these two events opens a band gap, ultimately transforming the metallic tetragonal VO₂ into a monoclinic insulator.

In recent years, strain modification has emerged as one of the most successful methods for manipulating complex oxide electronic structures<sup>25-29</sup>. In VO₂, the MIT is modified by strain since it alters the interatomic distances; hence, the orbitals overlap, with consequences for the transition properties. The two most studied cases are those where tensile or compressive strains on the c<sub>r</sub> axis are applied through epitaxial growth of VO₂ thin films by tuning the lattice mismatch as a function of the chosen substrate. Multiple studies have reported the MIT properties of VO₂ films grown along the (110), (100) and (001) surfaces of TiO₂<sup>11,30-35</sup>. The c<sub>r</sub> axis is oriented parallel (110 and 100 orientations) or perpendicular (001 orientation) to the film surface. Since the lattice parameters of TiO₂ are greater than those of VO₂, compressive out-of-plane strain and in-plane tensile strain occur. In VO₂ films oriented along the (110) and (100) planes, the critical temperature is higher than that in the bulk<sup>36,37</sup>, and the severe in-plane tensile strain applied to the c<sub>r</sub> axis allows the emergence of metastable phases<sup>31,38</sup>. However, for this reason, the MIT of these films is usually quite broad<sup>35,36</sup>, which hinders their potential for various applications. On the other hand, VO₂ films oriented along the (001) direction experience compressive strain in the c<sub>r</sub> axis. The transition of these materials is quite sharp (which is favorable for producing devices with high ON-OFF ratios), whereas the critical temperature is lower than that of the bulk material (as low as 295 K)<sup>33</sup>. The suppressed critical temperature may be unfavorable for devices operating at room temperature. Moreover, the high surface energy may result in undesired surface roughening, hindering the integration of these films in complex electronics<sup>39-41</sup>. The (001), (110) and (100) VO₂ film orientations have been the most studied since they heavily strain (compressive or tensile) the c<sub>r</sub> axis.

An intermediate case is that of VO₂ films grown on the TiO₂ (101) surface. For this orientation, the lattice mismatch is small, resulting in a reduced strain on the c<sub>r</sub> axis that it is oriented diagonally out of plane<sup>37,41</sup>. Compared with the other cases, these films combine sharp bulk-like MITs, as in the case of films those grown along the (001) direction, with approximately room-temperature Tcs and atomically smooth surfaces, which is ideal for implementation into heterostructures<sup>34,35,41</sup>. In addition, an intermediate strain configuration is likely to minimize crack formation and self-pixelation on the film surface because the elastic stress is relieved across the MIT<sup>42-44</sup>, increasing the stability of the transition. However, a detailed study of the band structure of VO₂ (101) as a function of strain is, to the best of our knowledge, still

lacking. In particular, the effect of moderate strain on band structure anisotropy has yet to be explored.

In this framework, we investigated the role of strain as a control parameter for the band structure anisotropy of VO₂ single-crystal films. Strain modulation was achieved by using VO₂ thin films of 8, 16 and 32 nm thickness on TiO₂ (101) substrates. The use of TiO₂ (101) is relatively less studied and hence still largely unexplored, and it is expected to apply an intermediate amount of strain along the c<sub>r</sub> axis compared with that of TiO₂ (001)- and (110)-oriented films<sup>34,35</sup>. The thin films set was characterized via X-ray diffraction (XRD) and resistivity measurements to determine the dependence of the film thickness on the MIT and the effect of substrate-induced strain on the lattice, respectively. The electronic structure evolution was then probed via X-ray absorption spectroscopy (XAS) and X-ray linear dichroism (XLD) at the V L₃ edge and resonant photoemission spectroscopy (ResPES). These measurements were performed using linearly polarized light to maximize d<sub>||</sub>- and π*-band sensitivity. The combined use of XLD and ResPES provides a complete overview of the band-selective projections of the unoccupied and occupied density of states of VO₂.

