# Volume Contraction Upon Resistive Switching in Cr-Doped V2O3 as a Key Mechanism for Mottronics Applications

Danylo Babich, Julien Tranchant, Coline Adda, Benoit Corraze, Marie-paule Besland, Peter Warnicke, Daniel Bedau, Patricia Bertoncini, Jean-yves Mevellec, Bernard Humbert, et al.

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## To cite this version:

Danylo Babich, Julien Tranchant, Coline Adda, Benoit Corraze, Marie-paule Besland, et al. Vol- ume Contraction Upon Resistive Switching in Cr-Doped V2O3 as a Key Mechanism for Mottronics Applications. Advanced Electronic Materials, 2025, 10.1002/aelm.202500077. hal-05340212

HAL Id: hal-05340212

https://hal.science/hal-05340212v1

Submitted on 31 Oct 2025

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# Volume Contraction Upon Resistive Switching in Cr-Doped $V_2O_3$ as a Key Mechanism for Mottronics Applications

Danylo Babich, Julien Tranchant, Coline Adda, Benoit Corraze, Marie-Paule Besland, Peter Warnicke, Daniel Bedau, Patricia Bertoncini, Jean-Yves Mevellec, Bernard Humbert, Jonathan Rupp, Tyler Hennen, Dirk Wouters, Roger Llopis, Laurent Cario,* and Etienne Janod*

The rise of the electronic age sparked a quest for increasingly faster and smaller switches, since this element is ubiquitous and foundational in any electronic circuit to regulate the flow of current. Mott insulators are promising candidates to meet this need as they undergo extremely fast resistive switching under electric field initiated by an avalanche phenomena. However, the nature of the final switched state is still under debate. The spatially resolved micro-X-ray Diffraction imaging and micro-Raman experiments carried out on the prototypal Mott insulator ($V_{0.95}Cr_{0.05}O_3$ show that the resistive switching is associated with the creation of a conducting filamentary path consisting in an isosymmetric compressed phase without any chemical or symmetry change. This strongly suggests that the avalanche initiated resistive switching mechanism is inherited from the bandwidth-controlled Mott-Hubbard transition just like the laser induced insulator to metal transition recently studied in the same system. This discovery may hence ease the development of a new branch of electronics called Mottronics.

## 1. Introduction

Much of the digital revolution that humanity is currently experiencing is due to the amazing development of a fundamental building block, the transistor. All key electronic components such as processors, volatile or non-volatile memories, running everyday objects like smartphones or computers are indeed based on the control of the conducting versus insulator state

of the transistor. However, the dimensional downscaling of this building block is now approaching fundamental limits giving an end to the Moore's law and to traditional means of development of the microelectronics industry. As a result, new concepts for system architecture[1] and new materials for information processing and memory are being explored to extend the historical pace of progress observed over the last half-century. One of the proposed solutions is Mottronics, i.e., the use of Mott insulators in microelectronic devices.[2-5] These materials were among the most studied ones during the last decades owing to their outstanding electronic properties.[6,7] However, an insulator to metal transition (IMT) driven by a control parameter compatible with microelectronics, i.e., the electrical pulse, has

only been demonstrated recently in Mott insulators. This property, called Electric Mott Transition, enabled the realization of breakthrough microelectronic devices, such as a Mott artificial neuron,[8,9] a key building block for unconventional computing, or a new class of non-volatile memories and selectors,[2,10] and thus gives hope in the realm of the Mottronics.

