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Polarized Raman scattering of large crystalline domains in VO2 films on sapphire
Accepted Manuscript Title: Polarized Raman scattering of large crystalline domains in VO2 films on sapphire Author: Mustapha Zaghrioui Joe Sakai Nurul Hanis Azhan Kui Su Kunio Okimura PII: DOI: Reference:
S0924-2031(15)30009-6 http://dx.doi.org/doi:10.1016/j.vibspec.2015.08.003 VIBSPE 2451
To appear in:
VIBSPE
Received date: Revised date: Accepted date:
13-7-2015 24-8-2015 25-8-2015
Please cite this article as: Mustapha Zaghrioui, Joe Sakai, Nurul Hanis Azhan, Kui Su, Kunio Okimura, Polarized Raman scattering of large crystalline domains in VO2 films on sapphire, Vibrational Spectroscopy http://dx.doi.org/10.1016/j.vibspec.2015.08.003 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Polarized Raman scattering of large crystalline domains in VO2 films on sapphire Mustapha Zaghriouia* [email protected], Joe Sakaia, Nurul Hanis Azhanb, Kui Sub, Kunio Okimurab a
GREMAN, UMR 7347 CNRS, Université François Rabelais de Tours, Parc de Grandmont
37200 Tours, France b *
Graduate School of Science and Technology, Tokai University, Hiratsuka 259-1292, Japan
Corresponding author. Tel.: +33 254552105; fax: +33 254552137.
1
Abstract Polarized Raman scattering measurements were performed on (011)-oriented, over 10 µm-size VO2 grains on an Al2O3 (001) substrate. Angular intensity dependence of Raman active modes allowed to observe 17 modes among the 18 expected and to demonstrate the single crystalline character of the large domains. Analyses of intensity evolution have been used to correctly assign phonon modes and to calculate the Raman tensor elements. In addition, a Raman Ag mode related to the V-V stretching vibration was found to have a different behavior versus angle rotation from other Ag modes, which supports the previous theoretical study and photoexcitation measurements. Keywords: Polarized Raman spectroscopy; Phonon modes assignment; Vanadium dioxide VO2; Thin films
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1. Introduction Vanadium dioxide VO2 belongs to the strongly correlated electron materials and presents insulator-metal transition at 68°C accompanied by a structural transition, from the monoclinic M1 phase (P21/c) to the rutile R phase (P42/mmm) [1,2]. In stressed VO2, a transient monoclinic M2 (C2/m) phase occurs before entering into the rutile phase. M1 structure is characterized by a dimerization of vanadium atoms (V-V pairs) and a tilting along a-axis, forming two chains. In contrast, M2 phase is characterized by a pairing in one chain [3-6]. Despite the numerous studies on VO2, the mechanism driving insulator-metal transition is still under debate, demonstrating the complexity of this binary oxide as the transition exhibits both Peierls-like and Mott-like characteristics [4, 7-13]. Understanding this mechanism is a key of the applicability of VO2 material as thermochromics coatings, transistors, ultrafast optical switching or temperature sensors [14-21]. Adopting Raman scattering, which is a phenomenon sensitive to crystalline structure and stress, Raman spectroscopy technique is one of the most popular tools to characterize VO2 films, enabling identification of the synthesized phase or investigation of the structural transitions induced by doping, temperature or stress [22-36]. It is therefore more pertinent in the case of VO2 as it can adopt various crystal structure phases as monoclinic (M1 and M2), rutile (R) and triclinic (T) phases [32-34]. One important thing in Raman spectroscopy is the mode symmetry assignment, which is performed on single crystals along precise crystallographic directions using polarized Raman scattering. Mode assignment is done on the basis of the group theory analysis and selection rules. Phonon mode symmetry, if known, allows precise structural or electronic discussions. Despite the numerous studies, no consensus was reached for Raman modes assignment of M1 phase VO2. This is largely due to the lack of single crystal that is used to perform such a task. Most studies conducted on this subject were performed on oriented or epitaxial thin films and nanorods. In all the cases, grain size is nanometric while the laser spot, in the best cases, can only reach about 300 nm in diameter, which means that the recorded Raman spectrum represents contributions of multiple
3
grains, and that single crystalline character that needs to perform precise assignment is therefore lost. Nonetheless, Schilbe et al. have performed polarized Raman measurements, at 83 K, on crystals (2 mm x 2 mm x 1 mm) obtained by chemical vapor deposition and presented (011)oriented surface,1 which leads to observe 17 Raman modes among the 18 allowed (9 Ag + 9 Bg) [26, 27]. Their assignment was done by measuring spectra in parallel and cross configurations. But as we will show in this study, this assignment is not complete since spectra recorded in both configurations do not show a complete extinction of Bg modes in the parallel configuration as is predicted by the group theory analysis. In this paper, we report on a new phonon modes assignment of the monoclinic M1 phase using polarized Raman scattering measurements at various in-plane rotation angles, which allows a minute study of intensity mode evolution and thus deeper mode symmetry analysis. Recently, we succeeded to grow thin films of M1 phase VO2 on the Al2O3 (001) substrate with large grains (larger than 10 µm in size) that present out-of-plane orientation along (011) direction [37, 38]. Their grain size is sufficient for micro Raman observation of a single grain. At the same time, the single-crystalline character of this novel type grains was confirmed by the present angle-dependent polarized Raman observation.
2. Experimental details The VO2 film was deposited on an Al2O3 (001) substrate using rf-biased reactive sputtering. In this technique, rf power is applied to the substrate holder as well as to the target, enabling control of stress and thus transition temperature of VO2 films. The deposition was performed at substrate temperature of 400°C under substrate biasing of 10 W. Total pressure of gases (Ar and O2), target rf-power and deposition time were set to 0.5 Pa, 200 W and 40 min, respectively (See references 37 and 38 for more details). The resulting film contained two domains characterized by grains with nano and micro size (Fig. 1a). X-ray diffraction and SEM analyses have shown that domains with nano-grains and large grains have, respectively, (010) and (011) out-of-plane orientations. 1
All lattice indices described in this paper represent those of the monoclinic M1 phase. 4
Polarized Raman scattering were performed using Renishaw Invia Reflex spectrometer at fixed polarization of the scattered light and with or without the /2 plate of the incident light for cross or parallel configurations, respectively. An excitation, 514 nm-line beam of an argon-ion laser with a power of 0.5 W, was focused by a x100 lens (0.85NA), which was also used to collect the scattered light in a backscattering configuration. The scattered light passes through an analyzer and is dispersed on a 2400 lines/mm grating. In this configuration the spatial resolution is close to 1 µm with the spectral resolution of 0.5 cm-1. In order to collect Raman spectra versus rotation angle, the film was mounted on a rotating sample holder. All measurements were performed in the air at room temperature.