Our results revealed a progressive reduction in the anisotropy of the electronic structure of the VO₂/TiO₂(101) films as the thickness decreased; this is accompanied by an effective mass renormalization tending toward a scenario where d|| and π* become increasingly similar as the film thickness decreases. These results highlight the key role of strain as a control parameter and the deep interconnection among band occupation, band curvature and anisotropy, which can be exploited for technological purposes.

## Experimental

All the measurements were performed at 355 K except where specified otherwise. The VO₂/TiO₂(101) films were grown with an RF-plasma assisted oxide– molecular beam epitaxy (MBE) instrument at the University of Science and Technology of China, Hefei. The deposition chamber had a base pressure of less than 4 × 10⁻⁹ mbar. The substrate temperature was 823 K during deposition.

The synthesized thin films were characterized using XRD and resistivity measurements.

XRD measurements, both symmetric θ–2θ scans and asymmetric reciprocal space maps, were performed using a PanAnalytical X'Pert Pro diffractometer (Cu–Kα wavelength).

The Tcs of the MITs for all the samples were evaluated through transport measurements using the van der Pauw method.

The spectroscopy measurements were performed at the NFFA APE-HE beamline at the Elettra synchrotron radiation facility<sup>45</sup>. XAS measurements were performed in
total electron yield (TEY) mode at the V L$_3$ edge while increasing the temperature from RT to 370 K via horizontal polarization. XLD measurements were obtained as the difference between the XAS spectra of the sample surface in different orientations with respect to the beam, as shown below. ResPES measurements were taken with a ScientaOmicron R3000 hemispherical analyzer, in which the photon energy across the V L$_3$ edge was scanned in horizontal polarization with the sample surface normal with respect to the analyzer. The binding energies were calibrated with respect to the Fermi level of a gold reference foil.

The (101) surface of the metallic VO$_2$ phase has [010] and [−101] vectors as in-plane lattice vectors. The a$_r$ [100] and c$_r$ [001] axes are inclined with respect to the normal to the surface with angles β ≈ 58° and γ ≈ 32° (values calculated using the data reported in JCPDS no. 76-0675). The sample surface was rotated by an angle of α = +45° or −45° with respect to the beam to align the electric field vector of the photon beam (⃗E) in a parallel orientation with respect to either c$_r$ or a$_r$ (i.e., perpendicular to c$_r$), as shown in the sketch of Fig. 1. This configuration creates an effective angle between ⃗E and c$_r$ (a$_r$) of δ ≈ 13°. This small angle does not significantly affect our data since both the absorption and photoemission intensities depend on cos$^2$(δ)$^{46}$, which in this case corresponds to ≈ 0.95 ensuring that the orbital polarization of our data is 95%. Polarization-dependent measurements with similar values of δ have been successfully carried out in the literature$^{47}$.

By setting the electric field to be aligned parallel (E || c$_r$) or perpendicular (E ⊥ c$_r$, i.e., E || a$_r$) to c$_r$, it is possible to probe the empty d$_{‖}$ and π* bands, respectively$^{48}$.

Linear dichroism provides information on the evolution of the empty states relative to a specific band as a function of the film thickness. The XLD is calculated as follows:

$$XLD = 100 \times \frac{I_{\parallel} - I_{\perp}}{I_{\parallel} + I_{\perp}} \quad (1)$$

where I$_{‖}$ is the integrated intensity of the XAS acquired with E$_{‖}$ c$_r$ and I$_{⊥}$ is that of the XAS acquired with E$_{⊥}$c$_r$. In this form, Eq. (1) can be used to determine the percentage of empty states in d$_{‖}$ with respect to those in the π* band.

# Results and discussion

## Resistivity

The resistivity measurements as a function of temperature for the entire set of films are reported in Fig. 1c.

All the resistivity curves exhibit a variation of approximately 3 orders of magnitude across the MIT, confirming the good quality of the films for all thicknesses. The critical temperature T$_C$ (calculated as the average

temperature position between the two minima of $\frac{\partial \log \rho}{\partial T}$ and the transition width ΔT are reported in Table 1.

