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

TL;DR

This study uses spectromicroscopy to reveal that in strained VO2, the long-range order of V-V dimers weakens at mesoscopic scales near the MIT, while electrical conductivity transitions uniformly.

Contribution

It uncovers the dissociation of V-V dimer order from crystal symmetry at mesoscopic scales in strained VO2, providing new insights into the MIT mechanism.

Findings

Long-range V-V dimer order weakens beyond ~200 nm.

Conductivity transition remains homogeneous in a narrow temperature window.

Mesoscopic stripe order involves periodic modulations in symmetry and dimerization.

Abstract

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.

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The recent observations of the separation of the electronic and structural transitions of VO2 have shed new light on the microscopic mechanism of the metal-insulator transition (MIT) of this exemplar MIT material.laverock2014 ; arcangeletti2007et ; kim2008et Bulk VO2 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.morin1959et ; goodenough1973 The advantageous properties of this transition,jeong2013 ; cavalleri2001 ; park2013 have placed VO2 at the forefront of exploitable new technologies,jeong2013 ; nakano2012et particularly when married with recent advances in its preparation and growth.muraoka2002 ; cao2009 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.goodenough1973 ; haverkort2005 ; zylbersztejn1975 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, VO2 is host to a rich set of structural phases in close proximity to its solid-state triple point,park2013 which are accessible by alloying and/or strain,muraoka2002 ; pouget1974 ; pouget1975et and are suggestive of a highly contoured energy landscape with competing structural instabilities.park2013 ; gu2010 ; budai2014 For example, whereas each V ion is paired via dimerization and twisted about its dimer axis in the $M_{1}$ structure,goodenough1973 the related $M_{2}$ and triclinic T structures both contain alternating strongly and weakly dimerized V bonds.pouget1974 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.huffman2017 Other apparently distinct phases have also been proposed either as intermediate in the MIT or in close proximity, such as monoclinic metalliclaverock2014 ; arcangeletti2007et ; kumar2014 and insulating rutile phases.kumar2014 ; laverock2012 ; kittiwatanakul2014et The key to understanding the origin of the MIT in VO2 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.yao2010

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 VO2 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 VO2 via the leading edge of the spectrum, which exhibits $\sim 0.2$ eV shift between insulating and metallic phases.abbate1991et ; laverock2012b

High quality, 300 nm thin films of VO2 were grown on (110)-oriented rutile TiO2 substrates, leading to biaxial in-plane strain (tensile along $c_{\rm R}$ and compressive along $[110]_{\rm R}$).west2008 ; kittiwatanakul2013 ; supplementary Spectromicroscopic measurements were performed using low energy electron microscopybauer1994 (LEEM, 7 eV electron energy) and XAS-PEEMbauer2001 ; supplementary (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,supplementary and diffraction patterns were regularly monitored for electron or x-ray damage.laverock2015 Depth sensitivities of LEEM and XAS-PEEM are 1 and 5 nm, respectively. Crucially, our biaxially strained VO2(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 important stages in the MIT of VO2(110) [Fig. 1(a-i)], alongside spatially-averaged O K edge XAS [Fig. 1(j)]. The three temperatures chosen representlaverock2014 (i) 51 *∘*C: insulating, emerging rutile-like stripes; (ii) 58 *∘*C: stripes fully established, both metallic and insulating monoclinic-like phases coexist; and (iii) 69 *∘*C: fully metallic, small stripes of monoclinic-like symmetry persist.

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 $\pi^{*}$ states, followed by a prominent $d_{\|}$ peak at 530.7 eV due to V-V dimerization.abbate1991et ; laverock2012b 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 $\geq 57$ *∘*C show the same leading edge and $\pi^{*}$ spectra as rutile VO2, indicating the sample predominantly contains metallic VO2, 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 $\pi^{*}$ 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 VO2(110) system, where fully metallic photoemission spectra were observed at 61 *∘*C and above.laverock2014

