Unveiling the Electronic Structure of Pseudotetragonal WO3 Thin Films

WO3 is a 5d compound that undergoes several structural transitions in its bulk form. Its versatility is well-documented, with a wide range of applications, such as flexopiezoelectricity, electrochromism, gating-induced phase transitions, and its ability to improve the performance of Li-based batteries. The synthesis of WO3 thin films holds promise in stabilizing electronic phases for practical applications. However, despite its potential, the electronic structure of this material remains experimentally unexplored. Furthermore, its thermal instability limits its use in certain technological devices. Here, we employ tensile strain to stabilize WO3 thin films, which we call the pseudotetragonal phase, and investigate its electronic structure using a combination of photoelectron spectroscopy and density functional theory calculations. This study reveals the Fermiology of the system, notably identifying significant energy splittings between different orbital manifolds arising from atomic distortions. These splittings, along with the system’s thermal stability, offer a potential avenue for controlling inter- and intraband scattering for electronic applications.

C ontrolling the electronic properties of quantum systems allows us to realize technological applications with improved performance, stability, and durability, as well as a significantly lower level of dissipation. 1−3 This is particularly relevant for 5d-based transition metal oxides, which might provide a platform for integration into existing technology, with improved current densities, enhanced electrochromic and photovoltaic responses, and reduced switching energies. 4−12 Therefore, understanding the electronic structure of quantum systems is a crucial task, especially for newly synthesized materials, and it allows us to pin down the hallmarks that describe their conductivity, their Fermi surfaces, and the relationship of the latter with symmetries and crystal structure. Among the 5d-based oxides, WO 3 has been shown to be promising for applications, with the appearance of flexopiezoelectricity 10 and electrochromism 11 and as a realistic candidate for improving the performance of Li-based batteries. 13 The range of applicability of this material extends also toward gas sensor applications, 14 water splitting, 15 memory devices, 16 high-temperature diodes, 17,18 and photodetectors. 19,20 WO 3 can be used to make faster and more efficient electronics, 4−12, 21 and it has been proposed theoretically as a candidate system for low-dissipation Rashba ferro-and antiferroelectrics. 22 However, WO 3 generally undergoes several different phase changes that make it difficult to be realistically used over a wide temperature range. Additionally, its electronic structure has not been experimen-tally investigated, although a few theoretical predictions have been reported.
Here, by using pulsed laser deposition (PLD), 23−26 we exploit epitaxial strain to synthesize a thermally stable phase in thin films of the 5d compound WO 3 (on a LaAlO 3 substrate, LAO), and by using angle-resolved photoelectron spectroscopy (ARPES), we unveil the electronic structure and properties, which describe the Fermi surface. Here, we uncover the reference experimental benchmarks for the electronic band structure of WO 3 thin films, which despite the numerous studies that rely on it 27−33 is still lacking. In addition, by combining the experimental results with theoretical calculations, we report the existence of large distortion-induced band splitting, further enhanced by spin−orbit coupling (SOC), shedding light on the mechanisms by which orbital hybridization occurs. WO 3 thin films were grown by PLD at the NFFA facility. 25,26 The growth was performed at ∼1000 K in an oxygen background pressure of 1 × 10 −3 mbar (the typical deposition rate was 0.07 nm per laser shot). All of the investigated samples were grown on (001)-oriented LAO substrates. The ARPES measurements were performed in situ by using a Scienta DA30 hemispherical analyzer with energy and momentum resolutions better than 15 meV and 0.02 Å −1 , respectively. The density functional theory (DFT) calculations were carried out within the CRYSTAL17 code 34 based on a linear combination of localized basis functions and the B1-WC hybrid functional. 35 To estimate/quantify the SOC, we also used the ABINIT code, 36,37 as described in Methods.