The data show that the T$_C$ slightly increased by ~4 K when the film thickness was reduced. This agrees well with other studies reporting the temperature trend of VO$_2$/TiO$_2$(101) films$^{41}$ and with what was observed for the twin VO$_2$/TiO$_2$(011) orientation$^{34}$. On the other hand, the transition width (ΔT) roughly doubles from 32 to 8 nm in thickness, indicating that strain reduces the lattice compatibility between the insulating and metallic phases of VO$_2$/TiO$_2$(101)$^{49}$.

## XRD

For all the films, the diffraction pattern shows the presence of a single-crystal phase. The θ − 2θ scans of the 32 nm film of both the metallic and insulator phases are reported in Fig. 1d. The presence of Laue fringes indicates a sharp VO$_2$/TiO$_2$ interface. To calculate the a$_r$ and c$_r$ lattice parameters of metallic VO$_2$, we measured the reciprocal space map (RSM) of the (301) peak (shown in Fig. 1f, right panel). The calculated a$_r$ and c$_r$ are 4.556 and 2.834 Å, respectively. Compared with the reference value for tetragonal (metallic) VO$_2$ reported in JCPDS no. 76-0675, we observe a shortening of the c$_r$ axis by approximately 0.7%, whereas the a$_r$ axis remains mostly unchanged. The signal from the (301) reflection of the 16 and 8 nm films was below our detection threshold; thus, we could not measure the changes in their a$_r$ and c$_r$ axes. The (101) reflection of the metallic phase for the 8, 16 and 32 nm films is shown in Fig. 1e. The increase in the full width at the half maximum of the (101) peak agrees with the reduced thickness of the films and with what has been reported in the literature$^{41,50,51}$.

## XAS and ResPES

To study the change in the electronic structure of metallic VO$_2$ as a function of the film thickness, we performed XLD and ResPES measurements at the V L$_3$ edge of the VO$_2$/TiO$_2$(101) films. The effect of compressive strain along c$_r$ on the band structure involves transferring part of the electron population of the d$_{‖}$ band to the π* band$^{2,11,30,47,52,53}$. This population transfer is more pronounced for thinner films since the strain increases.

The linearly polarized XAS spectra and the calculated dichroism measured at 350 K are reported in Fig. 2a, b.

Clear spectroscopic differences are observable in the XAS spectra for the two different orientations. The dichroic percentage as a function of the film thickness, calculated according to Eq. (1), is reported in Fig. 2b. The dichroic percentage decreases as the film thickness increases, a trend that is in very good agreement with similar quantifications of the d$_{‖}$−π* linear dichroism$^{47}$; this means that by reducing the film thickness, the empty states of d$_{‖}$ increase with respect to that of the π* band. In
<figure><img src="image_1.png" /><figcaption>**Fig. 1** Resistivity and XRD measurements of VO₂(101) thin films. **a** Resistivity and XRD measurements. Schematic representation of the lattice unit cell of metallic VO₂. **b** Top view of the polarization dependence measurements. The sample surface was rotated by an angle of ± α = 45° with respect to the incident beam direction. The angle δ is the angle between the direction of the c axis and the direction of the incident beam. In the right panel, the lengths of aᵣ and cᵣ are equal for simplicity. **c** Resistivity of the three VO₂/TiO₂(101) films as a function of temperature. The continuous lines indicate the heating cycles, and the broken lines indicate the cooling cycles. **d** θ – 2θ scan of the 32 nm film across the phase transition. The insulating phase (indicated with M) is measured at room temperature. **e** (101) peak of metallic VO₂ for the 8, 16 and 32 nm films. These spectra are vertically shifted for clarity. **f** RSM of the (301) peak for the 32 nm film in the metallic phase.</figcaption></figure>

<table><caption>**Table 1** Critical temperatures T<sub>c</sub> and transition widths ΔT as a function of the film thickness.</caption><thead><tr><td>Thickness [nm]</td><td>T<sub>c</sub> [K]</td><td>ΔT [K]</td></tr></thead><tbody><tr><td>8</td><td>321</td><td>8.2</td></tr><tr><td>16</td><td>318.4</td><td>6.8</td></tr><tr><td>32</td><td>316.8</td><td>4.3</td></tr></tbody></table>

other words, the *d*<sub>||</sub> electron population decreases as π* increases. These measurements demonstrate the *d*<sub>||</sub>–π* band population transfer for VO<sub>2</sub>/TiO<sub>2</sub>(101) films.

