Observation of weakened V-V dimers in the monoclinic metallic phase of strained VO2

Emergent order at mesoscopic length scales in condensed matter can provide fundamental insight into the underlying competing interactions and their relationship with the order parameter. Using spectromicroscopy, we show that mesoscopic stripe order near the metal-insulator transition (MIT) of strained VO2 represent periodic modulations in both crystal symmetry and V-V dimerization. Above the MIT, we unexpectedly find the long range order of V-V dimer strength and crystal symmetry become dissociated beyond ~ 200 nm, whereas the conductivity transition proceeds homogeneously in a narrow temperature range.

The recent observations of the separation of the electronic and structural transitions of VO 2 have shed new light on the microscopic mechanism of the metal-insulator transition (MIT) of this exemplar MIT material. 1-3 Bulk VO 2 at low temperature exists in a strongly dimerized (between neighboring V ions) and insulating monoclinic structure (the M 1 phase), which transitions to the high symmetry tetragonal rutile (R) phase at 65 • C concomitant with a huge change in the conductivity of 4 orders of magnitude. 4,5 The advantageous properties of this transition, [6][7][8] have placed VO 2 at the forefront of exploitable new technologies, 6,9 particularly when married with recent advances in its preparation and growth. 10,11 However, the coincidence of these large structural and electronic transitions preclude the unambiguous untangling of the mechanism behind the transition, leading to decades of debate as to the whether the MIT is driven by structural instabilities towards dimerization, or as a consequence of the effects of strong electron correlation. 5,12,13 In this context, the details of the low symmetry monoclinic-like metallic phase(s) that develops intermediate between M 1 and R offer a unique and crucial insight into these questions.
In addition to the well-known M 1 and R phases, VO 2 is host to a rich set of structural phases in close proximity to its solid-state triple point, 8 which are accessible by alloying and/or strain, 10,14,15 and are suggestive of a highly contoured energy landscape with competing structural instabilities. 8,16,17 For example, whereas each V ion is paired via dimerization and twisted about its dimer axis in the M 1 structure, 5 the related M 2 and triclinic T structures both contain alternating strongly and weakly dimerized V bonds. 14 The similar magnitude of the band gaps in all three of these insulating structures, despite differing V-V bonding patterns, has been taken as evidence that electron correlations dominate the MIT. 18 Other apparently distinct phases have also been proposed either as intermediate in the MIT or in close proxim-ity, such as monoclinic metallic 1,2,19 and insulating rutile phases. [19][20][21] The key to understanding the origin of the MIT in VO 2 may lie with a microscopic understanding of such phases, particularly whether V-V dimers remain strongly paired despite remaining metallic; recent measurements suggest the conductivity is intimately linked to the "twisting angle" of the V-V pairs. 22 Here, we employ spatially-resolved x-ray absorption spectroscopy (XAS) by imaging the secondary electron yield using photoemission electron microscopy (XPEEM) in concert as a spectromicroscopic technique (XAS-PEEM), which we apply in detail to the intermediate region of the MIT. XAS at the O K edge in VO 2 is sensitive to both V-V dimerization through the so-called d peak, which arises due to the absorption of x-rays into unoccupied dimer (a 1g ) orbitals, and to the metallicity of VO 2 via the leading edge of the spectrum, which exhibits ∼ 0.2 eV shift between insulating and metallic phases. 23,24 High quality, 300 nm thin films of VO 2 were grown on (110)-oriented rutile TiO 2 substrates, leading to biaxial in-plane strain (tensile along c R and compressive along [110] R ). 25,28,29 Spectromicroscopic measurements were performed using low energy electron microscopy 26 (LEEM, 7 eV electron energy) and XAS-PEEM 25,27 (1.7 eV) at the SPELEEM endstation of Beamline I311, MAX-lab (Lund, Sweden), with x-ray energy and position resolutions of 0.2 eV and 40 nm, respectively, 25 and diffraction patterns were regularly monitored for electron or x-ray damage. 30 Depth sensitivities of LEEM and XAS-PEEM are 1 and 5 nm, respectively. Crucially, our biaxially strained VO 2 (110) thin films serve two purposes, allowing both the intermediate region of the phase diagram to be explored, and the different coexisting phases to be probed independently but at the same time. Figure 1 summarises the main experimental results: LEEM and XAS-PEEM images are shown at three im- Below the MIT at 24 • C, the characteristic M 1 phase spectrum is observed in Fig. 1(j), consisting of a peak at 530.0 eV due to π * states, followed by a prominent d peak at 530.7 eV due to V-V dimerization. 23,24 The complete suppression of the d peak above the MIT (97 • ) is due to the absence of V-V dimers in the R phase, and the shift downwards by 0.2 eV of the leading edge arises due to its metallicity. At intermediate temperatures, some excess intensity exists at the d peak, suggestive of the presence of V-V dimers. Spectra recorded at temperatures ≥ 57 • C show the same leading edge and π * spectra as rutile VO 2 , indicating the sample predominantly contains metallic VO 2 , despite the persistence of rutile and monoclinic stripes up to 87 • C. However, at intermediate temperatures of 51 • C and below, the absorption onset follows the insulating monoclinic shape, and the π * feature appears intermediate between the M 1 and R phase spectra. These results are in good agreement with our previous LEEM and photoemission measurements on the same VO 2 (110) system, where fully metallic photoemission spectra were observed at 61 • C and above. 1 Structural stripes oriented along the c R axis are clearly observed in the LEEM images, Figs. 1(a,d,g). The contrast in the LEEM is due to diffraction contrast, in which bright intensity corresponds to the rutile-like phase. 1 Corresponding contrast is visible in the XAS-PEEM images recorded at the d energy shown in Fig. 1 31 This strong contrast gradually weakens before becoming faintly visible again just above the σ * states [e.g. at 58 • C in Fig. 1(k)].