3. Theoretical background At room temperature and under atmospheric pressure, VO2 crystallizes in a monoclinic 5 structure so-called M1 phase, which corresponds to a distorted rutile structure with C2h point group
(P21/c space group). Group theory analysis predicts 18 Raman active modes (9Ag + 9Bg). The Raman tensor, Rj, for the space group (unique axis b) expressed in the unit cell are:
RAg
a 0 d 0 b 0 d 0 c
0 RBg e 0
e 0 f
0 f , 0
where a, b, c, d, e and f are the tensor elements. In this study, Cartesian laboratory coordinates (X, Y, Z) were chosen to simplify the measurements and the calculations. The choice of these coordinates is shown in Fig. 1b. At the initial position, VO2 cell is disposed with its a-axis along X and b-axis along Y (Fig. 1b). As Raman tensors are expressed in the unit cell, it is necessary to transform them into the laboratory coordinates by using the Euler’s angles. Recall that Euler’s angles (, , ) correspond, in our case, 5
to the first rotation by around Z-axis, the second rotation by around Y-axis and the third rotation
around Z-axis. Thus the transformation matrix of Euler’s angles, is as follows: cos cos cos sin sin cos cos sin cos sin cos sin
cos cos sin cos sin cos cos cos sin sin sin sin
cos sin sin sin . cos
The general expression of the Raman tensor is thus expressed, in the laboratory coordinates (X, Y, Z), as:
RXYZ Φ.R j .Φ
(1)
corresponds to the inverse matrix of . where Φ
For each phonon mode, the Raman intensity can be thus calculated from the Raman tensor as 2
I j ei .RXYZ .es
(2)
where es and ei correspond to the unit polarization vectors of scattered and incident light, respectively. The setup used in this study allows the following polarization vectors:
XX i
e
10 0 ; e
YX i
1 (010) and es 0 , 0
where the superscripts XX and YX correspond, respectively, to the parallel and cross configurations.
4. Results and discussions
4.1. Nano-domains Fig. 2 shows Raman spectra obtained on the nano-grain domains at various rotation angle for both polarization configurations. It can be seen that the spectrum is independent of the rotation for parallel and cross configurations. A difference in peak intensities is also observed between both configurations, suggesting a preferential out-of-plane orientation of nano-grains. Indeed, X-ray diffraction (XRD) analyses have evidenced out-of-plane (010)-orientation in agreement with these results [38]. Concerning in-plane orientation, XRD has shown epitaxial growth of the nano-grains 6
through -scan profiles of this region, presenting three sets of (011) reflection peaks rotated each other by 60°, because of hexagonal ab plane of the alumina substrate [38]. On the other hand, the Raman spectra reported here seem to be similar to that obtained on films presenting random inplane distribution. This discrepancy is explained as follows. As the laser spot size used for the measurements is about 1 µm, the collected Raman spectrum is representative of the three types of grains, i.e. that the intensity of each mode corresponds to the contribution of the intensities from the three types. Using equations 1 and 2, Raman intensity was simulated considering the first type of grains at angle , the second at + 60° and the third at + 120°. Other Euler’s angles () were determined so as to make (010) plane parallel to the (X, Y) plane, i.e. and are equal to 90°. Evolution of the simulated intensity was found to be independent in agreement with our experimental results (inset in Fig. 2). In previous studies, phonon modes assignment was done on the basis of results obtained on the films similarly oriented [31]. As shown here, it is risky to assign phonon modes on such grains of six-fold symmetry, because all the modes are observed in both parallel and cross configurations, in spite of the zero intensity of Bg mode for parallel configuration predicted by the selection rules.
4.2. Micro-domains Fig. 3 shows Raman spectra obtained for one large grain (diameter> 10 µm) at several eff values. Note that these results are representative of the large grains (more than 10 were checked seriously and 20 roughly). In addition, eff angle corresponds to the angle between laser polarization, fixed along X axis, and the starting position, which is different from the real angle because the origin is unknown. This will be estimated in the following of this section. As it can be seen in Fig. 3, the evolution of peak intensities is apparently rotation angle dependent for both XX and YX configurations, strongly suggesting single crystalline character of the large grains. Moreover, spectra recorded for several grains at the same eff angle present difference in mode intensities, indicating a random in-plane orientation among different grains. These results 7
are consistent with those of XRD where 2- scans showed out-of-plane (011)-orientation and scans showed non-epitaxial growth of the grains. Moreover, Raman spectra recorded between 180 and 360° are similar to those acquired between 0 and 180°. Thus, mode intensity evolution was treated in the range 0-180°. At least 17 Raman modes could be observed among the 18 expected. The missing mode cannot be observed at room temperature but probably becomes visible at low temperature; Schilbe
et al. observed it at 265 cm-1 close to the mode at 262 cm-1, in a low temperature measurement at 83 K [26,27]. Among Raman modes observed in this work, two modes located at 138 cm-1 and 144 cm1
are reported for the first time in this spectral range, whereas only one mode is observed in the
previous studies. In order to extract intensity/area of each peak as functions of eff, the spectra were fitted using Lorentzian functions. Peak intensities deduced from the fit for both configurations are plotted in Fig. 4 for some selected modes in parallel and cross configurations. Two behaviors could be observed in intensity evolution for parallel configuration. Some modes present one maximum (Fig. 4a), while others have two maxima (Fig. 4b). In contrast to the parallel configuration, all modes have two maxima in cross configuration (Fig. 4c and 4d). This intensity behavior could be related to the symmetry of the modes, i.e. it could be used to assign phonon modes. Let us compare these results to the theoretical intensities in order to check this assumption. Recall that the initial position of the cell is positioned with c-axis along Z and b-axis along Y. To bring (011) plane parallel to (X, Y) plane, the cell should be rotated first by = 90° around Z and then along Y by = 44.97°. Expressions of the intensities are the following: 2
I
XX Ag
1 1 A B cos 2 C sin 2 2 2
I
XX Bg
1 1 F F cos 2 E sin 2 2 2
(3a)
(3b)
(3c)
2
YX I Ag C cos 2
2
1 B sin 2 2 8
2
1 YX I Bg E cos 2 F sin 2 2
(3d)
where
A a b cos 2 c sin 2
B a b cos 2 c sin 2
C d sin
F f sin 2 E e cos .
As stated by these expressions, both Ag and Bg symmetry modes should have two maxima in
YX configuration in agreement with experimental results. For XX configuration, depending on tensor elements, both expressions could present one or two maxima since they are similar. Thus XX is null phonon mode assignment could not be done on the basis of the periodicity. However, I Bg XX for while I Ag is not (In this case, a-axis is parallel to the laser polarization).