To investigate the effect of the population redistribution of the *d*<sub>||</sub> and π* bands on the electronic structure of VO<sub>2</sub> thin films, we performed linearly polarized photoemission

measurements at the V L<sub>3</sub> edge in resonance. This technique increases the sensitivity of the bands to the photoelectron spectra and, at the same time, maximizes the photoelectron yield. In particular, when E || c<sub>r</sub>, the dipole matrix element of the V 3d photoemission spectra maximize the contribution from the *d*<sub>||</sub> orbital, whereas for E⊥c<sub>r</sub>, it maximizes the π* orbital<sup>54</sup>; this is particularly relevant in proximity to the FL since electron population redistribution occurs in this energy region.

We studied the VB spectra of the 8, 16, and 32 nm samples in the –2; 8 eV binding energy (BE) region collected at the maximum V L<sub>3</sub> (518.4 ± 0.1 eV) resonance with E || c<sub>r</sub> and E⊥c<sub>r</sub>.

The spectra are reported in Fig. 2c and are in good agreement with previous ResPES measurements reported in the literature for the same compound<sup>53,55–58</sup>. Two
<figure><img src="image_2.png" /><figcaption>**Fig. 2 XLD, resonant photoemission and mass renormalization.** a V L$_{3}$ XAS spectra for the 32 nm, 16 and 8 nm thick films (from top to bottom) at 355 K, i.e., the metallic phase. In the reported spectra, the electric field vectors of the incident photon beam were aligned parallel (red spectra) and perpendicular (blue spectra) to the c$_{r}$ axis, corresponding to impinging angles of $\alpha = +45$ and $-45$, respectively (see Fig. 1). The spectra are normalized via the procedure described in ref. 47 and vertically shifted for clarity. The photon energy region where the XLD is calculated is highlighted by a black dotted box, chosen in accordance with what was reported in ref. 47, to provide the best possible frame of reference for our data. b XLD signal percentage calculated as described in Eq. (1). The broken line acts as a guide. The inset shows a sketch of the $d_{||} - \pi$ population redistribution as a function of compressive strain and film thickness. c VB spectra at V L$_{3}$ edge resonance for the metallic phase of the VO$_{2}$/TiO$_{2}$(101) films acquired with light polarization directed parallel and perpendicular to the c$_{r}$ axis. The spectra are normalized with respect to the incident photon flux and vertically shifted for clarity. d Screening length linear dichroism (in red, left axis) and effective mass linear dichroism (in black, right axis) calculated via Eqs. (4) and (5), respectively. The belts represent the uncertainty range for the points. Between the experimental points, the uncertainty value is interpolated via a polynomial function.</figcaption></figure>

main features are observable. The peak centered at approximately 6 eV is due to hybridization between V 3d and O 2p electrons, whereas the feature that crosses the FL is generated by unpaired 3d electrons. The L (ligand

hole) and C (coherent hole) features are centered at BEs of approximately 1.7 and 0.5 eV, respectively$^{53,56,59}$ for all the samples and for both orientations. The intensity of the L and C contributions changes as a function of the
polarization, mirroring the band orientation in the samples. The C feature is less intense than the L feature for the 8 and 32 nm samples, whereas the opposite is true for the 16 nm sample; this may be due to surface contamination of the samples since the measurements were performed ex situ. Nonetheless, this does not influence our analysis for three main reasons: a) the photon energy is set at the VO₂ V L₃ resonance; therefore, the contributions from other undesired vanadium oxides (such as V₂O₅ or V₂O₃) are damped[4]; b) at 355 K, VO₂ is the only metallic oxide contributing to the valence band close to the FL (except for V₆O₁₃⁶⁰, which is not observed at low temperature and can thus be ruled out; and c) the orientation-dependent intensity variations of the VB at the V L₃ edge are due to the orbital anisotropy of VO₂ since spurious oxides are expected to contribute isotropically to the photoemission intensity.