We now quantitatively compare XAS-PEEM and LEEM to understand the nature of the V-V pairing in the monoclinic metallic phase. We extract the XAS spectra corresponding to the two LEEM structures by constructing a mask from the LEEM by thresholding its intensity. 25 The results are summarised in The extracted XAS-PEEM spectra are shown in Fig. 2(g), alongside the insulating M 1 and metallic R phase XAS spectra. At 51 • C, there is clear contrast near the d photon energy, however the intensity is intermediate between M 1 and R, suggesting both monocliniclike and rutile-like regions of the sample retain V-V dimer bonds to some extent. The "dark LEEM" spectrum, representing monoclinic-like VO 2 (110), was obtained using a threshold of 40% of the LEEM pixels at 51 • C, though this spectrum hardly changes at a threshold of 1%, indicating that M 1 VO 2 has already been destroyed. Similarly, the "bright LEEM" spectrum does not approach the R phase spectrum down to 1% threshold. In particular, the shapes of the leading edges of the 51 • C spectra imply this is a spectrally distinct phase of VO 2 . 25   XAS-PEEM spectra at select temperatures obtained as a result of applying masks to the energy-dependent XPEEM images. The dark and bright LEEM masks are shown at each temperature in (a-f), overlaid on the corresponding d peak XPEEM images. The thresholds used were 40%, 30% and 30% for dark masks in (a,c,e), and 15%, 33% and 40% for the bright masks in (b,d,f). Transparent regions are those that contribute to the XAS-PEEM spectra. (g) XAS-PEEM spectra obtained by applying the masks, vertically offset for clarity, and shown alongside reference M1 and R phase spectra. Also shown is the r.m.s. magnitude of the energy-dependent cross-correlation function at 58 • C. Scale bar 1 µm.
contains neither M 1 nor R phase VO 2 , and that the contrast in both LEEM and XAS-PEEM is more complex.
At 58 • C, both extracted spectra show the same leading edge and π * structures, supporting the homogeneity of the metallicity. On the other hand, clear contrast between the two spectra is observed at the d peak, supported by the peak in the r.m.s. cross-correlation coefficient. 25 The "bright LEEM" spectrum approaches the metallic rutile spectrum at all energies, whereas the "dark LEEM" spectrum exhibits weak enhancement in the absorption coefficient near the d peak, and does not approach the M 1 phase spectrum at thresholds down to 1%. The monoclinic metallic phase is therefore spectrally distinct from the M 1 phase, consisting of weakened V-V dimers. Similar results are found at 69 • C, but with reduced contrast and an overall reduction in the intensity at the d photon energy.
By examining the correlation between the XAS-PEEM image at the d energy and the LEEM image, we are able to assess how closely related the spatial variations in crystal (LEEM) and dimerization (XAS-PEEM) structures are; 1,32 auto-and cross-correlation coefficients at different temperatures are shown in Fig. 3. Perpendicular to the stripe axis, the images [panels (a-c)] show strong oscillatory behavior typical of stripe order, 1 from which we estimate the stripe widths as 235 ± 12 (51 • C), 207 ± 18 (58 • C), and 170 ± 33 nm (69 • C), measured from the mean first zero-crossing (with standard error). Note that the damping of these oscillations along the perpendicular axis is similar in each correlation coefficient, suggesting equivalent long-range order in both LEEM and XAS-PEEM contrast mechanisms. At 51 • C [ Fig. 3(d)], there is excellent agreement between structures in the LEEM and XAS-PEEM auto-and cross-correlations, indicating that the two contrast mechanisms are strongly coupled. However, at 58 • C [ Fig. 3(e)], these begin to diverge and, crucially, are qualitatively different from one another. arated from the first satellites (which represent the mean stripe separation, 580 nm from LEEM and 520 nm from XAS-PEEM) by a negative trough, which has a specific meaning here. 25 Similar behavior is observed at 69 • C [ Fig. 3(f)]. This disparity in the structure of the correlation above 58 • C is not expected if the mechanism for contrast in the two measurement techniques is sensitive to the same underlying structure, i.e. in our case, if the crystal symmetry and V-V dimerization are directly and causally linked. Nevertheless, it is clear from Fig. 3, and in Figs. 1 and 2 above, that sufficiently similar patterns are observed in both images that the two contrasts are related. We therefore conclude that the symmetry and V-V dimerization are different, albeit related, responses to the structural and electronic instabilities that develop in the system in this intermediate part of the phase diagram.