As reviewed in many articles[3,11-15] electric field may induce resistive switching in Mott insulators owing to three different

D. Babich, J. Tranchant, C. Adda, B. Corraze, M.-P. Besland, P. Bertoncini, J.-Y. Mevellec, B. Humbert, L. Cario, E. Janod
Nantes Université, CNRS
Institut des Matériaux de Nantes Jean Rouxel (IMN)
Nantes 44000, France
E-mail: laurent.cario@cnrs-imn.fr; etienne.janod@cnrs-imn.fr

The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/aelm.202500077

© 2025 The Author(s). Advanced Electronic Materials published by Wiley-VCH GmbH. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

DOI: 10.1002/aelm.202500077

P. Warnicke
microXAS Beamline, Center for Photon Science
Paul Scherrer Institute
Villigen PSI 5232, Switzerland

D. Bedau
Western Digital Co
HGST
San Jose, CA 95135, USA

J. Rupp, T. Hennen, D. Wouters
Institut für Werkstoffe der Elektrotechnik II and Jülich-Aachen Research Alliance on Fundamentals of Information Technology (JARA-FIT)
RWTH Aachen University
D-52056 Aachen, Germany

R. Llopis
CIC nanoGUNE
Tolosa Hiribidea 76, Donostia-San Sebastian 20018, Spain
mechanisms. The unipolar resistive switching observed in VO₂ involves for example a Joule heating effect that enables an insulator to metal transition between the low-temperature insulating phase and the high temperature metallic phase.[16] On the other hand, in some other transition metal oxides, a bipolar resistive switching is observed that is explained by a valence change mechanism. In this mechanism, the electric field induces an electromigration of oxygen and a concomitant reduction of the transition metals which can lead to the formation of a metallic filamentary path.[13] Finally, the last type of resistive switching observed in Mott insulators is unipolar and related to an avalanche phenomenon[17–21] In this work, we focus on this last type of resistive switching that is universal among Mott Insulators and that was already demonstrated in many systems like AM₄O₈, NiS₂·xSeₓ, V₂O₃·Cr, or molecular systems.[17,18,22–24] Despite some significant advances in the understanding of this resistive switching mechanism, the nature of the metallic phase that persists after the application of the electric pulse and the exact role of the electronic correlation in the transition are not fully elucidated.[25]

To tackle this issue we have studied the avalanche-type electric Mott transition in the emblematic Mott insulator (V₁ₓCrₓ)₂O₃ and we show that the main difference between the filamentary metallic phase and the insulating pristine material is an isosymmetric volume contraction of the lattice. Combining electronic transport, conducting-atomic force microscopy, Raman spectroscopy and micro-X-ray Diffraction (μ-XRD) measurements, we bring out the strong analogy between the compressed phase within the filament and the metallic phase stable under pressure beyond the Mott insulator to metal transition.[26] The mechanism of the avalanche-type Electric Mott transition seems therefore deeply related to the physics of the Mott-Hubbard insulator to metal transition.

## 2. Results and Discussion

Modern band structure theories of Mott insulators predict the occurrence of two types of insulator to metal transitions (IMT), induced either through a change of the electronic filling or of the bandwidth, with practical near equilibrium implementations with charge doping and pressure application.[27,29] Studies dedicated to out-of-equilibrium IMT's in correlated systems are more recent. The first evidence of insulator to metal transitions induced by electric field in Mott insulators dates back to the early 2000s[29] and the same phenomenology was found afterwards in numerous other narrow gap Mott insulators, including the prototypal Mott insulator systems (V₁ₓCrₓ)₂O₃.[30] In all these compounds, an electric field above a threshold value of a few kV/cm is able to break the Mott insulating state and to induce a resistive switching. Several theoretical or experimental studies have explained the destabilization of the Mott state thanks to an electronic avalanche effect[17,18,20,21,31] and have revealed that the subsequent resistive switching is unipolar and related to the formation of a metastable filamentary conducting path.[10,17,30,32] The stability in time of this filament depends on the electric pulse applied to the system. For pulses just above the threshold electric field, a volatile transition is observed as the filamentary path may fully relax after the pulse. For higher electric fields, a non-volatile transition is observed as the metallic filamentary path becomes metastable.

In this work, we aim to clarify the nature of this metastable metallic phase. **Figure 1** summarizes the approach used to unravel the nature of the electric-field-induced filamentary metallic phase created in the chromium-doped vanadium sesquioxide (V₁ₓCrₓ)₂O₃. We studied both the macroscopic electronic response and the concomitant lattice response of this emblematic Mott insulator. We mapped single crystals and patterned thin films using two techniques, spatially resolved at the micrometer scale and able to detect possible symmetry breakings and/or volume changes, namely Raman spectroscopy and X-ray diffraction. **Table 1** lists the (V₁ₓCrₓ)₂O₃ samples used in this study, and the type of measurements performed on each of them.