Experimentally, this will correspond to a small or a minimum intensity depending on the degree of the sample misalignment, and imperfection of the laser polarization and the analyzer. According to this, evolution of peak intensity was checked and a minimum or null intensity was observed for some modes for eff ranging between 160 and 170° (Fig. 4a and 4b). Detailed measurements in this range allowed us to estimate eff that presents a minimum in intensity of these modes, which was found to be 165 1°. This step was essential for knowing the real origin of angle and thus to assign correctly phonon modes and to determine Raman tensor elements for most of the observed modes. Indeed, it was not possible for certain modes to perform precise calculations because of the low intensity (mode 482 cm-1) or overlapping with other modes (modes 144 cm-1 and 663 cm-1). On the basis of these results, phonon modes assignment was done. First, Raman spectra were performed in parallel and cross configurations at = 90° and 147°. For = 90°, laser polarization is parallel or perpendicular to a-axis, whereas it is parallel or perpendicular to 0 11 direction for 9
= 147°. At both positions, Bg modes have their intensities at the minimum for parallel configuration and are higher for the cross configuration. In addition, at = 90°, identification of Bg modes is difficult because of the increase in intensity of Ag mode at the same manner as that of Bg modes; while at = 147° the scenario is in opposite where, in cross configuration, Ag modes have lower intensities. This is more visible if the laser excitation is more energetic as shown in Fig. 5a for the blue laser excitation ( = 457 nm). It seems that this energy is close to an electronic transition, which exalts the Raman scattering (resonance Raman scattering). The fact that only Bg phonon modes are affected by this phenomenon suggests a correlation between these modes and the corresponding electronic transition. In agreement with the observations above, we were able to correctly assign Raman modes of VO2 monoclinic M1 phase as shown in Fig. 5. These results are, in our opinion, the first Raman polarized spectra that clearly show a huge difference between Ag and Bg mode symmetries. Until now, all polarized Raman spectra were reported on (010)-oriented epitaxial films or nanorods [26,27,29,31,32]. However, as it was shown in this study, epitaxial films do not provide clear and precise assignment. The most thorough study is the one performed by Schilbe et al. on crystals obtained by chemical vapor transport [26,27]. Indeed, large crystals were obtained presenting some defects such as cracks and dislocations. Our assignment is in general in agreement with that performed by Schilbe et al. except for three modes located at 138, 338 and 452 cm-1. Both modes at 138 and 452 cm-1 have Bg symmetry while the mode at 338 cm-1 has Ag symmetry. In addition, the data show clearly that 138 cm-1 mode has Bg symmetry in agreement with the time-resolved optical spectroscopy measurement reported by Cavalleri et al. [39]. Note that this measurement, detecting the coherent excitations, reveals only Ag modes and that 138 cm-1 phonon mode was not observed. On the other hand, our assignment is consistent with phonon calculations reported by Yuan et al. [40], where frequencies of Ag modes are reproducible whereas those of Bg modes are somewhat far notably for the lower and the higher frequency modes. The same observation could be done for the high frequency Ag mode. Note that in previous studies, the Raman mode at about 138 cm-1 was 10
always assigned as Ag mode symmetry and was attributed to the calculated one at 152 cm-1 [40]. However, the latter could correspond to the small mode observed in this study at 144 cm-1. This mode is visible on the most spectra reported in literatures but had never mentioned; maybe its small intensity and its overlapping with the mode at 138 cm-1 are the reasons for this unconcern. As we can see in Fig. 6b, this mode presents angular dependence and its intensity evolution follows the same behavior as Ag modes. All active Raman modes are thus identified and assigned, 17 modes observed in this work plus the small mode reported by Schilbe et al. at 265 cm-1, which could be clearly observed at low temperature (83 K) [26,27]. Frequencies and symmetry of active Raman modes is summarized in table 1 together with the calculated tensor elements. According to our assignment, mode intensity versus rotation angle was fitted using equations
XX in the case of parallel configuration. The obtained fitting parameters were then used to check the results of cross configuration. Indeed, experimental data obtained in this latter configuration were not used to calculate Raman tensor elements because of (i) the insertion of /2 plate on the incident path that introduces a small deviation from the ideal orthogonal polarization, and (ii) the low Raman intensity that introduces a higher background signal. The best fitting parameters are summarized in table 1 and the obtained curves are plotted in Fig. 6 together with experimental data. Interestingly, we find that Ag modes present one maximum, except 222 cm-1 mode, whereas Bg modes have two maxima and the maximum of intensity in Ag modes pointed at least at the same direction for each group with the exception of the 338 cm-1 mode. Its maximum intensity is just below = 90°, that is, incident polarization is nearly parallel to a-axis, indicating that this vibration is along V-V pair direction and corresponding to the V-V stretching mode. In addition, the intensity of other Ag modes is maximized on average at about = 150°, i.e. close to 60° relative to the maximum of 338 cm-1 mode, suggesting that these vibrations are mainly close to 0 11 in direction, in good agreement with atomic displacements reported by Yuan et al. for two calculated Ag vibrations at 339 cm-1 and 197 cm-1 where the first vibration was found to present atomic displacements along a-axis and the second along c-axis [40]. Bg modes, on the other hand, show 11
maximum intensity on average at about = 30°, which corresponds to 1 11 crystallographic direction. From first-principles calculations on M1 phase VO2, Yuan et al. conclude that the calculated Raman modes at 339 cm-1 and 197 cm-1 correspond well to the calculated forces on V atoms when holes or electrons are added into the system, respectively [35]. These modes were then connected to the observed sub-picosecond and sub-nanosecond movement of V atoms in time-resolved x-ray diffraction and four-dimensional femtosecond electron diffraction experiments [41-43]. Thus the observed mode here at 338 cm-1 corresponds well to the calculated one at 339 cm-1. Consequently, it presents a strong hole-lattice coupling and plays a role in the rapid V-V bond separation along aaxis. A minute study of this phonon mode versus temperature could provide new elements in the understanding of the transitional structures of VO2. On the other hand, the observed mode at 195 cm-1, and maybe other Ag modes also, is related to the zigzag motion of V atoms observed at a longer time scale and presents electron-lattice coupling.
5. Conclusion Polarized Raman spectra were collected on a VO2 monoclinic M1 film presenting (010) and (011) out-of-plane orientations. Large (011)-oriented grains were used to study angular dependence of Raman modes intensity, which demonstrates single crystalline character of these domains. This allowed determining optimal experimental conditions to record precise spectra for parallel and cross configurations in order to assign phonon modes. Thus 17 modes were assigned among 18 expected modes for the monoclinic M1 phase and their Raman tensor components were estimated. Raman intensity versus rotation angle has evidenced a particular behavior of Ag mode (338 cm-1) related to hole-state and responsible of the V-V separation under photoexcitation.
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References [1] F.J. Morin, Phys. Rev. Lett. 3 (1959) 34. [2] J.P. Pouget, H. Launois, T.M. Rice, P. Dernier, A. Gossard, G. Villeneuve, P. Hagenmuller, Phys. Rev. B 10 (1974) 1801. [3] J.P. Pouget, H. Launois, J.P. Dhaenens, P. Merenda, T.M. Rice, Phys. Rev. Lett. 35 (1975) 873875. [4] T. M. Rice, H. Launois, J. P. Pouget, Phys. Rev. Lett. 73 (1994) 3042. [5] T. Mitsuishi, Jpn. J. Appl. Phys. 6 (1967) 1060. [6] M. Imada, A. Fujimori, Y. Tokura, Rev. Mod. Phys. 70 (1998) 1039. [7] M.M. Qazilbash, M. Brehm, B.-G. Chae, P.-C. Ho, G. O. Andreev, B.-J. Kim, S.-J. Yun, A.V. Balatsky, M.B. Maple, F. Keilmann, H.-T. Kim, D.N. Basov, Science 318 (2007) 1750. [8] C. Weber, D.D. O’Regan, N.D.M. Hine, M.C. Payne, G. Kotliar, P.B. Littlewood, Phys. Rev. Lett. 108 (2012) 265402. [9] N.F. Mott, Rev. Mod. Phys. 40 (1968) 677. [10] J. B. Goodenough, J. Solid State Chem. 3 (1971) 490. [11] A. Zylbersztejn, N. F. Mott, Phys. Rev. B 11 (1975) 4383. [12] D. Paquet, P. Leroux-Hugon, Phys. Rev. B 22 (1980) 5284. [13] R.M. Wentzcovitch, W.W. Schulz, P.B. Allen, Phys. Rev. Lett. 72 (1994) 3389. [14] H. Lim, N. Stavrias, B. C. Johnson, R. E. Marvel, R. F. Haglund and J. C. McCallum, J. Appl. Phys. 115 (2014) 093107. [15] C. Ko and S. Ramanathan, J. Appl. Phys. 104 (2008) 086105. [16] S. D. Ha, Y. Zhou, C. J. Fisher, S. Ramanathan and J. P. Treadway, J. Appl. Phys. 113 (2013) 184501. [17] X.-Y. Peng, B. Wang, J. Teng, J. B. Kana Kana and X. Zhang, J. Appl. Phys. 114 (2013) 163103.