The WO 3 films were grown with thicknesses from 10 to 30 nm. We also used transmission electron microscopy (TEM) and X-ray diffraction to estimate the extent of relaxation as a function of thickness and also the surface roughness (see the Supporting Information). Within the range of thicknesses considered, we did not see by TEM any change in the lattice parameters or any change in the relaxation. By X-ray diffraction (XRD), the thinner films instead appeared to be flatter; therefore, we used these for the ARPES measurements (10 nm). Importantly, we also collected low-energy electron diffraction (LEED) (see the Supporting Information) both to monitor the quality of the surface and to look for possible surface reconstructions, which were not observed. WO 3 can be seen as an ABO 3 cubic perovskite with a missing cation. It has, however, never been observed in the reference cubic structure, which exhibits various unstable phonon modes, including antipolar motion of W against O in various directions [X 5 − and M 3 − (see Figure 1a)] and oxygen octahedral rotations with different tilt patterns (M 3 + and R 4 + ). 30,38 Accordingly, in the bulk form, WO 3 undergoes several phase transitions as a function of temperature. Between 1300 and 1500 K, its structure is tetragonal (space groups P4/ nmm and P4/ncc). 39,40 At 1000 K it becomes orthorhombic (Pbcn), 35,39,40 at room temperature monoclinic (P2 1 /n), 40,41 and at 273 K triclinic (P1̅ ), 42 and finally at 200 K, it enters a second monoclinic phase (P2 1 /c), 30,38,43,44 with no further transitions down to 5 K. This implies that this monoclinic phase is the ground state of bulk WO 3 . 30 The lattice parameters of the room-temperature monoclinic P2 1 /n phase of bulk WO 3 are as follows: a = 0.732 nm, b = 0.756 nm, and c = 0.772 nm. 40,41 These remain very similar in the Pbcn, P1̅ , and P2 1 /c phases. When the cell doubling in all three directions is taken into account, these lattice constants correspond to lattice spacings of ∼0.366 nm along a, ∼0.378 nm along b, and ∼0.386 nm along c. In the P4/nmm phase, the lattice spacing is instead ∼0.375 nm along a and b and ∼0.392 nm along c. With respect to the LAO substrate, characterized by an in-plane pseudocubic lattice parameter of 0.379 nm, an epitaxial tensile strain is therefore expected for all phases. In our work, the stabilization of a structural phase with a tetragonal metric at room temperature has been confirmed by XRD data of Figure 1b. From the (002) Bragg reflection, a caxis parameter of 0.385 nm has been measured. The c value of this pseudotetragonal phase apparently matches that of the bulk P2 1 /n phase and other low-temperature bulk phases. This is, however, surprising in view of the tensile epitaxial strain conditions, expected to produce a significant contraction along c, and better suggests that our film could adopt a P4/nmm type of structure. It has nevertheless been shown that changing the oxygen pressure during PLD growth has a major impact on the film out-of-plane lattice constant. 32,45 According to the report by Ning et al., 45 oxygen vacancies result in an increase in the c parameter of ≤5%. As in other oxides, 46,47 oxygen vacancies appear to be preferentially located at specific positions of the perovskite structure rather being randomly distributed within the materials. 46−48 The outof-plane lattice expansion due to oxygen vacancies is often termed chemical strain. 49,50 The measured c value of 0.385 nm obtained from our experiment is in very good agreement with the trend of the variation of the c lattice parameter with oxygen pressure reported in ref 45 for the P2 1 /n phase, suggesting that our pseudotetragonal film might in fact better adopt either that structure or that of the similar low-temperature phases.
To clarify this issue, we adopted an atomistic approach and performed DFT calculations. To determine the theoretical ground state of the WO 3 film, we focused on the six phases that are observed experimentally in the sequence of structural phase transitions of bulk WO 3 38−44 and explored their energy gain under tensile strain. Starting from the atomic positions of their fully relaxed bulk structures, we fixed their a and b lattice parameters to the pseudocubic a LAO of 0.379 nm while relaxing the c parameter. Our calculations suggest that the theoretical ground state of the film should be the strained monoclinic P2 1 / n phase with a c parameter of 0.738 nm. This result is in line with previous studies of stoichiometric WO 3 films, for which the c parameter was measured to be 0.733 nm 45,51,52 and the structure of the film identified as being similar to that of the monoclinic P2 1 /n phase. 45 This result is, however, questioned by the observed c parameter of 0.77 nm in our XRD.