The rich phase diagram of the prototypal Mott insulator (V₁ₓCrₓ)₂O₃ reproduced in **Figure 2a** was established thanks to the pioneering work of McWhan et al. at Bell Labs more than fifty years ago.[26] Depending on chromium content (x), pressure (P) and temperature (T), three phases appear: the Paramagnetic (Mott) Insulator (PI), the Anti-Ferromagnetic (Mott) Insulator (AFI), and the Paramagnetic Metal (PM) phase. For a single crystal with chemical composition (V₀.975Cr₀.025)₂O₃, a PI state is expected at room temperature, with a transition to an AFI state below 180 K. Figure 2b presents the main results of our electronic transport study conducted on a (V₀.975Cr₀.025)₂O₃ single crystal (SC-1, see Table 1). The resistance *R* versus temperature *T* dependence in the pristine state (curve #1) is in perfect agreement with the phase diagram (Figure 2a), with a semiconducting-like behavior (d*R*/d*T* < 0) in the whole studied temperature range. Moreover, a ten-fold increase of resistance appears at the transition between the small gap insulator (PI phase) and the large gap insulator (AFI phase) at *T*<sub>P1→AFI</sub> = 184 K, as expected for a composition (V₀.975Cr₀.025)₂O₃.[33] This sample was then submitted to a 1 µs electric pulse (150 V ≡ 35 kV cm⁻¹) at 180 K, leading to a non-volatile Electric Mott Transition. The subsequent *R*(*T*) curve measured upon cooling (see curve #2 in Figure 2b) reveals a substantial drop of electrical resistance and a remarkable additional feature at low temperature: a well-defined increase of resistance at 93 K. The resistance drop may be easily explained by a simple model proposed for other Mott insulators[30,32] considering the creation of a conducting filament embedded in the pristine material and that percolates between the contact electrodes (see Figure 2c). In this model, the conductance of the filament becomes predominant at low temperature.[26,34] Therefore, the additional resistance jump at 93 K in (V₁ₓCrₓ)₂O₃ (see curve #2) hence originates from a transition within the conductive filament. This gives some interesting clues about the nature of the metallic phase created after the electric pulse. According to the phase diagram shown in Figure 2a, a resistivity jump at 93 K is indeed expected at the PM – AFI transition of (V₀.975Cr₀.025)₂O₃ put under a pressure of ≈ 2.2 GPa. Furthermore, a hysteresis of ≈7 K appears in *R*(*T*) between cooling (red curve in Figure 2b) and subsequent heating (purple curve). This behavior is expected since it is well established that the PM-AFI transition in the V₂O₃ system is first order and exhibits such an hysteresis.[33] Additional transport data on another (V₀.975Cr₀.025)₂O₃ crystal (SC-2, see Table 1) confirming the reproducibility of this phenomenology after electric Mott transition are presented in Supplementary Materials (see Figure S5, Supporting Information). Overall, this macroscopic transport study suggests therefore that the electric pulse has created a filamentary path made of the same phase, but with a compressive
<figure><img src="image_4.png" /><figcaption>**Figure 1.** Overview of techniques used in this study to probe the electronic and structural consequences of the Electric Mott Transition (EMT) in Cr-doped $V_2O_3$. a) View of the corundum structure of $(V_{1-x}Cr_x)_2O_3$ in the paramagnetic Mott insulator (PI) phase. b,c) Schematic drawings of the samples (either a single crystal or a 150 nm thick thin film) patterned with electrodes (in yellow) before b) and after c) a non-volatile Electric Mott Transition. The path created after a non-volatile EMT, represented in red, is a conducting filament with modified electronic and structural properties. d) In order to clarify the evolution (in particular a possible symmetry-breaking or a volume change) with respect to the pristine phase, the EMT-induced metallic filamentary phase was studied by μ-Raman and μ-XRD. As the creation of the conducting filament results from a *non-volatile* EMT (i.e., it persists after the end of electric pulse application), the μ-Raman and μ-XRD experiments were performed afterwards without any concomitant electrical biasing.</figcaption></figure>

strain strong enough to push it from the Mott insulator (PI) to the correlated metal phase (PM) at room temperature.

