r* (right).</figcaption></figure>

(X-FEL) [12] with a temporal resolution of ~25 fs, made it possible to directly observe the co-herent structural dynamics of the ligand during the LIESST effect (Figure 3). XANES also allowed for discriminating the mean change of electronic state and the structural dynamics. The optical excitation $t_{2g} \rightarrow L$ induces a state of metal-ligand charge transfer (MLCT $t_{2g}^5 e_g^0 L^1$), and this change from $Fe^{2+}$ to $Fe^{3+}$ decreases the absorption of X-rays. This state then relaxes towards the HS state via activation and damping of the breathing mode, corresponding to an elongation of the Fe–L bonds, which is characterized by an increase and oscillation of the X-rays absorption. It is then possible to disentangle the electronic and structural dynamics, as shown in Figure 3.

Some molecular systems exhibit intermediate situation, in which the electronic excitation involves several molecules. This is the case for charge-transfer systems undergoing insulator-metal [6] or para- to ferroelectric [32] phase transitions. The past 15 years witnessed development of a broad and expanding spectrum of complementary optical and X-ray techniques, including spectroscopy and diffraction [4]. These techniques have delivered new insights into the dynamics of molecular systems and solids, by investigating how an ultrafast and intense optical pulse drives the transformation process, and how electronic and structural degrees of freedom are coupled, and evolve in real time. For condensed matter, the topics concern a broad variety of mechanisms including coherent structural dynamics [4, 6, 12, 31, 32], cooperative transformation [30], charge-orbital orders [33], etc.

A recent study of a photomagnetic CoFe Prussian blue analogue investigated how coupled charge-transfer and spin transition evolve in time [34]. These systems are coordination networks where cyanide groups connect the Co and the Fe ions in octahedral crystal fields. There are two bistable electronic-structural configurations (Figure 4) linked to a charge transfer (CT) between Fe and Co: the ground $Co^{III}$ (S = 0) $Fe^{II}$ (S = 0) state or the photoinduced $Co^{II}$ (S = 3/2) $Fe^{III}$ (S = 1/2). In the HS $Co^{II}Fe^{III}$ state, the population of anti-binding Co ($e_g$) orbitals lengthens Co–N bonds by ≈0.2 Å and this spin transition (ST) on the Co is the main reaction coordinate. The photoinduced
<figure><img src="image_7.png" /><figcaption>**Figure 4.** Photomagnetic transition between low and high spin states [34]. XANES spectroscopy measurements show that it is the photoinduced spin transition (ST) around the Co, occurring within ~50 fs as observed at 7770 eV, which induces the charge transfer (CT) within ~200 fs, as observed around the Fe edge (7152 eV), thus following the transformation path STICT.</figcaption></figure>

Fe → Co charge transfer process remained inaccessible and it was then considered that the path followed during the transformation is a photoinduced charge transfer, which induces its turn the spin transition (CTIST transformation lane). The time-resolved XANES measurements performed at the X-FEL LCLS with ≈25 fs time resolution allowed probing selectively the dynamics of electronic and structural degrees of freedom around Fe and Co ions [34]. These results provided a direct insight into electronic and structural dynamics: the Co<sup>III</sup> ($t_{2g}$) → Co<sup>III</sup> ($e_g$) optical excitation induces the spin transition on Co and elongates the Co–N bonds within ≈50 fs, as characterized by a rapid variation in absorption above the threshold Co (7770 eV, Figure 4). XANES, which is a technique of choice for measuring changes in the oxidation state of metals, revealed that the Fe → Co (CT) charge transfer takes place in a second step within ≈200 fs, as characterized by the spectral shift at the Fe absorption edge (7152 eV). These results provide a clear answer to a question debated for decades, by demonstrating that in this photoexcited prototype CoFe compound, the transformation pathway is a photoactivated spin transition, which induces charge transfer (STICT in Figure 4).
<figure><img src="image_8.png" /></figure>

**Figure 5.** (a) Crystalline structure of RbMnFe PBA in the cubic HT phase. (b) Schematic valence states and electronic configurations in the LT Mn<sup>III</sup>Fe<sup>II</sup> and HT Mn<sup>II</sup>Fe<sup>III</sup> phases. (c) The Mn<sup>III</sup>Fe<sup>II</sup> → Mn<sup>II</sup>Fe<sup>III</sup> charge transfer, populating the antibonding Mn *d*(*x*<sup>2</sup> − *y*<sup>2</sup>) state, is stabilized by the reverse Jahn–Teller distortion elongating Mn–N bonds along *a* and *b* and shrinking the ones along *c*. (d) Schematic representation of the lattice expansion in the (*a*, *b*) plane distortion due to the CT small-polaron. (e) The CT populates the Mn *d*(*x*<sup>2</sup> − *y*<sup>2</sup>) state and is self-trapped by Mn–N bond elongation. Reprinted with permission from [35].