13
[18] Y. Zhao, C. Chen, X. Pan, Y. Zhu, M. Holtz, A. Bernussi and Z. Fan, J. Appl. Phys. 114 (2013) 113509. [19] S. Lysenko, F. Fernández, A. Rúa and H. Liu, J. Appl. Phys. 114 (2013) 153514. [20] A. Beaumont, J. Leroy, J.-C. Orlianges and A. Crunteanu, J. Appl. Phys. 115 (2014) 154502. [21] J. Sakai, J. Appl. Phys. 103 (2008) 103708. [22] A. G. Aronov, D. N. Mirlin, I. I. Reshina, F. A. Chudnovskii, Sov. Phys. Solid State 19 (1977) 110. [23] V. S. Vikhnin, I. N. Goncharuk, V. Y. Davydov, F. A. Chudnovskii, E. B. Shadrin, Phys. Solid State 37 (1995) 1971. [24] R. R. Andronenko, I. N. Goncharuk, V. Y. Davydov, F. A. Chudnovskii, E. B. Shadrin, Phys. Solid State 36 (1994) 1136. [25] R. Srivastava and L. L. Chase, Phys. Rev. Lett. 27 (1971) 727. [26] P. Schilbe, Physica B 316-317 (2002) 600. [27] P. Schilbe and D. Maurer, Mater. Sci. Eng. A 370 (2004) 449. [28] K. Shibuya, J. Tsutsumi, T. Hasegawa, A. Sawa, Appl. Phys. Lett. 103 (2013) 021604. [29] J. Y. Chou, J. L. Lensch-Falk, E. R. Hemesath, L. J. Lauhon, J. App. Phys. 105 (2009) 034310. [30] L. Bai, Q. Li, Serena A. Corr, Y. Meng, C. Park, Stanislav V. Sinogeikin, C. Ko, J. Wu, and G. Shen, Phys. Rev. B 91 (2015) 104110. [31] X. B. Chen, J. Korean Phys. Soc. 58 (2011) 100. [32] A. C. Jones, S. Berweger, J. Wei, D. Cobden, M.B. Raschke, Nano Lett. 10 (2010) 1574. [33] Y. Ji, Y. Zhang, M. Gao, Z. Yuan, Y. Xia, C. Jin, B. Tao, C. Chen, Q. Jia and Y. Lin, Sci. Rep. 4 (2014) 4854. [34] S.-J. Chang, J. B. Park, G. Lee, H. J. Kim, J.-B. Lee, T.-S. Bae, Y.-K. Han, T. J. Park, Y. S. Huh and W.-K. Hong, Nanoscale 6 (2014) 8068. [35] E. Strelcov, A. Tselev, I. Ivanov, J. D. Budai, J. Zhang, J. Z. Tischler, I. Kravchenko, S. V Kalinin, and A. Kolmakov, Nano Lett. 12 (2012) 6198.
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[36] G. I. Petrov, V. V. Yakovlev and J. Saquier, J. Appl. Phys. 81 (2002) 1023. [37] N. H. Azhan, K. Su, K. Okimura and J. Sakai, J. Appl. Phys. 117 (2015) 185307. [38] N. H. Azhan, K. Su, K. Okimura, M. Zaghrioui and J. Sakai, J. Appl. Phys. 117 (2015) 245314. [39] A. Cavalleri, Th. Dekorsy, H. H. W. Chong, J. C. Kieffer, and R. W. Schoenlein, Phys. Rev. B 70 (2004) 161102 (R). [40] X. Yuan, W. Zhang, and P. Zhang, Phys. Rev. B 88 (2013) 035119. [41] P. Baum, D. S. Yang, A. H. Zewail, Science 318 (2007) 788. [42] H.-T. Kim, Y. W. Lee, B.-J. Kim, B.-G. Chae, S. J. Yun, K.-Y. Kang, K.-J. Han, K.-J. Yee, and Y.-S. Lim, Phys. Rev. Lett. 97 (2006) 266401. [43] A. Cavalleri, Cs. Toth, C.W. Siders, J.A. Squier, F. Raksi, P. Forget, J.C. Kieffer, Phys. Rev. Lett. 87 (2001) 237401.
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Figure Captions
Fig. 1. (a) Optical image of the film surface showing region A (nano-grains) and region B (micrograins). (b) Schematic illustration of the experimental setup. Inset: monoclinic M1 VO2 structure with the (011) plane denoted in dark gray.
16
Fig. 2. Raman spectra recorded at various rotation angle from 0 to 180°, on nano-domains for parallel (XX) and cross (YX) configurations. Inset represents the simulated Raman intensity for the three types of grains (square symbols) and their sum (circle symbol).
17
Fig. 3. Raman spectra collected at different eff angles on large (size > 10µm) (011)-oriented grain in the parallel configuration (left panel) and the cross configuration (right panel). Arrows in magnified spectra in the parallel configuration indicate two modes that exist at 138 and 144 cm-1.
18
Fig. 4. Mode intensity versus rotation angle for XX (a)(b) and YX (c)(d) configurations.
19
Fig. 5. Raman spectra at = 147° in XX and YX configurations for two laser excitations, 457 nm (top) and 514 nm (bottom). Inset shows crystal orientation relative to the laboratory coordinates.
20
Fig. 6. Polar plot of Raman intensity as a function of the rotation angle for some selected Ag (a) and Bg (b) modes. Symbols correspond to the experimental intensities and solid lines are the theoretical fitting.
21
Tables Table 1. Raman tensor elements calculated from experimental intensities in parallel configuration.
Ag (1)
Bg
Exp.
Calc.
a
b+c
144
152
-
195
197
222
(2)
(1)
d
Exp.