Nevertheless, the lattice contraction phenomenon requires further confirmation by direct visualization and study at the local scale of the crystallographic structure within the filament. Another crystal of composition $(V_{0.975}Cr_{0.025})_2O_3$ issued from the same batch (SC-3, see Table 1) was hence subjected to a non-volatile Electric Mott Transition. **Figure 3a,b** shows that this transition leads to the formation of a 4 µm wide filamentary path bridging the two 25 µm apart conductive electrodes. The size of this filamentary structure allows to use Raman scattering to probe its crystallographic structure, thanks to the micrometric spatial resolution of this technique. The Raman spectra measured with a laser beam size of 1–2 µm both inside and outside the filament are shown in Figure 3c and in Figures S6 and S7 (Supporting Information). Both spectra show only the usual signatures of the corundum structure of the $(V_{1-x}Cr_x)_2O_3$ system,[35,36] i.e., a broad structure located between 180 and 280 cm⁻¹ and two peaks around 300 and 500 cm⁻¹. We did not detect

any additional Raman peaks within the filament, which rules out the scenarios of a structural phase transition including a symmetry breaking, or of the formation of other $VO_x$ phases. However, the $A_{lg}$ Raman peak around 240–250 cm⁻¹ measured in the filament is shifted by more than −20 cm⁻¹ compared to the pristine Raman spectrum (see Figure 3c). Moreover, a significant increase of the Raman signal is observed below 200 cm⁻¹. These modifications of Raman spectra, discussed in more detail in Supplementary Materials, support the existence of electronic and structural changes within the filament. In order to determine if the Raman shift could be attributed to a volume contraction of the lattice, we conducted a Raman study under pressure at room temperature on a $(V_{0.962}Cr_{0.038})_2O_3$ single crystal (SC-4, see Table 1). For this composition, a pressure-induced Mott insulator-to-metal transition is observed for a pressure above 1.2 GPa. A transition of the same nature occurs around 0.6 and 2 GPa for $x_{Cr} = 0.025$ and 0.05, respectively. The Raman spectra measured under 1.8 GPa and at ambient pressure, displayed in Figure 3f, disclose that this Mott transition causes both a shift of the $A_{lg}$ Raman
<table><caption>**Table 1.** Overview of samples and experimental conditions.</caption><thead><tr><th>ID</th><th>Composition (Cr-% x)</th><th>Form/Dimensions</th><th>Measurement(s) performed</th><th>Key operating conditions<sup>a)</sup></th><th>Notes and figure refs.</th></tr></thead><tbody><tr><td>SC-1</td><td>(V<sub>0.975</sub>Cr<sub>0.025</sub>)<sub>2</sub>O<sub>3</sub></td><td>Single crystal, ≈300 µm</td><td>Low-bias R(T) before/after EMT; µ-Raman mapping</td><td>1 µs, 150 V ≈ 35 kV cm<sup>-1</sup> pulse at 180 K (EMT trigger); R(T): 300 → 2 K cycles</td><td>Transport &amp; pulse specs Figure 2; Raman map Figure 3</td></tr><tr><td>SC-2</td><td>(V<sub>0.975</sub>Cr<sub>0.025</sub>)<sub>2</sub>O<sub>3</sub></td><td>Single crystal, ≈300 µm</td><td>Low-bias R(T) before/after EMT; µ-Raman mapping</td><td>5 µs, 75 V = 18 kV/cm pulse at 155 K; R(T)</td><td>Transport, Figure S5 (Supporting Information)</td></tr><tr><td>SC-3</td><td>(V<sub>0.975</sub>Cr<sub>0.025</sub>)<sub>2</sub>O<sub>3</sub></td><td>Single crystal, 4 µm-wide filament between 25 µm electrodes</td><td>High-resolution µ-Raman map of filament core vs matrix</td><td>Room T (298 K); no external field (post-pulse)</td><td>Filament imaging/spectra Figure 3, Figures S6 and S7 (Supporting Information)</td></tr><tr><td>SC-4</td><td>(V<sub>0.962</sub>Cr<sub>0.038</sub>)<sub>2</sub>O<sub>3</sub></td><td>Single crystal, 200–300 µm</td><td>SEM imaging; Raman under hydrostatic pressure (DAC)</td><td>0 → 1.8 GPa at 300 K</td><td>SEM image Figure 3d; DAC Raman Suppl. Figure S1 (Supporting Information)</td></tr><tr><td>TF-1</td><td>(V<sub>0.95</sub>Cr<sub>0.05</sub>)<sub>2</sub>O<sub>3</sub></td><td>Granular film, 150 nm thick, 170 × 20 µm stripe on SiO<sub>2</sub>/Si</td><td>Electric-pulse EMT; c-AFM; SEM/EDS imaging; µ-Raman; µ-XRD mapping</td><td>1 µs, 70 V ≈ 35 kV cm<sup>-1</sup> pulse at 160 K; micro-probes at 300 K</td><td>Device fabrication Suppl. Figure S3 (Supporting Information); SEM/EDS Suppl. Figure S4 (Supporting Information); post-EMT charac. Figures 4,5</td></tr></tbody></table>

