The influence of structural disorder and phonon on metal-to-insulator transition of VO2

We used temperature-dependent x-ray absorption fine structure (XAFS) measurements to examine the local structural properties around vanadium atoms at the V K edge from VO2 films. A direct comparison of the simultaneously-measured resistance and XAFS regarding the VO2 films showed that the thermally-driven structural transition occurred prior to the resistance transition during a heating, while this change simultaneously occured during a cooling. Extended-XAFS (EXAFS) analysis revealed significant increases of the Debye-Waller factors of the V-O and V-V pairs in the {111} direction of the R-phase VO2 that are due to the phonons of the V-V arrays along the same direction in a metallic phase. The existance of a substantial amount of structural disorder on the V-V pairs along the c-axis in both M1 and R phases indicates the structural instability of V-V arrays in the axis. The anomalous structural disorder that was observed on all atomic sites at the structural phase transition prevents the migration of the V 3d1 electrons, resulting in a Mott insulator in the M2-phase VO2.

(b) was obtained from the positions of the main absorption edge and the first pre-edge peak. The main absorption edge is mainly contributed by the V 4p levels and the geometry of the nearest neighboring O atoms in VO2. The ∆E mainly corresponds to the change of the main edge position because the position of the first pre-edge peak did not change much in the temperature range of 30 -110 o C, as shown in Fig. S2(a). The temperature-dependent behavior of the main absorption edge position could be ascribed to a change in the local structure, including the bond lengths, the Debye-Waller factors, and the geometry of neighboring atoms around the V atoms.
The temperature-dependent behaviors of the second pre-edge peak are shown in Fig. S2 -110 o C, as shown in Fig. S2(b), (d). The intensity of the second pre-edge peak in the R phase was decreased by approximately 40%, compared to that in the M1 phase. The second pre-edge peak corresponds to the empty states of the V 3d band. The intensity decrease of the second pre-edge peak in the R phase implies that V 3d 1 electrons filled the band because the FWHM of the peak was nearly constant, resulting in the decrease of the peak area. The electrons in the band could play an important role in the metallic phase VO2 because the band lies just above the Fermi energy level.
The transition temperatures of the peak intensity are approximately 75 o C and 69 o C during heating and cooling, respectively, as shown in Fig. S2(c). These values correspond to none of the transition temperatures which are shown in Table 1, although they are relatively closer to the transition temperatures of the resistivity. The analysis results of the second pre-edge peak show that the state change of the band does not correspond to either the SPT or the change of the main absorption edge.
XANES does not directly reflect the LDOS due to the quantum selection rules. The LDOS at the V K edge for the VO2 were calculated using FEFF9 code 39 with the crystalline structures of the M1 and the R phases that were determined by the best fits of EXAFS. Figure S3(a) shows the calculated x-ray absorption coefficient spectrum near the V K edge, XANES, for 27 atoms in a cluster with the diameter of ~1.2 nm. The calculated XANES spectra for the M1 and the R phases are comparable to the measured XANES. The calculations show that the first pre-edge positions of both M1 and R phases appear at ~5469 eV and that the Fermi levels are placed at -12.016 eV and -12.254 eV for the M1 and the R phases, respectively. Lowering the Fermi level corresponds to raising the first pre-edge peak position, therefore, the energy gap between the positions of the main absorption edge and the first pre-edge peak decreases in the R phase, compared to that in the M1 phase. This calculation is in sound agreement with the measurements that are shown in Fig. 5(b). The LDOS of the V 3d orbitals is nearly independent of the M1 and the R phases, as shown in Fig. S3(b). The two peaks at -10.2 and -8 eV in Fig

EXAFS Analysis
The main contributors to EXAFS(χ) are neighboring atoms around a probing atom 36,37 . After the atomic background was determined using AUTOBK 38 , the EXAFS was extracted from the raw data as a function of the photoelectron wave number, = �2 ( − 0 )/ħ, where m is the electron mass, E is the incident x-ray energy, E0 is the absorption edge energy, and ћ is the Planck constant, as shown in The Fourier-transformed EXAFS consists of two parts, real and imaginary, as shown in Fig. S4 (c),(d), and these correspond to the EXAFS magnitudes in Fig. S4 (c),(d), respectively. The real and imaginary EXAFS parts were simultaneously fitted to the EXAFS theoretical calculations 39 using the same variables. The EXAFS(χ) is theoretically described, as follows 36,37,S1 : Where ̂ is the electric field direction of the incident x-rays, S0 2 accounts for the change of passive photoelectron waver functions in the presence of a core hole and multi-excitations, Nj is the mean coordination number, Fj is the photoelectron back-scattering amplitude, Rj is the jth shell atomic distance, σj² is the relative distance disorder (Debye-Waller factor) between the probing atom and the jth shell atoms, Φj is the total global phase shift of the photoelectrons from the probing atom and the jth shell atoms, and λ is the effective mean free path of the photoelectrons.
The (1) pairs was used. The E0 was initially fitted and finally fixed at the best value that was determined by the best fit because of its correlation to the other variables; therefore, ten and seven variables were in the final fits for the M1 and R phases, respectively, as shown in Table S1. All of the independent data points of the fits were estimated as approximately 12.7 using Stern's rule S3 , as N = 2∆ ∆ + 2, where ∆R = 2.5 Å (fitted region) and ∆k = 8.0 Å -1 (Fourier-transformed region). The freedoms of the fits were 2.7 and 5.7 for the M1 and the R phases, respectively. The quality of the fits was determined using the R-factor and a reduced-χ 2 , where the goodness-fit criteria of the R-factor is < 0.02 and the reduced-χ 2 is ~1 S2,S3 . After satisfactory fits were obtained, the atomic-distance and σ 2 values of the V(0)-O and V(0)-V pairs were determined. The distance and the σ 2 of each atomic pair were independently determined using the best fits of the EXAFS data that were measured at a certain temperature. Table S1 summarizes the representative fitting results of the EXAFS data at 40 and 100℃. The temperature-dependent distances and σ 2 values that are shown in Fig. 3 and 4 were determined from the best fits of the EXAFS data at different temperatures using the same manner that is mentioned previously. Table S1. The results of EXAFS data fits of the VO2 film at 40 and 100℃, as shown in Fig. 3 and 4. S0 2 of 0.8 that was determined using a k-weight fit S2 of EXAFS data from a VO2 powder 33 was fixed for the other fits of EXAFS data from VO2 films. In the fits of the M1 phase, there were four variables (3 ds and 1 σ²) for the V(0)-O pairs, three variables (2 ds and 1 σ²) for the V(0)-V(1) pairs, and three variables (2 ds and 1 σ²) for the V(0)-V(2) pairs, while in the fits of the R phase, there were three variables for the V(0)-O pairs, two variables for the V(0)-V(1) pairs, and two variables for the V(0)-V(2) pairs.  Figure S1. Normalized total x-ray absorption coefficient (μt) from the VO2 films at the V K edge during (a) a heating and (b) a cooling as functions of the incident x-ray energy at different temperatures.