Calc.
e
f
-
-
138
212
0.81
0.21
0.64
-0.68
-0.11
262
231
0.86
0.14
224
0.09
0.30
-0.79
265(3)
247
-
-
308
331
0.42
0.64
0.43
400
374
0.48
0.27
338
339
0.70
0.56
0.06
441
432
-0.35
0.33
382
389
0.66
-0.14
-0.34
452
447
-0.43
-0.31
500
508
0.74
-0.20
-0.21
482
495
-
-
582
605
0.49
0.82
0.25
663
593
-
-
619
675
0.77
-0.42
-0.10
824
758
0.34
0.45
(1)
Frequency values after reference 40. b+c values correspond to values obtained assuming that is equal to 45° instead of 44.97°. (3) Not observed in present study but has been reported in refs. 26 and 27. (2)
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S0924-2031(15)30009-6 http://dx.doi.org/doi:10.1016/j.vibspec.2015.08.003 VIBSPE 2451
To appear in:
VIBSPE
Received date: Revised date: Accepted date:
13-7-2015 24-8-2015 25-8-2015
Please cite this article as: Mustapha Zaghrioui, Joe Sakai, Nurul Hanis Azhan, Kui Su, Kunio Okimura, Polarized Raman scattering of large crystalline domains in VO2 films on sapphire, Vibrational Spectroscopy http://dx.doi.org/10.1016/j.vibspec.2015.08.003 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Polarized Raman scattering of large crystalline domains in VO2 films on sapphire Mustapha Zaghriouia* [email protected], Joe Sakaia, Nurul Hanis Azhanb, Kui Sub, Kunio Okimurab a
GREMAN, UMR 7347 CNRS, Université François Rabelais de Tours, Parc de Grandmont
37200 Tours, France b *
Graduate School of Science and Technology, Tokai University, Hiratsuka 259-1292, Japan
Corresponding author. Tel.: +33 254552105; fax: +33 254552137.
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Abstract Polarized Raman scattering measurements were performed on (011)-oriented, over 10 µm-size VO2 grains on an Al2O3 (001) substrate. Angular intensity dependence of Raman active modes allowed to observe 17 modes among the 18 expected and to demonstrate the single crystalline character of the large domains. Analyses of intensity evolution have been used to correctly assign phonon modes and to calculate the Raman tensor elements. In addition, a Raman Ag mode related to the V-V stretching vibration was found to have a different behavior versus angle rotation from other Ag modes, which supports the previous theoretical study and photoexcitation measurements. Keywords: Polarized Raman spectroscopy; Phonon modes assignment; Vanadium dioxide VO2; Thin films
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1. Introduction Vanadium dioxide VO2 belongs to the strongly correlated electron materials and presents insulator-metal transition at 68°C accompanied by a structural transition, from the monoclinic M1 phase (P21/c) to the rutile R phase (P42/mmm) [1,2]. In stressed VO2, a transient monoclinic M2 (C2/m) phase occurs before entering into the rutile phase. M1 structure is characterized by a dimerization of vanadium atoms (V-V pairs) and a tilting along a-axis, forming two chains. In contrast, M2 phase is characterized by a pairing in one chain [3-6]. Despite the numerous studies on VO2, the mechanism driving insulator-metal transition is still under debate, demonstrating the complexity of this binary oxide as the transition exhibits both Peierls-like and Mott-like characteristics [4, 7-13]. Understanding this mechanism is a key of the applicability of VO2 material as thermochromics coatings, transistors, ultrafast optical switching or temperature sensors [14-21]. Adopting Raman scattering, which is a phenomenon sensitive to crystalline structure and stress, Raman spectroscopy technique is one of the most popular tools to characterize VO2 films, enabling identification of the synthesized phase or investigation of the structural transitions induced by doping, temperature or stress [22-36]. It is therefore more pertinent in the case of VO2 as it can adopt various crystal structure phases as monoclinic (M1 and M2), rutile (R) and triclinic (T) phases [32-34]. One important thing in Raman spectroscopy is the mode symmetry assignment, which is performed on single crystals along precise crystallographic directions using polarized Raman scattering. Mode assignment is done on the basis of the group theory analysis and selection rules. Phonon mode symmetry, if known, allows precise structural or electronic discussions. Despite the numerous studies, no consensus was reached for Raman modes assignment of M1 phase VO2. This is largely due to the lack of single crystal that is used to perform such a task. Most studies conducted on this subject were performed on oriented or epitaxial thin films and nanorods. In all the cases, grain size is nanometric while the laser spot, in the best cases, can only reach about 300 nm in diameter, which means that the recorded Raman spectrum represents contributions of multiple
3
grains, and that single crystalline character that needs to perform precise assignment is therefore lost. Nonetheless, Schilbe et al. have performed polarized Raman measurements, at 83 K, on crystals (2 mm x 2 mm x 1 mm) obtained by chemical vapor deposition and presented (011)oriented surface,1 which leads to observe 17 Raman modes among the 18 allowed (9 Ag + 9 Bg) [26, 27]. Their assignment was done by measuring spectra in parallel and cross configurations. But as we will show in this study, this assignment is not complete since spectra recorded in both configurations do not show a complete extinction of Bg modes in the parallel configuration as is predicted by the group theory analysis. In this paper, we report on a new phonon modes assignment of the monoclinic M1 phase using polarized Raman scattering measurements at various in-plane rotation angles, which allows a minute study of intensity mode evolution and thus deeper mode symmetry analysis. Recently, we succeeded to grow thin films of M1 phase VO2 on the Al2O3 (001) substrate with large grains (larger than 10 µm in size) that present out-of-plane orientation along (011) direction [37, 38]. Their grain size is sufficient for micro Raman observation of a single grain. At the same time, the single-crystalline character of this novel type grains was confirmed by the present angle-dependent polarized Raman observation.
2. Experimental details The VO2 film was deposited on an Al2O3 (001) substrate using rf-biased reactive sputtering. In this technique, rf power is applied to the substrate holder as well as to the target, enabling control of stress and thus transition temperature of VO2 films. The deposition was performed at substrate temperature of 400°C under substrate biasing of 10 W. Total pressure of gases (Ar and O2), target rf-power and deposition time were set to 0.5 Pa, 200 W and 40 min, respectively (See references 37 and 38 for more details). The resulting film contained two domains characterized by grains with nano and micro size (Fig. 1a). X-ray diffraction and SEM analyses have shown that domains with nano-grains and large grains have, respectively, (010) and (011) out-of-plane orientations. 1
All lattice indices described in this paper represent those of the monoclinic M1 phase. 4
Polarized Raman scattering were performed using Renishaw Invia Reflex spectrometer at fixed polarization of the scattered light and with or without the /2 plate of the incident light for cross or parallel configurations, respectively. An excitation, 514 nm-line beam of an argon-ion laser with a power of 0.5 W, was focused by a x100 lens (0.85NA), which was also used to collect the scattered light in a backscattering configuration. The scattered light passes through an analyzer and is dispersed on a 2400 lines/mm grating. In this configuration the spatial resolution is close to 1 µm with the spectral resolution of 0.5 cm-1. In order to collect Raman spectra versus rotation angle, the film was mounted on a rotating sample holder. All measurements were performed in the air at room temperature.