<figure><img src="image_5.png" /><figcaption>**Figure 2.** a) Temperature – composition x – pressure phase diagram of (V<sub>1-x</sub>Cr<sub>x</sub>)<sub>2</sub>O<sub>3</sub>. The pressure scale is positioned for the composition x = 0.025, using the equivalence of 0.4 GPa per Cr percent proposed in ref.[56]. b) Electrical resistance versus temperature R(T) of a (V<sub>0.975</sub>Cr<sub>0.025</sub>)<sub>2</sub>O<sub>3</sub> single crystal in its initial insulating state (curve in blue), and after application of an electric pulse at 180 K creating a conducting filamentary path measured upon cooling (in red) and after subsequent warming (purple). The black arrow between b) and a) indicates the compression state of the conductive filament and its PM/AFI transition temperature around 95K. c) Schematic description of the sample state before and after creation of a non-volatile filamentary conducting path by electric pulse.</figcaption></figure>

<footnote>a) Raman, SEM/EDS, µ-XRD were performed after the pulse with no electric bias. Abbreviations: EMT = Electric Mott Transition; DAC = diamond-anvil cell; c-AFM = conductive atomic force microscopy; µ-XRD = micro-X-ray diffraction; SEM = scanning electron microscopy; EDS = energy-dispersive spectroscopy.</footnote>
<figure><img src="image_6.png" /><figcaption>**Figure 3.** Comparison of Raman spectra of the metallic states obtained in $(V_{1-x}Cr_x)_2O_3$ by application of an electric field (left, $x = 0.025$) and of hydrostatic pressure (right, $x = 0.038$). a) Image of the $(V_{0.975}Cr_{0.025})_2O_3$ crystal, with four electrodes made of gold wires and carbon paste. Electric pulses were applied between neighboring electrodes, resulting in the creation of conducting filamentary paths. b) Zoom on the region close to a filamentary path. c) Raman spectra of the $(V_{0.975}Cr_{0.025})_2O_3$ crystal obtained at room temperature inside and outside the 4 µm wide conducting filament shown in (b). d) Scanning Electron Microscope image of the $(V_{0.962}Cr_{0.038})_2O_3$ single crystal used for Raman scattering experiments under pressure. e) Schematics of the Diamond Anvil Cell used for Raman scattering under pressure. f) Raman spectra of a $(V_{0.962}Cr_{0.038})_2O_3$ crystal measured at room temperature in the Diamond Anvil Cell close to ambient pressure in the Mott insulator states (PI) and at 1.8 GPa in the metallic state (PM, see Figure 2). Details about the fit of Raman spectra (dotted lines in c) and f)) are presented in Supplementary Materials.</figcaption></figure>