As previously discussed, our films grown at a low oxygen pressure are deficient in oxygen. This was further confirmed by our photoemission data, which report metallic character for the samples, with the Fermi level crossing the conduction band, instead of an insulating behavior expected for the stoichio-  Figure 2a indicates that in this specific case, the most stable configuration corresponds to the Pbcn structure. This suggests that our pseudotetragonal films might likely adopt that structure, which will be further confirmed later via inspection of the electronic properties. By using AMPLIMODE software, 53 we performed symmetry-adapted mode analysis to identify the distortions, which play a major role in the stabilization of such a Pbcn strained phase. It can be characterized (see Figure 2a) by (i) octahedral rotations (R 4 + and M 3 + modes) with tilt pattern a 0 b + c − in Glazer's notation, 54 (ii) an antipolar motion along y (X 5 − mode), (iii) a small contribution of a bending mode (X 5 + ), and (iv) an antipolar motion along the z-and x-axes (M 3 − mode), where the x component of the M 3 − mode appears through anharmonic coupling. 38 This is in contrast with the P2 1 /c ground state of bulk WO 3 that arises from the contributions of (i) R 4 + with tilt pattern a − a − c − , (ii) antipolar motion along the z-axis (M 3 − ), and (iii) antipolar motion with the same amplitude along the x-and y-axes (X 5 − ). 55 Remarkably, we note that the pseudotetragonal thin films are incredibly resilient and their structure survives within a large temperature range, i.e., from room temperature (as demonstrated by XRD) to, at least, 77 K (as confirmed by ARPES). This indicates that WO 3 on LAO is highly structurally and thermally stable and that the substrate can freeze the overgrown thin layers and make them robust against temperature variations. This is in contrast to the bulk behavior, in which orthorhombic (or tetragonal) phases have never been found at low temperatures but only at temperatures as high as 800 K. [39][40][41]56,57 Again, this result points to the importance of epitaxial strain in realizing films with enhanced thermal stability compared to that of their bulk counterpart.
To understand the role of the crystal structure in the electronic properties of this compound, we performed ARPES with in-vacuum transfer without exposing the samples to air. First, we notice that the tetragonal metric of the WO 3 films is also reflected in the symmetries of the reciprocal space, namely in the symmetry of the Fermi surface (see Figure 3a). The  Figure 3a. From the Γ to X points of the Brillouin zone (BZ) (Figure 3a), we did not observe any appreciable change in the Fermi surface volume within our experimental resolution range; however, an overall different shape is visible, as expected for this system, which electronically speaking still behaves as a bulklike system for the ARPES probing depth. To locate the high-symmetry positions along the k z direction, we performed photon energy-dependent scans (see the Supporting Information for a plot of k z vs photon energy dependence), and we show them in Figure 3b. Here, we see "hot spots" of spectral intensity at several k z values. This repeating behavior helps us to fix the k z corresponding to the high-symmetry points of the Brillouin zone, namely, X and Γ, and allows us to make an estimate of the c-axis from ARPES.