Given the above results, we can establish a detailed picture of the progression of the MIT in strained VO 2 (110). Initially, VO 2 is insulating and resides in the M 1 structure, as is well known. With raising temperature, the strict M 1 structure is quickly lost, as the dimerization of the V ions along the rutile c R -axis is weakened, though the system remains electronically insulating. By 51 • C, the system separates into more strongly and weakly dimerized V-V bonds, yielding XAS-PEEM stripe contrast at the d energy. Initially, the spatial variation in the magnitudes of the dimer strength and the monoclinic distortion are strongly coupled to one another.
On further increasing the temperature, the V-V bonds are weakened further, resulting in a decrease in intensity of the XAS-PEEM near the d photon energy. By 58 • C, the system transitions to a metallic state, but this transition does not follow the underlying stripe structure. Rather, we suggest that once a critical mean V-V bond length is reached, the metallic phase is stabilized and propagates rapidly through the sample. Although there exist short-range correlations between the monoclinic distortion and V-V dimerization, these are not commensurate with one another over long length-scales. Above this temperature, however, monoclinic-like stripes remain over a wide temperature range, corresponding to weak dimers in a distorted rutile structure. In terms of the mechanism of the MIT, our key observation is that the metallic phase is not correlated with the stripe structure, but rather advances in a narrow temperature range independent of the variations in crystal structure, which is easily reconciled in the presence of strong electron correlations.
It is pertinent to ask what role, if any, other lower symmetry phases of VO 2 might play in our interpretation. 8,16 It is well known that the monoclinic M 2 phase, for example, consists of one half of the V-V ions arranged in a twisted (undimerized) 1D chain and the other half arranged in a dimerized (untwisted) chain (compared with fully dimerized and twisted V-V bonds in M 1 VO 2 ). 14 However, the M 2 phase is an insulator with a sizeable gap, and experimental XAS spectra bear little resemblance to those of our intermediate phase. 33 The triclinic T phase, although insulating with a band gap comparable to the M 1 and M 2 phases, 13,18 is transitional between these two structures, whereby the equally paired and twisted dimers in M 1 gradually and continuously differentiate into the structures in M 2 . 14 The T phase illustrates the inherent structural instability of the V-V dimers, and that a continuous evolution in their strength and orientation towards a gradual breaking of these bonds is already well established in VO 2 , which has recently been suggested to play a role in the M 1 → R transition of bulk VO 2 . 22 In order to test our interpretations, we have performed electronic structure calculations of VO 2 using the Elk code 35 within the GGA+U formalism (U = 2.8 eV), 22 explicitly separating the two structural components of the MIT into independent evolutions in the V-V bond length and the twisting of the dimer and VO 6 octahedra within the unit cell. 25 All solutions using the rutile V-V bond length (i.e. un-dimerized) are metallic, Fig. 4(a,d).
On the other hand, varying the bond lengths between those of the rutile and M 1 phases leads to an insulating solution for dimer strengths of 50% and greater towards the M 1 structure [ Fig. 4(c)]. The significance of this result is that for "weak dimerization", characterized by dimers of ≤ 25% of the M 1 bond strengths, GGA+U predicts that VO 2 is metallic, irrespective of the twisting of the dimer and VO 6 octahedra [ Figs. 4(b,d)]. In the presence of biaxial strain, these intermediate structures may be metastable during the progress of the MIT, in qualitative agreement with our XAS-PEEM results.
Without strong electron correlations, the band gap in insulating M 1 VO 2 is anticipated to be small. 13,34 Partly, this may be explained by the reduced screening available in the M 1 phase due to the emptying of the π * (e π g ) orbital and the narrowing of the occupied d (a 1g ) due to a reduction in mixing. 13 It is therefore noteworthy that contrast spectra (i.e. the difference between "dark LEEM" and "bright LEEM" spectra) based on our XAS-PEEM results indicate a broader width (≈ 1.4 eV) at ≥ 58 • C (i.e. in the metallic phases). In the insulating phases (≤ 51 • C), the contrast spectra have a width of ≈ 1.0 eV, comparable to the difference spectrum of (M 1 − R). Together with the details of the stripes discussed above, these results represent strong evidence that electron correlations are central to the MIT mechanism in VO 2 .
In summary, the M 1 VO 2 is quickly destroyed on heating, and is replaced by an insulating monoclinic phase that gradually separates into strongly-and weakly-paired dimers that are coupled to the underlying symmetry of the crystal structure. The electronic transition occurs over a narrow temperature range within this structural evolution, giving way to a monoclinic-like metallic phase that still contains bimodal dimer pairing and symmetry. The continuous weakening of the structural distortion eventually establishes the rutile phase. These details are inconsistent with a structural MIT model, depending instead on the effects of strong electron correlation.