vibration mode and an increase of Raman intensity below 200 cm⁻¹. Both changes are similar to the one observed between the pristine material and the core of the filamentary path created by the Electric Mott transition. Overall, this micro-Raman study provides additional evidence that the Electric Mott Transition yields a compressed, isosymmetric, and metallic $(V_{1-x}Cr_x)_2O_3$ filamentary phase. It strongly supports the scenario of a volume contraction of the lattice presented above based on resistivity measurements.

To further confirm the volume contraction within the filament, a spatially resolved X-ray diffraction experiment was engaged using a 1-µm beam size at the micro-XAS beamline of the Swiss Light Source synchrotron facility. The penetration depth of X-ray being far bigger than the thickness of the filamentary path, we worked on polycrystalline thin films to maximize the signal coming from the filament over that of the matrix. In that

purpose, a 150 nm polycrystalline $(V_{0.95}Cr_{0.05})_2O_3$ thin film with a rectangular 170 x 20 µm shape was deposited on a $SiO_2$/Si substrate patterned with TiN metallic electrodes (sample TF-1, see Table 1; see **Figures 4** and S4, Supporting Information). Details about the preparation method of this device are given in Supplementary Materials. A 1 µs / 70 V electric pulse (≡ electric field $E \approx 35$ kV cm⁻¹) was applied at 160 K between two TiN electrodes to induce a non-volatile Electric Mott Transition. The sample was then characterized by conducting-atomic force microscopy (c-AFM) and by Raman spectroscopy. Atomic Force Microscopy (AFM) images shown in Figure 4d,e reveals that the inter-electrode domain of the $(V_{0.95}Cr_{0.05})_2O_3$ film affected by the Electric Mott Transition does not display any morphological change. Figure 4d,e also shows the distribution of current measured by applying a 25 mV bias between the conductive AFM tip
<figure><img src="image_7.png" /><figcaption>**Figure 4.** Characterization of pristine and transited thin-film device by µ-Raman and conducting-AFM. a) General image of 150 nm thick polycrystalline (V<sub>0.95</sub>Cr<sub>0.05</sub>)<sub>2</sub>O<sub>3</sub> thin film with a rectangular 170 × 20 µm shape deposited on a SiO<sub>2</sub>/Si substrate patterned with TiN metallic electrodes. A schematic illustration of electrodes connected to the electric pulse generator is shown. b,c) Mapping of Raman intensities ratio measured at 210 and 230 cm<sup>-1</sup> in the inter-electrode domains in the pristine b) and transited (c) cases. d,e) Conducting-AFM mapping of the same regions shown in b,c). All Raman and conducting-AFM measurements shown in b–e) were made at room temperature. Additional scanning electron microscopy (SEM)/energy dispersive spectroscopy (EDS) mapping demonstrating a chemical homogeneity across pristine and transited regions is provided in Figure S4 (Supporting Information) of the Supplementary Materials.</figcaption></figure>

and the neighboring electrode, integrated over similar areas in regions affected by the EMT (Figure 4e) and in pristine regions (Figure 4d). Interestingly, the map shown in Figure 4e unveils a clear ≈2 µm wide zone of higher conductivity close to the left edge of the (V<sub>0.95</sub>Cr<sub>0.05</sub>)<sub>2</sub>O<sub>3</sub> stripe. Figure 4c shows that the Raman mapping measured in the highly conducting region uncovered by c-AFM presents a tendency toward metallicity (ratio of Raman intensities between 210 and 230 cm<sup>-1</sup> > 1, see Figure 3) compared to spectra measured outside of this zone. The c-AFM and Raman measurements confirm therefore the presence of a metallic filamentary path between the two inner electrodes of the polycrystalline device with features similar to those observed on the crystal.