RbMn[Fe(CN)₆] Prussian blue analogues also exhibit diverse CT-based functionalities [36–38]. The additional complexity comes the fact that the bistability between the high-temperature cubic (HT) Mn¹¹(S = 5/2)Fe³³(S = 1/2) state and the low-temperature (LT) Mn³³(S = 2)Fe¹¹(S = 0) state is also coupled to a symmetry breaking towards a tetragonal lattice, due to Jahn–Teller distortion around the Mn³³ [39, 40]. Since CT couples to Jahn–Teller distortion, the nature of the photoinduced process was questioned: is it a Jahn–Teller-induced CT or a CT-induced structural trapping? Femtosecond optical pump–probe spectroscopy revealed that two photoswitching pathways exist, depending on the excitation pump wavelength, which is confirmed by band structure calculations [41]. Photoexcitation of α spins corresponds to the Mn(d–d) band, which drives reverse Jahn–Teller distortion through the population of antibonding Mn–N orbitals, and induces CT within ~190 fs. Photoexcitation of β spins drives intervalence Fe → Mn CT towards non-bonding states and results in a slower dynamic. Time resolved X-ray diffraction studies also revealed the anisotropic out-of-equilibrium lattice dynamics triggered by the self-trapping of photo-induced Mn³³Fe¹¹ → Mn¹¹Fe³³ CT [35]. The observed dynamics evidenced a decoupling in time of the lattice expansion and the ferroelastic Jahn–Teller distortion. The anisotropic out-of-equilibrium lattice dynamics is triggered by the self-trapping of photo-induced Mn³³Fe¹¹ → Mn¹¹Fe³³CT. The impulsive lattice response is driven by the local Jahn–Teller reorganization, which elongates the *a* and *b* lattice parameters and shrinks the *c* axis (Figure 5). The structural reorganization is stabilized by a displacive volume expansion, controlled by the long-lived
photo-induced CT small-polarons. Indeed, CT populates the lowest unoccupied crystalline orbital, with electronic density highly localized on antibonding Mn(d<sub>x<sup>2</sup>-y<sup>2</sup></sub>) and N orbitals. This change of electronic state elongates Mn–N bonds in the (a, b) lattice plane and is therefore responsible for the anisotropic volume expansion.

Photoinduced phenomena are often multi-scale processes. The recent study by Mariette *et al.* [36], based on femtosecond X-ray diffraction experiments, revealed how electronic and structural precursor phenomena generate strain waves and coherent macroscopic transformation pathway for the semiconducting-to-metal transition in bistable Ti₃O₅ nanocrystals [42]. The authors have measured the lattice deformation in the photoinduced phase transition as a function of time, and monitored the intra-cell distortions around the light absorbing metal dimer and the long-range deformations governed by acoustic waves. The photoinduced phase propagates from the laser-exposed surface.

The scale of energy involved in optical excitation is the limiting factor in many of the previous studies. The energy difference between the starting and the final phases in bistable systems for instance is of the order of thermal energy ($k_B T < 30$ meV at $T = 300$ K), which is much lower than the energy of optical photons (eV) [1]. PIPTs driven by optical excitation are then often dominated by heat dissipation, which hinders establishment of ordered state or destroys the coherent dynamics. Temperature rise inevitably favors states of higher entropy and higher symmetry. Since emergence of functions like ferro-electricity is related to symmetry breaking, and hence to lower entropy states, a new suitable control method is required. By acting on lattice vibration modes at a resonant and relevant energy scale (10–250 meV), the nonlinear phononics (NLP) is a potential candidate method for tuning materials along a transformation pathway while allowing to circumvent the above-mentioned limitations (Figure 6). It preserves all advantages intrinsic to the ultrafast time-scales while alleviating the shortcomings of electronic excitations, whereby electron–phonon couplings are not controlled, and selectively activates a highly responsive phonon mode. NLP is based on a strong and resonant excitation of low-energy IR phonon $Q_{IR}$ (frequency $\Omega_{IR}$) by high-power femtosecond mid-IR lasers (1000 s·cm⁻¹). A. Cavalleri’s group demonstrated that NLP can favors superconductivity or drive insulator-metal transition [43–48]. According to the theory of nonlinear phononics developed by Subedi and Georges [43, 49] the intense laser field $F(t)$ of the IR pulse populates a significant quanta of $Q_{IR}$ phonons ($n \gg 1$) with large amplitude $\langle Q_{IR}^2 \rangle$. The non-linear coupling to a phonon mode $Q_{TS}$ moves its equilibrium position by $\propto F^2(\Omega_{IR}/\Omega_{TS})^2$. NLP allows then to tune the potential $V_{TS}$ along a transformation pathway, towards another phase of different structural-electronic orders. Some recent uses of NLP via mid-IR phonon excitations in hard condensed matter include large perturbations of orbital [50], magnetic [51–53] and ferroelectric [54] orders. Hence, NLP promises capabilities insofar unachieved in PIPT, as the ultrafast modification of the potential, occurring on a few $Q_{IR}$ phonon periods, will drive coherent and collective transformations.

The field of ultrafast phenomena in condensed matter is rapidly expending, with a large variety of topics and techniques, and this special issue perfectly illustrates this diversity. Recent advances allowing monitoring ultrafast phenomena are presented by Chong-Yu Ruan *et al.* for ultrafast electron diffraction and Michael Wulff *et al.* for X-ray techniques at synchrotron and X-FEL. Yoichi Okimoto *et al.* show how time-resolved Raman spectroscopy can be used to study the picosecond dynamics of the photo-excited charge-ordered perovskite-type cobalt oxides. Marino Marsi *et al.* present time-resolved Angle Resolved Photoemission Spectroscopy ARPES, which allows for visualizing directly on the femtosecond time scale the evolution of band dispersion of photoexcited solids. Stefan Haacke *et al.* revisit with optical spectroscopy the sub-picosecond photo-isomerization process. Claire Laulhé *et al.* use X-ray diffraction to investigate to ultrafast photoinduced dynamics of an incommensurate charge density wave in 1T–TaS₂. Alaska Subedi is reviewing the emerging field of non-linear phononics and its underlying theory.
<figure><img src="image_9.png" /><figcaption>**Figure 6.** Nonlinear phononics drives transformation in the electronic ground state: a highly excited $\langle Q_{IR}^2 \rangle$ anharmonically couples to a totally symmetric mode $Q_{TS}$, rectifies its potential $V_{TS}$ and drives a structural reorganisation by modifying the equilibrium position of $Q_{TS}$.</figcaption></figure>

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