3. Theoretical background At room temperature and under atmospheric pressure, VO2 crystallizes in a monoclinic 5 structure so-called M1 phase, which corresponds to a distorted rutile structure with C2h point group
(P21/c space group). Group theory analysis predicts 18 Raman active modes (9Ag + 9Bg). The Raman tensor, Rj, for the space group (unique axis b) expressed in the unit cell are:
RAg
a 0 d 0 b 0 d 0 c
0 RBg e 0
e 0 f
0 f , 0
where a, b, c, d, e and f are the tensor elements. In this study, Cartesian laboratory coordinates (X, Y, Z) were chosen to simplify the measurements and the calculations. The choice of these coordinates is shown in Fig. 1b. At the initial position, VO2 cell is disposed with its a-axis along X and b-axis along Y (Fig. 1b). As Raman tensors are expressed in the unit cell, it is necessary to transform them into the laboratory coordinates by using the Euler’s angles. Recall that Euler’s angles (, , ) correspond, in our case, 5
to the first rotation by around Z-axis, the second rotation by around Y-axis and the third rotation
around Z-axis. Thus the transformation matrix of Euler’s angles, is as follows: cos cos cos sin sin cos cos sin cos sin cos sin
cos cos sin cos sin cos cos cos sin sin sin sin
cos sin sin sin . cos
The general expression of the Raman tensor is thus expressed, in the laboratory coordinates (X, Y, Z), as:
RXYZ Φ.R j .Φ
(1)
corresponds to the inverse matrix of . where Φ
For each phonon mode, the Raman intensity can be thus calculated from the Raman tensor as 2
I j ei .RXYZ .es
(2)
where es and ei correspond to the unit polarization vectors of scattered and incident light, respectively. The setup used in this study allows the following polarization vectors:
XX i
e
10 0 ; e
YX i
1 (010) and es 0 , 0
where the superscripts XX and YX correspond, respectively, to the parallel and cross configurations.
4. Results and discussions
4.1. Nano-domains Fig. 2 shows Raman spectra obtained on the nano-grain domains at various rotation angle for both polarization configurations. It can be seen that the spectrum is independent of the rotation for parallel and cross configurations. A difference in peak intensities is also observed between both configurations, suggesting a preferential out-of-plane orientation of nano-grains. Indeed, X-ray diffraction (XRD) analyses have evidenced out-of-plane (010)-orientation in agreement with these results [38]. Concerning in-plane orientation, XRD has shown epitaxial growth of the nano-grains 6
through -scan profiles of this region, presenting three sets of (011) reflection peaks rotated each other by 60°, because of hexagonal ab plane of the alumina substrate [38]. On the other hand, the Raman spectra reported here seem to be similar to that obtained on films presenting random inplane distribution. This discrepancy is explained as follows. As the laser spot size used for the measurements is about 1 µm, the collected Raman spectrum is representative of the three types of grains, i.e. that the intensity of each mode corresponds to the contribution of the intensities from the three types. Using equations 1 and 2, Raman intensity was simulated considering the first type of grains at angle , the second at + 60° and the third at + 120°. Other Euler’s angles () were determined so as to make (010) plane parallel to the (X, Y) plane, i.e. and are equal to 90°. Evolution of the simulated intensity was found to be independent in agreement with our experimental results (inset in Fig. 2). In previous studies, phonon modes assignment was done on the basis of results obtained on the films similarly oriented [31]. As shown here, it is risky to assign phonon modes on such grains of six-fold symmetry, because all the modes are observed in both parallel and cross configurations, in spite of the zero intensity of Bg mode for parallel configuration predicted by the selection rules.
4.2. Micro-domains Fig. 3 shows Raman spectra obtained for one large grain (diameter> 10 µm) at several eff values. Note that these results are representative of the large grains (more than 10 were checked seriously and 20 roughly). In addition, eff angle corresponds to the angle between laser polarization, fixed along X axis, and the starting position, which is different from the real angle because the origin is unknown. This will be estimated in the following of this section. As it can be seen in Fig. 3, the evolution of peak intensities is apparently rotation angle dependent for both XX and YX configurations, strongly suggesting single crystalline character of the large grains. Moreover, spectra recorded for several grains at the same eff angle present difference in mode intensities, indicating a random in-plane orientation among different grains. These results 7
are consistent with those of XRD where 2- scans showed out-of-plane (011)-orientation and scans showed non-epitaxial growth of the grains. Moreover, Raman spectra recorded between 180 and 360° are similar to those acquired between 0 and 180°. Thus, mode intensity evolution was treated in the range 0-180°. At least 17 Raman modes could be observed among the 18 expected. The missing mode cannot be observed at room temperature but probably becomes visible at low temperature; Schilbe
et al. observed it at 265 cm-1 close to the mode at 262 cm-1, in a low temperature measurement at 83 K [26,27]. Among Raman modes observed in this work, two modes located at 138 cm-1 and 144 cm1
are reported for the first time in this spectral range, whereas only one mode is observed in the
previous studies. In order to extract intensity/area of each peak as functions of eff, the spectra were fitted using Lorentzian functions. Peak intensities deduced from the fit for both configurations are plotted in Fig. 4 for some selected modes in parallel and cross configurations. Two behaviors could be observed in intensity evolution for parallel configuration. Some modes present one maximum (Fig. 4a), while others have two maxima (Fig. 4b). In contrast to the parallel configuration, all modes have two maxima in cross configuration (Fig. 4c and 4d). This intensity behavior could be related to the symmetry of the modes, i.e. it could be used to assign phonon modes. Let us compare these results to the theoretical intensities in order to check this assumption. Recall that the initial position of the cell is positioned with c-axis along Z and b-axis along Y. To bring (011) plane parallel to (X, Y) plane, the cell should be rotated first by = 90° around Z and then along Y by = 44.97°. Expressions of the intensities are the following: 2
I
XX Ag
1 1 A B cos 2 C sin 2 2 2
I
XX Bg
1 1 F F cos 2 E sin 2 2 2
(3a)
(3b)
(3c)
2
YX I Ag C cos 2
2
1 B sin 2 2 8
2
1 YX I Bg E cos 2 F sin 2 2
(3d)
where
A a b cos 2 c sin 2
B a b cos 2 c sin 2
C d sin
F f sin 2 E e cos .
As stated by these expressions, both Ag and Bg symmetry modes should have two maxima in
YX configuration in agreement with experimental results. For XX configuration, depending on tensor elements, both expressions could present one or two maxima since they are similar. Thus XX is null phonon mode assignment could not be done on the basis of the periodicity. However, I Bg XX for while I Ag is not (In this case, a-axis is parallel to the laser polarization).