A µ-XRD experiment was then engaged by mapping a 200 × 45 µm zone containing the whole patterned (V<sub>0.95</sub>Cr<sub>0.05</sub>)<sub>2</sub>O<sub>3</sub> stripe of the device (170 × 20 µm). Details about the fabrication of the device (Figure S3, Supporting Information) and about µ-XRD experiments are provided in Supplementary Materials. The map consists of 9191 (101 × 91) "pixels" of 5 × 1 µm, each of them corresponding to a 2D powder X-Ray diffractogram (see Figure 5a). An azimuthal integration of the Debye rings was performed for each 2D powder X-Ray diffractogram to extract the intensity versus 2θ plots. Representative examples of the integrated diffraction patterns outside and inside the filament are shown in Figure 5b. Outside the filament, the diffraction pattern exhibits the expected Bragg peaks (104), (110), and (113) of the corundum

structure. Inside the filament the same peaks are observed, but slightly shifted. Moreover, the absence of new diffraction peak discards the change of crystallographic symmetry or the formation of a chemical phase with a different composition. The mechanism proposed in ref. [37] which suggests the creation of a V<sub>5</sub>O<sub>9</sub> phase to explain the resistivity jumps in the low temperature phase, can therefore be excluded in our case. This crude comparison of XRD patterns in Figure 5b already confirms that the (V<sub>0.95</sub>Cr<sub>0.05</sub>)<sub>2</sub>O<sub>3</sub> phase within the filament keeps the corundum structure but with a different cell volume. The *a* and *c* unit cell parameters were then refined for each pixel based on the position of the (104), (110), and (113) Bragg peaks and were represented as maps in Figure 5c. These maps reveal a remarkable feature: in the filamentary region bridging the two central electrodes, an increase of the *c* parameter (from 13.95 to 13.97 Å, ≈ + 0.15%) with respect to the pristine parts of the sample is clearly observed. Conversely, the unit cell parameter *a* is contracted by ≈-0.4% compared to the normal zones. This leads to a *c/a* ratio close to 2.81 in the filament, a value for which a metallic state is achieved in V<sub>2</sub>O<sub>3</sub> thin films.[39–41] Overall, the unit cell volume within this filament undergoes a contraction of -0.6% compared to the pristine material. These structural evolutions within the filament are particularly interesting, since they allow discarding two trivial scenarios. First, a filament's creation due exclusively to Joule heating followed by a thermal quench is not compatible with our data, since it would result in an *increase*
<figure><img src="image_8.png" /><figcaption>**Figure 5.** µ-XRD mapping experiment performed at room temperature on a (V<sub>0.95</sub>Cr<sub>0.05</sub>)<sub>2</sub>O<sub>3</sub> thin-film device submitted to a Electric Mott Transition. a) Schematic view of the µ-XRD geometry, with a fixed incident angle of 11° between the X-Ray beam and the film, leading to an X-ray beam footprint of 1 µm wide and 5 µm long. A Dectris Eiger 4 M 2D detector was used to register the Debye diffraction rings. The mapping was obtained by moving the sample holder with steps of 0.5 and 2.5 µm along two directions. b) Comparison of µ-XRD diffractograms inside and outside the filamentary path. c) Maps of lattice parameters *a* and *c*, as well as of the *c/a* ratio and the hexagonal unit cell volume extracted from XRD refinements of the 9191 measured diffractograms.</figcaption></figure>