Structural stripes oriented along the $c_{\rm R}$ 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.laverock2014 Corresponding contrast is visible in the XAS-PEEM images recorded at the $d_{\|}$ energy shown in Fig. 1(b,e,h), but is absent in XAS-PEEM at the $\pi^{*}$ energy [Fig. 1(c,f,i)].contrast This strong contrast gradually weakens before becoming faintly visible again just above the $\sigma^{*}$ 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.supplementary The results are summarised in Fig. 2. As an example of the process at 58 *∘*C, Fig. 2(c,d) shows the XAS-PEEM image in the $d_{\|}$ energy window, overlaid with two LEEM masks, corresponding to the dark LEEM intensities [monoclinic-like phase, Fig. 2(c)] and bright LEEM intensities [rutile-like phase, Fig. 2(d)]. The agreement between the stripe structure observed in LEEM and XAS-PEEM at the $d_{\|}$ photon energy is excellent, confirming the contrast in both images has the same spatial origin. Similar results are found at 51 *∘*C [Fig. 2(a,b)] and 69 *∘*C [Fig. 2(e,f)].

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 monoclinic-like and rutile-like regions of the sample retain V-V dimer bonds to some extent. The “dark LEEM” spectrum, representing monoclinic-like VO2(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 $M_{1}$ VO2 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 VO2.supplementary These observations demonstrate that even at this temperature, the intermediate “mixed” phase of strained VO2(110) contains neither $M_{1}$ nor R phase VO2, 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 $\pi^{*}$ 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.supplementary 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;laverock2014 ; mcleod2017 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,laverock2014 from which we estimate the stripe widths as $235\pm 12$ (51 *∘*C), $207\pm 18$ (58 *∘*C), and $170\pm 33$ 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. For example, the second satellites are found at 1.28 µm in the LEEM [Fig. 3(a)] compared with 870 nm in the XAS-PEEM [Fig. 3(c)] auto-correlations. These are separated 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.supplementary 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 VO2(110). Initially, VO2 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 $c_{\rm R}$-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 VO2 might play in our interpretation.park2013 ; gu2010 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 $M_{1}$ VO2).pouget1974 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.quackenbush2016 The triclinic T phase, although insulating with a band gap comparable to the $M_{1}$ and $M_{2}$ phases,zylbersztejn1975 ; huffman2017 is transitional between these two structures, whereby the equally paired and twisted dimers in $M_{1}$ gradually and continuously differentiate into the structures in $M_{2}$.pouget1974 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 VO2, which has recently been suggested to play a role in the $M_{1}\rightarrow R$ transition of bulk VO2.yao2010

In order to test our interpretations, we have performed electronic structure calculations of VO2 using the Elk codedewhurst2016 within the GGA+U formalism ($U=2.8$ eV),yao2010 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 VO6 octahedra within the unit cell.supplementary 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 $\leq 25$% of the $M_{1}$ bond strengths, GGA+U predicts that VO2 is metallic, irrespective of the twisting of the dimer and VO6 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 $M_{1}$ VO2 is anticipated to be small.zylbersztejn1975 ; eyert2002et Partly, this may be explained by the reduced screening available in the $M_{1}$ phase due to the emptying of the $\pi^{*}$ ($e_{g}^{\pi}$) orbital and the narrowing of the occupied $d_{\|}$ ($a_{1g}$) due to a reduction in mixing.zylbersztejn1975 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 ($\approx 1.4$ eV) at $\geq 58$ *∘*C (i.e. in the metallic phases). In the insulating phases ($\leq 51$ *∘*C), the contrast spectra have a width of $\approx 1.0$ 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 VO2.

In summary, the $M_{1}$ VO2 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.

Acknowledgments

The Boston University program is supported in part by the Department of Energy under Grant No. DE-FG02-98ER45680. S.K., J.W.L. and S.A.W. gratefully acknowledge financial support from the Army Research Office through MURI grant No. W911-NF-09-1-0398. J.L. acknowledges the EPSRC Centre for Doctoral Training in Condensed Matter Physics (CDT-CMP), Grant No. EP/L015544/1. Calculations were performed using the computational facilities of the Advanced Computing Research Centre, University of Bristol (http://www.bris.ac.uk/acrc/). The underlying research materials can be accessed at the following DOI: 10.5523/xxx.