Experimentally, this will correspond to a small or a minimum intensity depending on the degree of the sample misalignment, and imperfection of the laser polarization and the analyzer. According to this, evolution of peak intensity was checked and a minimum or null intensity was observed for some modes for eff ranging between 160 and 170° (Fig. 4a and 4b). Detailed measurements in this range allowed us to estimate eff that presents a minimum in intensity of these modes, which was found to be 165 1°. This step was essential for knowing the real origin of angle and thus to assign correctly phonon modes and to determine Raman tensor elements for most of the observed modes. Indeed, it was not possible for certain modes to perform precise calculations because of the low intensity (mode 482 cm-1) or overlapping with other modes (modes 144 cm-1 and 663 cm-1). On the basis of these results, phonon modes assignment was done. First, Raman spectra were performed in parallel and cross configurations at = 90° and 147°. For = 90°, laser polarization is parallel or perpendicular to a-axis, whereas it is parallel or perpendicular to 0 11 direction for 9
= 147°. At both positions, Bg modes have their intensities at the minimum for parallel configuration and are higher for the cross configuration. In addition, at = 90°, identification of Bg modes is difficult because of the increase in intensity of Ag mode at the same manner as that of Bg modes; while at = 147° the scenario is in opposite where, in cross configuration, Ag modes have lower intensities. This is more visible if the laser excitation is more energetic as shown in Fig. 5a for the blue laser excitation ( = 457 nm). It seems that this energy is close to an electronic transition, which exalts the Raman scattering (resonance Raman scattering). The fact that only Bg phonon modes are affected by this phenomenon suggests a correlation between these modes and the corresponding electronic transition. In agreement with the observations above, we were able to correctly assign Raman modes of VO2 monoclinic M1 phase as shown in Fig. 5. These results are, in our opinion, the first Raman polarized spectra that clearly show a huge difference between Ag and Bg mode symmetries. Until now, all polarized Raman spectra were reported on (010)-oriented epitaxial films or nanorods [26,27,29,31,32]. However, as it was shown in this study, epitaxial films do not provide clear and precise assignment. The most thorough study is the one performed by Schilbe et al. on crystals obtained by chemical vapor transport [26,27]. Indeed, large crystals were obtained presenting some defects such as cracks and dislocations. Our assignment is in general in agreement with that performed by Schilbe et al. except for three modes located at 138, 338 and 452 cm-1. Both modes at 138 and 452 cm-1 have Bg symmetry while the mode at 338 cm-1 has Ag symmetry. In addition, the data show clearly that 138 cm-1 mode has Bg symmetry in agreement with the time-resolved optical spectroscopy measurement reported by Cavalleri et al. [39]. Note that this measurement, detecting the coherent excitations, reveals only Ag modes and that 138 cm-1 phonon mode was not observed. On the other hand, our assignment is consistent with phonon calculations reported by Yuan et al. [40], where frequencies of Ag modes are reproducible whereas those of Bg modes are somewhat far notably for the lower and the higher frequency modes. The same observation could be done for the high frequency Ag mode. Note that in previous studies, the Raman mode at about 138 cm-1 was 10
always assigned as Ag mode symmetry and was attributed to the calculated one at 152 cm-1 [40]. However, the latter could correspond to the small mode observed in this study at 144 cm-1. This mode is visible on the most spectra reported in literatures but had never mentioned; maybe its small intensity and its overlapping with the mode at 138 cm-1 are the reasons for this unconcern. As we can see in Fig. 6b, this mode presents angular dependence and its intensity evolution follows the same behavior as Ag modes. All active Raman modes are thus identified and assigned, 17 modes observed in this work plus the small mode reported by Schilbe et al. at 265 cm-1, which could be clearly observed at low temperature (83 K) [26,27]. Frequencies and symmetry of active Raman modes is summarized in table 1 together with the calculated tensor elements. According to our assignment, mode intensity versus rotation angle was fitted using equations
XX in the case of parallel configuration. The obtained fitting parameters were then used to check the results of cross configuration. Indeed, experimental data obtained in this latter configuration were not used to calculate Raman tensor elements because of (i) the insertion of /2 plate on the incident path that introduces a small deviation from the ideal orthogonal polarization, and (ii) the low Raman intensity that introduces a higher background signal. The best fitting parameters are summarized in table 1 and the obtained curves are plotted in Fig. 6 together with experimental data. Interestingly, we find that Ag modes present one maximum, except 222 cm-1 mode, whereas Bg modes have two maxima and the maximum of intensity in Ag modes pointed at least at the same direction for each group with the exception of the 338 cm-1 mode. Its maximum intensity is just below = 90°, that is, incident polarization is nearly parallel to a-axis, indicating that this vibration is along V-V pair direction and corresponding to the V-V stretching mode. In addition, the intensity of other Ag modes is maximized on average at about = 150°, i.e. close to 60° relative to the maximum of 338 cm-1 mode, suggesting that these vibrations are mainly close to 0 11 in direction, in good agreement with atomic displacements reported by Yuan et al. for two calculated Ag vibrations at 339 cm-1 and 197 cm-1 where the first vibration was found to present atomic displacements along a-axis and the second along c-axis [40]. Bg modes, on the other hand, show 11
maximum intensity on average at about = 30°, which corresponds to 1 11 crystallographic direction. From first-principles calculations on M1 phase VO2, Yuan et al. conclude that the calculated Raman modes at 339 cm-1 and 197 cm-1 correspond well to the calculated forces on V atoms when holes or electrons are added into the system, respectively [35]. These modes were then connected to the observed sub-picosecond and sub-nanosecond movement of V atoms in time-resolved x-ray diffraction and four-dimensional femtosecond electron diffraction experiments [41-43]. Thus the observed mode here at 338 cm-1 corresponds well to the calculated one at 339 cm-1. Consequently, it presents a strong hole-lattice coupling and plays a role in the rapid V-V bond separation along aaxis. A minute study of this phonon mode versus temperature could provide new elements in the understanding of the transitional structures of VO2. On the other hand, the observed mode at 195 cm-1, and maybe other Ag modes also, is related to the zigzag motion of V atoms observed at a longer time scale and presents electron-lattice coupling.
5. Conclusion Polarized Raman spectra were collected on a VO2 monoclinic M1 film presenting (010) and (011) out-of-plane orientations. Large (011)-oriented grains were used to study angular dependence of Raman modes intensity, which demonstrates single crystalline character of these domains. This allowed determining optimal experimental conditions to record precise spectra for parallel and cross configurations in order to assign phonon modes. Thus 17 modes were assigned among 18 expected modes for the monoclinic M1 phase and their Raman tensor components were estimated. Raman intensity versus rotation angle has evidenced a particular behavior of Ag mode (338 cm-1) related to hole-state and responsible of the V-V separation under photoexcitation.
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References [1] F.J. Morin, Phys. Rev. Lett. 3 (1959) 34. [2] J.P. Pouget, H. Launois, T.M. Rice, P. Dernier, A. Gossard, G. Villeneuve, P. Hagenmuller, Phys. Rev. B 10 (1974) 1801. [3] J.P. Pouget, H. Launois, J.P. Dhaenens, P. Merenda, T.M. Rice, Phys. Rev. Lett. 35 (1975) 873875. [4] T. M. Rice, H. Launois, J. P. Pouget, Phys. Rev. Lett. 73 (1994) 3042. [5] T. Mitsuishi, Jpn. J. Appl. Phys. 6 (1967) 1060. [6] M. Imada, A. Fujimori, Y. Tokura, Rev. Mod. Phys. 70 (1998) 1039. [7] M.M. Qazilbash, M. Brehm, B.-G. Chae, P.-C. Ho, G. O. Andreev, B.-J. Kim, S.-J. Yun, A.V. Balatsky, M.B. Maple, F. Keilmann, H.-T. Kim, D.N. Basov, Science 318 (2007) 1750. [8] C. Weber, D.D. O’Regan, N.D.M. Hine, M.C. Payne, G. Kotliar, P.B. Littlewood, Phys. Rev. Lett. 108 (2012) 265402. [9] N.F. Mott, Rev. Mod. Phys. 40 (1968) 677. [10] J. B. Goodenough, J. Solid State Chem. 3 (1971) 490. [11] A. Zylbersztejn, N. F. Mott, Phys. Rev. B 11 (1975) 4383. [12] D. Paquet, P. Leroux-Hugon, Phys. Rev. B 22 (1980) 5284. [13] R.M. Wentzcovitch, W.W. Schulz, P.B. Allen, Phys. Rev. Lett. 72 (1994) 3389. [14] H. Lim, N. Stavrias, B. C. Johnson, R. E. Marvel, R. F. Haglund and J. C. McCallum, J. Appl. Phys. 115 (2014) 093107. [15] C. Ko and S. Ramanathan, J. Appl. Phys. 104 (2008) 086105. [16] S. D. Ha, Y. Zhou, C. J. Fisher, S. Ramanathan and J. P. Treadway, J. Appl. Phys. 113 (2013) 184501. [17] X.-Y. Peng, B. Wang, J. Teng, J. B. Kana Kana and X. Zhang, J. Appl. Phys. 114 (2013) 163103.