of the unit cell parameter *a* and of the unit cell volume *V*. Second, our data do not point toward the creation, within the filament, of a non-stoichiometric phase with a (V+Cr): O ratio departing from 2:3. Indeed such non-stoichiometry induces a concomitant decrease of both *a* and *c* parameters<sup>[41,42]</sup> (see discussion about non stoichiometry in V<sub>2</sub>O<sub>3</sub> provided in Supplementary Materials), which contrasts with the observed increase of the *c* parameter measured in the filamentary path shown in Figure 5c. Conversely, the structural modifications we unveiled within the filament are strikingly similar to those observed at the isosymmetric Mott insulator (PI) to metal (PM) transition driven by hydrostatic pressure.<sup>[26,43]</sup> Figure S2 (Supporting Information) indeed shows that the pressure-driven transition involves, as the electric-field-driven one, a first order drop of both *a* parameter and unit cell volume (−0.65% and −1.04%, respectively), but more significantly a counterintuitive *increase* of the *c*-parameter (+ 0.26%). Overall, the µ-Raman and µ-XRD results presented in this work show that the responses to apparently very different stimuli, electric-field-pulse and pressure, are strikingly similar in the Mott insulator (V<sub>0.95</sub>Cr<sub>0.05</sub>)<sub>2</sub>O<sub>3</sub>. Interestingly, an analogous situation exists in the widely studied correlated insulator VO<sub>2</sub>: a transient monoclinic metallic phase accessible at equilibrium only with pressure (and

not with temperature) also appears under an electric field.[44–46] This similarity in electric field and pressure effects, clearly observed but not noted in refs. [44–46] suggests that the lattice compression in response to a massive electronic excitation might be a more general property also present in other correlated insulators such as VO<sub>2</sub>. On the theoretical side, we note that the sudden lattice volume drop occurring at the pressure-induced Mott insulator to metal transition can be rationalized within the compressible Hubbard model.[47,48] In this approach, the lattice reacts to the delocalization of electrons occurring at the first order insulator-to-metal transition, resulting in a lattice volume drop in order to avoid the unphysical situation of negative bulk compressibility.[57] The results presented in this paper strongly suggest that a similar mechanism is also at play at the Electric Mott transition, i.e., that the creation of excited and delocalized electrons during the electric pulses leads to a compressive lattice response. Our work hence provides a strong indication that Mott physics plays a pivotal role in the insulator to metal transition observed under electric field (V<sub>1-x</sub>Cr<sub>x</sub>)<sub>2</sub>O<sub>3</sub> and possibly in other correlated insulators like VO<sub>2</sub>. Our study, therefore suggests that the minimal theoretical approach required to capture the physics of non-equilibrium Mott insulators, whether via electrical or light
pulses, is the non-equilibrium Hubbard model on a compressible lattice. Indeed, the compression effect induced by an electrical stimulus, shown in this work, is strongly reminiscent of the result of our recently published work on the Mott insulating phase of $V_2O_3$, [50] where a strong electronic excitation induced by ultrafast laser pulses yields a similar lattice compression. [51] Finally, the direct evidence of a lattice compression at the Electric Mott Transition in $(V_{1-x}Cr_x)_2O_3$ shown in this work might rationalize a posteriori the presence of electric-field-induced superconductivity in the canonical Mott insulator $GaTa_4Se_8$, [52,53] which is also superconducting under pressure. [54] This strengthens the above-mentioned claim that the lattice compression at the Electric Mott Transition could be a universal property of Mott insulators. Overall, the advances in understanding the nature of the filamentary path created at the Electric Mott Transition gained in this study will greatly facilitate the implementation of advanced Mottronics applications such as Resistive Mott memories and neuromorphic components in the near future. [8,55]

## Supporting Information

Supporting Information is available from the Wiley Online Library or from the author.

## Acknowledgements

The authors Zohra Khaldi for her help in the preparation of single crystals. The authors thank Nantes Université for funding the Ph.D. of D. B. in the framework of the French-Japanese International Associated Laboratory "Impacting Materials by Light and Electric pulses, and watching real-time Dynamics" (IM-LED). The authors acknowledge the Paul Scherrer Institut, Villigen, Switzerland for the provision of synchrotron radiation beamtime at beamline microXAS. This work was partly supported by the ANR (Elastica project, grant ANR-16-CE30-0018) and the Région Pays de la Loire (Mott-IA project). The research leading to these results has received funding from the European 2020 research and innovation program under grant agreement n°730872 project CALIPSOplus.

## Conflict of Interest

The authors declare no conflict of interest.

## Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

## Keywords

metal-insulator transition, Mott insulator, resistive switching

Received: January 25, 2025

Revised: August 19, 2025

Published online:

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