We used linearly polarized ResPES to probe the dichroism in the metallicity (i.e., the ability to screen an electric field) induced by the change in the band population⁶¹⁻⁶³. The maximum intensity (normalized with respect to the photon flux) of the resonant photoemission feature can be linked to the screening length via Eq. (2)⁶¹⁻⁶³

$$ \frac{I}{I_0} \propto \lambda \qquad (2) $$

where I is the VB peak integral intensity, $I_0$ is the incident photon flux and $\lambda$ is the screening length. Owing to the orbital sensitivity of the measurements, the variation in the screening length $\Delta\lambda$ along the c_r axis and along the a_r axis is calculated as follows:

$$ \Delta\lambda_{ca} = 100 \times \frac{I_c - I_a}{I_c + I_a} \propto 100 \times \frac{\lambda_c - \lambda_a}{\lambda_c + \lambda_a} \qquad (3) $$

where $\Delta\lambda_{ca}$ is expressed as a percentage; $I_c$ and $I_a$ are the normalized integrated intensities of the VB spectra acquired with $E_{||}$ c_r and $E \perp c_r$, respectively; and $\lambda_c$ and $\lambda_a$ are the screening lengths due to the $d_{||}$ and $\pi^*$ bands, respectively. To calculate $\Delta\lambda_{ca}$, we integrated the intensity of the VB spectra in the binding energy region of 0–2 eV to include both L and C contributions. The data are represented as red dots in Fig. 2d.

$\Delta\lambda_{ca}$ increases as the film thickness increases, indicating that the screening capability of VO₂ decreases as the film thickness decreases. The anisotropy reduction also affects the effective masses of the $d_{||}$ and $\pi^*$ bands. The screening length can be expressed in a general form as follows⁶⁴:

$$ \lambda^{-2} = \frac{\sqrt{2}e^2 m^{*\frac{3}{2}}(k_b T)^{\frac{1}{2}}}{2\pi\epsilon_0\hbar^3} F_{\frac{1}{2}}'\left(\frac{\mu}{k_b T}\right) \qquad (4) $$

where e is the electron charge, $m^*$ is the effective mass, $k_b T$ is the temperature multiplied by the Boltzman

constant, $\hbar$ is the reduced Plank constant, $\epsilon_0$ is the vacuum permeability, and $F'_{1/2}(\mu/(k_b T))$ is the first derivative of the Fermi integral of order ½ with respect to $\mu/(k_b T)$, where $\mu$ is the chemical potential⁶⁵. $F'_{1/2}(\mu/(k_b T))$ depends on the temperature and the relative position of the conduction band edge with respect to the FL.

In our case, since the polarized ResPES were acquired at the same temperature and since the chemical potential within the same sample remains the same, from Eq. (4), we obtain

$$ \Delta m_{ca}^* = \frac{m_c^* - m_a^*}{m_c^* + m_a^*} = \frac{\lambda_c^{-\frac{4}{3}} - \lambda_a^{-\frac{4}{3}}}{\lambda_c^{-\frac{4}{3}} + \lambda_a^{-\frac{4}{3}}} \qquad (5) $$

where $\Delta m_{ca}^*$ is the difference between the effective masses $m_c^*$ and $m_a^*$. The calculated $\Delta m_{ca}^*$ values are reported in Fig. 2d as black squares. The trend is the same as that of $\Delta\lambda_{ca}$, where the dichroism decreases (in absolute value) with decreasing film thickness. Our results agree well with the effective mass difference calculated via the angle-resolved photoemission data reported in⁶⁶, for which $\Delta m_{ca}^* \approx 18-20\%$ for a 20 nm thick VO₂ film. By reducing the film thickness, we observe an effective mass renormalization, pointing toward a reduction in the anisotropy in the band structure.