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[18] Y. Zhao, C. Chen, X. Pan, Y. Zhu, M. Holtz, A. Bernussi and Z. Fan, J. Appl. Phys. 114 (2013) 113509. [19] S. Lysenko, F. Fernández, A. Rúa and H. Liu, J. Appl. Phys. 114 (2013) 153514. [20] A. Beaumont, J. Leroy, J.-C. Orlianges and A. Crunteanu, J. Appl. Phys. 115 (2014) 154502. [21] J. Sakai, J. Appl. Phys. 103 (2008) 103708. [22] A. G. Aronov, D. N. Mirlin, I. I. Reshina, F. A. Chudnovskii, Sov. Phys. Solid State 19 (1977) 110. [23] V. S. Vikhnin, I. N. Goncharuk, V. Y. Davydov, F. A. Chudnovskii, E. B. Shadrin, Phys. Solid State 37 (1995) 1971. [24] R. R. Andronenko, I. N. Goncharuk, V. Y. Davydov, F. A. Chudnovskii, E. B. Shadrin, Phys. Solid State 36 (1994) 1136. [25] R. Srivastava and L. L. Chase, Phys. Rev. Lett. 27 (1971) 727. [26] P. Schilbe, Physica B 316-317 (2002) 600. [27] P. Schilbe and D. Maurer, Mater. Sci. Eng. A 370 (2004) 449. [28] K. Shibuya, J. Tsutsumi, T. Hasegawa, A. Sawa, Appl. Phys. Lett. 103 (2013) 021604. [29] J. Y. Chou, J. L. Lensch-Falk, E. R. Hemesath, L. J. Lauhon, J. App. Phys. 105 (2009) 034310. [30] L. Bai, Q. Li, Serena A. Corr, Y. Meng, C. Park, Stanislav V. Sinogeikin, C. Ko, J. Wu, and G. Shen, Phys. Rev. B 91 (2015) 104110. [31] X. B. Chen, J. Korean Phys. Soc. 58 (2011) 100. [32] A. C. Jones, S. Berweger, J. Wei, D. Cobden, M.B. Raschke, Nano Lett. 10 (2010) 1574. [33] Y. Ji, Y. Zhang, M. Gao, Z. Yuan, Y. Xia, C. Jin, B. Tao, C. Chen, Q. Jia and Y. Lin, Sci. Rep. 4 (2014) 4854. [34] S.-J. Chang, J. B. Park, G. Lee, H. J. Kim, J.-B. Lee, T.-S. Bae, Y.-K. Han, T. J. Park, Y. S. Huh and W.-K. Hong, Nanoscale 6 (2014) 8068. [35] E. Strelcov, A. Tselev, I. Ivanov, J. D. Budai, J. Zhang, J. Z. Tischler, I. Kravchenko, S. V Kalinin, and A. Kolmakov, Nano Lett. 12 (2012) 6198.
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[36] G. I. Petrov, V. V. Yakovlev and J. Saquier, J. Appl. Phys. 81 (2002) 1023. [37] N. H. Azhan, K. Su, K. Okimura and J. Sakai, J. Appl. Phys. 117 (2015) 185307. [38] N. H. Azhan, K. Su, K. Okimura, M. Zaghrioui and J. Sakai, J. Appl. Phys. 117 (2015) 245314. [39] A. Cavalleri, Th. Dekorsy, H. H. W. Chong, J. C. Kieffer, and R. W. Schoenlein, Phys. Rev. B 70 (2004) 161102 (R). [40] X. Yuan, W. Zhang, and P. Zhang, Phys. Rev. B 88 (2013) 035119. [41] P. Baum, D. S. Yang, A. H. Zewail, Science 318 (2007) 788. [42] H.-T. Kim, Y. W. Lee, B.-J. Kim, B.-G. Chae, S. J. Yun, K.-Y. Kang, K.-J. Han, K.-J. Yee, and Y.-S. Lim, Phys. Rev. Lett. 97 (2006) 266401. [43] A. Cavalleri, Cs. Toth, C.W. Siders, J.A. Squier, F. Raksi, P. Forget, J.C. Kieffer, Phys. Rev. Lett. 87 (2001) 237401.
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Figure Captions
Fig. 1. (a) Optical image of the film surface showing region A (nano-grains) and region B (micrograins). (b) Schematic illustration of the experimental setup. Inset: monoclinic M1 VO2 structure with the (011) plane denoted in dark gray.
16
Fig. 2. Raman spectra recorded at various rotation angle from 0 to 180°, on nano-domains for parallel (XX) and cross (YX) configurations. Inset represents the simulated Raman intensity for the three types of grains (square symbols) and their sum (circle symbol).
17
Fig. 3. Raman spectra collected at different eff angles on large (size > 10µm) (011)-oriented grain in the parallel configuration (left panel) and the cross configuration (right panel). Arrows in magnified spectra in the parallel configuration indicate two modes that exist at 138 and 144 cm-1.
18
Fig. 4. Mode intensity versus rotation angle for XX (a)(b) and YX (c)(d) configurations.
19
Fig. 5. Raman spectra at = 147° in XX and YX configurations for two laser excitations, 457 nm (top) and 514 nm (bottom). Inset shows crystal orientation relative to the laboratory coordinates.
20
Fig. 6. Polar plot of Raman intensity as a function of the rotation angle for some selected Ag (a) and Bg (b) modes. Symbols correspond to the experimental intensities and solid lines are the theoretical fitting.
21
Tables Table 1. Raman tensor elements calculated from experimental intensities in parallel configuration.
Ag (1)
Bg
Exp.
Calc.
a
b+c
144
152
-
195
197
222
(2)
(1)
d
Exp.
Calc.
e
f
-
-
138
212
0.81
0.21
0.64
-0.68
-0.11
262
231
0.86
0.14
224
0.09
0.30
-0.79
265(3)
247
-
-
308
331
0.42
0.64
0.43
400
374
0.48
0.27
338
339
0.70
0.56
0.06
441
432
-0.35
0.33
382
389
0.66
-0.14
-0.34
452
447
-0.43
-0.31
500
508
0.74
-0.20
-0.21
482
495
-
-
582
605
0.49
0.82
0.25
663
593
-
-
619
675
0.77
-0.42
-0.10
824
758
0.34
0.45
(1)
Frequency values after reference 40. b+c values correspond to values obtained assuming that is equal to 45° instead of 44.97°. (3) Not observed in present study but has been reported in refs. 26 and 27. (2)
22