With an inner potential of 11 ± 3 eV, we obtain a c ARPES of 0.77 nm, in agreement with the results from XRD. We notice that ARPES gives exactly twice the XRD value, indicating that the unit cell has a doubling, here revealed by a resonant behavior of the spectra, which reflects in this case the major probability of initial−final state matching in the photoemission process for states excited from the Γ and X points. The structural distortions of the pseudotetragonal phase lead to large energy splittings, in contrast to the Pbcn, P2 1 /n, and P2 1 / c bulk phases (see Figure S2). In high-temperature tetragonal bulk WO 3 , the d xz and d yz orbitals are degenerate at the center of the BZ (see Figure S2a). However, in the pseudotetragonal thin film, the orbital degeneracy is removed, resulting in an energy splitting that can be resolved by ARPES measurements and takes the experimental value of 100 meV (Figure 2d,e). This splitting is consistent with our calculations in the strained Pbcn phase, although the computed value takes a smaller value of 60 meV (see Figure 2b). Upon inclusion of the SOC, which is expected to be relevant for 5d orbitals, this discrepancy finds a solution; our calculation in the strained Pbcn phase reproduces an energy splitting of ≈90 meV between the d yz and d xz orbitals, in perfect agreement with ARPES (Figure 2c). This emphasizes the SOC's critical role in hybridizing the orbitals in 5d oxides. However, our results suggest that the effect of structural distortions is greater than that of the SOC. In the WO 3 film, the amplitude of the antipolar distortion along y is greater than along x; as a result, the upshift of the d yz energy level is larger than that of the d xz energy level. This is because an increase in the y-direction antipolar distortion results in a stronger overlap between the O 2p y and W 5d yz orbitals, 54 which in turn causes an upshift in the related antibonding energy level. Thus, the splitting between the d yz and d xz orbitals in this pseudotetragonal phase (shown in Figure 2b,c) is caused by a proper balance between the amplitude of the antipolar motions along y (X 5 − mode) and x (M 3 − mode). Note that this splitting, with the d yz orbital located at an energy level higher than that of the d xz orbital, is absent in all of the bulk phases, including the Pbcn and P2 1 /n phases where the x component of the M 3 − mode is negligible, or in the bulk form of the ground state where the amplitudes of the antipolar motion along y and x are almost the same (see Figure S2). More importantly, as shown in Figure S3, this is not the case in any of the similar lowtemperature phases under strain, providing additional evidence that our pseudotetragonal film adopts a strained Pbcn structure.
A second splitting can also be observed in the DFT results between the d xz and d xy orbitals, and it is estimated to be ≈380 meV after inclusion of SOC (see Figure 2c). Our calculations indicate that octahedral tilting (M 3 + and R 4 + modes) with deviations of the W−O−W angle from 180°also involves tuning the overlap of orbitals in this case. 58 From ARPES (Figure 2d,e), it is more challenging to make a straightforward comparison with the DFT results, because the d xy band has strong matrix elements that suppress its intensity near the center of the BZ. 58,59 The matrix elements and the fact that varying the probe polarization vector allows us to measure different orbital contributions are well-known among the photoemission community and are described in a dedicated section of the Supporting Information. Despite the matrix elements, we can extrapolate the minimum by fitting the data, obtaining a d xz −d xy separation of ≈400 meV, which is also in close agreement with the calculated value. Thus, the structural distortions are very important in defining the electronic properties of WO 3 , and the strain is crucial for stabilizing the pseudotetragonal phase observed here.
In conclusion, we report the existence of a new phase in WO 3 , which we call a pseudotetragonal phase but reveals in fact a strained Pbcn phase. This phase observed in films grown at low oxygen pressures differs from the P2 1 /n phase previously reported in stoichiometric films. It accommodates antipolar distortions along all three axes. Such distortions are important  ■ METHODS

DFT Details.
To approximate the BZ, integration over 8 × 8 × 8 k-point meshes for the cubic symmetry or meshes with equivalent sampling for other phases (e.g., meshes of 6 × 6 × 8, 6 × 6 × 4, and 4 × 4 × 4 for the P4/nmm, P4/ncc, and Pbcn phsases, respectively) were used. In the CRYSTAL17 code, 33 the self-consistent-field (SCF) convergence's tolerance of the change in total energy was set to 10 −10 Hartrees. Geometry optimization was performed by employing a quasi-Newton approach with a BFGS Hessian scheme, so that a specific space group symmetry was preserved for each structure during the structural relaxations. The root-mean-square values of the gradient and displacements were converged to <5 × 10 −5 Hartrees/Bohr and 10 −3 Bohr, respectively. We also used the ABINIT code 36,37 with a plane-wave basis set and the LDA functional with Perdew−Wang's parametrization, 62 to include SOC for the electronic band structures. In this case, the electronic wave functions were expanded in plane waves up to an energy cutoff of 60 Hartrees, and the electronic selfconsistent calculations were converged until the difference in the total energy is <10 −9 Hartrees. ■ ASSOCIATED CONTENT