We can summarize our observations as follows: the strain-induced electronic population redistribution between $d_{||}$ and $\pi^*$ leads to increased homogeneity of the screening length and the effective mass along the a_r and c_r axes.

Our observations agree with the results of the LDA and DFT calculations for strained VO₂ films with a shortened c_r axis⁶⁷,⁶⁸. The reduction in the V–V pair distance increases the overlap of the a₁g ($d_{||}$) orbitals, leading to renormalization of the bandwidth. This renormalization generally results in different occupation numbers in different orbitals, i.e., in charge transfer between the $d_{||}$ and $\pi^*$ bands. In the case of a shortened c_r axis, this results in an increase in the a₁g–a₁g hopping terms and an increase in the corresponding bandwidth⁶⁷. This ultimately reduces the energy difference between the $d_{||}$ and $\pi^*$ bands, leading to a more even population of the two bands, which weakens the repulsive electron–electron interaction⁶⁸. Our data confirm the prediction of an emerging isotropization of the band structure of VO₂ films driven by strain, which acts as a parameter that control the Mott physics in multiband complex oxides.

## Conclusions

The role of strain in the modulation of band structure anisotropy in metallic VO₂/TiO₂(101) was investigated by combining XLD and ResPES. Our single-crystal films show compressive strain along the c_r axis, which leads to an electronic population redistribution between the $d_{||}$ and $\pi^*$ bands, with the two bands more evenly populated
for thinner (strained) films. This leads to a decrease in the
difference in screening length calculated along c<sub>r</sub> and a<sub>r</sub> as
a function of film thickness, indicating a reduction in the
anisotropy in the band structure of VO<sub>2</sub>. This is further
confirmed by the observation of an effective mass renor-
malization effect, which suggests that, in addition to the
redistribution between the d<sub>||</sub> and π* bands, the band
curvature itself is also influenced by strain.

In other words, in the presence of interfacial strain
along the (101) direction of the metallic phase, d|| and π*
become similar in terms of the electron population,
electric field screening performance and effective mass.
Strain emerges as a dominant parameter controlling the
Mott physics of multiband oxides, allowing for the tuning
of the anisotropy of the VO<sub>2</sub> band structure. Our results
shed light on the band structure properties of these poorly
investigated strained VO<sub>2</sub>(101) thin films, whose proper-
ties are promising for technological applications based on
intrinsic anisotropy of materials.

Acknowledgements

This work was partially performed in the framework of the Nanoscience Foundry and Fine Analysis (NFFA-MUR Italy Progetti Internazionali) facility (https://www.trieste.nffa.eu/).

Author details

¹Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Frascati, 00044 Frascati, Italy. ²CNR - Istituto Struttura della Materia, Basovizza Area Science Park, Trieste 34149, Italy. ³CNR - Istituto Officina dei Materiali (IOM), Area Science Park, S.S.14, km 163.5, I-34149 Trieste, Italy. ⁴National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei 230029, PR China. ⁵Scuola di Scienze e Tecnologie, Sezione di Fisica, Università di Camerino, Via Madonna delle Carceri 9, 62032 Camerino, Italy. ⁶Rome International Center for Materials Science Superstripes RICMASS, Via dei Sabelli 119A, Roma 00185, Italy. ⁷Present address: Université Paris-Saclay, UVSQ, CNRS, GEMaC, 78000 Versailles, France

Author contributions

A.D. conceived the experiment; G.V., V.P., A.P. performed the measurements, L.L., C.Z. synthesized the samples; A.D., J.R., data analysis; A.D. original manuscript writing; A.D.; V.P., G.V., A.P., C.Z., L.L., J.R., A.M., reviewed and revised the manuscript; all the authors reviewed and approved the final version of the manuscript.

Competing interests

The authors declare no competing interests.

Publisher's note

Springer Nature remains neutral with regard to jurisdictional claims in
published maps and institutional affiliations.

**Supplementary information** The online version contains supplementary
material available at https://doi.org/10.1038/s41427-024-00576-2.

Received: 24 January 2024 Revised: 20 September 2024 Accepted: 14
October 2024.

Published online: 22 November 2024

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