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Lattice dynamics in VO2 near the metal-insulator transition
Materials Science and Engineering A 370 (2004) 449–452
Lattice dynamics in VO2 near the metal-insulator transition P. Schilbe a,∗ , D. Maurer b b
a Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany Institut für Physik, Chemische Physik und Materialwissenschaften, Universität Augsburg, 86135 Augsburg, Germany
Received 12 July 2002
Abstract We present a comprehensive experimental study of the lattice dynamics in the vicinity of the metal-insulator transition in VO2 by means of combined use of Raman spectroscopy and ultrasonic microscopy. Single crystalline samples of high quality particularly allow quite a complete determination of all Raman modes in the insulating phase at the -point and the observation of an optical soft mode. In addition, the elastic behavior has been successfully investigated by measuring the propagation velocity of ultrasonic surface waves microscopically excited in various crystal directions. Our study reveals a striking coincidence of strong lattice softening attributable to certain acoustic branches and the occurrence of the optical soft mode, which precedes the metal-insulator transition over more than 100 K on approaching the critical temperature. © 2003 Elsevier B.V. All rights reserved. Keywords: Metal-insulator transition; Soft mode; Raman scattering; Ultrasonic microscopy
1. Introduction Among the transition metal oxides the vanadium oxides are of great current interest due to their potential applications and wealth of interesting physical properties. One of the most interesting problems is the metal-insulator transition in VO2 near ambient temperature [1–3] with a conductivity jump of up to five orders in magnitude. The microscopic origin and the mechanism stabilizing the low-temperature structural order is still a matter of debate. At TMI = 339 K the structure changes on cooling from a metallic tetragonal rutile structure to an insulting distorted rutile structure with monoclinic symmetry [4]. The cations form dimers in the insulating phase, which can be understood from simple tight binding arguments [5] although strong electronic correlation is also present. The metal-insulator transition is of first-order and the transformation entropy derived from latent heat data varies between 12.6 J mol−1 K−1 [6] and 13.8 J mol−1 K−1 [7], which is about five times larger than that what is expected from band-structure calculations due to electron localization. Hence, a realistic description must take into account changes in lattice entropy and for ∗ Corresponding author. Tel.: +49-30-838-56113; fax: +49-30-838-51355. E-mail address: [email protected] (P. Schilbe).
0921-5093/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2003.08.114
that detailed information on the lattice vibrations in VO2 is indispensable. Unfortunately, the vanadium ion has a large incoherent neutron scattering length so that inelastic neutron measurements are difficult to perform. Therefore, inelastic light scattering and ultrasonic investigations are the two main possibilities in order to study the vibrational behavior near the phase transition. 14 , In the low-temperature phase, with a space group D4h nine Ag and nine Bg modes are Raman allowed and in 5 , four the high-temperature phase, with a space group C2h modes: A1g , B1g , B2g and Eg . Former Raman studies on VO2 [8–11] were not able to detect the full spectrum in the low-temperature phase and to give a consistent assignment to the irreducible representations. In one investigation [10] a softening of the lowest Raman mode was observed, which was not observed in other investigations. In the high-temperature phase only broad structures in the Raman spectra remain, the origin of which is not understood.
2. Experimental set up The single crystals, used for the present investigation, were grown in the group of Prof. Horn in Augsburg by chemical vapor transport. The crystals were approximately
450
P. Schilbe, D. Maurer / Materials Science and Engineering A 370 (2004) 449–452
2 mm × 2 mm × 1 mm in size and had a specular (1 1 0)t surface from the growth process (all directions are given with respect to the tetragonal rutile unit cell of the high-temperature phase). The Raman spectra were taken with a double monochromator with a spectral resolution of <2 cm−1 and were excited by 0.1 W of the 514.5 nm line of an argon ion laser. All Raman measurements were done with a microprobe Raman facility in backscattering geometry. A high resolution ultrasonic microscope was used to excite Rayleigh-type surface acoustic waves (SAW) in small crystalline samples. Due to the high quality of the optically flat crystal surfaces the ultrasonic investigations could be performed at a high sound frequency of 1 GHz. The sound velocity was determined for various crystal directions from the interference pattern usually appearing close to the smooth crystal edges. Crystallites for investigation were chosen to be small enough so that we were able to pass through the phase transition without irreversible changes because cracking due to thermal cycling is a severe problem of larger VO2 single crystals, in particular. The diameter of the laser spot of the Raman system was approximately 5 m whereas the ultrasonic investigations probes a length scale of a few wave lengths (≈20 m). Thus, the investigated length scales in both methods are similar.
3. Experimental results and discussion In Fig. 1 Raman spectra from the (1 1 0)t surface are shown for polarizations perpendicular and parallel to the [0 0 1]t direction at 83 K. One can clearly distinguish 15 peaks and by close inspection two well reproducible addi-
Table 1 Optical phonon modes in the insulating and metallic phase from the Raman spectrum of Fig. 1 compared with the results from a shell model calculation for the monoclinic structure (cm−1 )
Raman data
Ag
149 225 392 503 618
199 313 453 595
254 225 420 500 732
201 303 451 586
Bg
259 339 444 670 830
265 395 489
185 331 451 682 829
244 405 487 722
>TMI
240 510
390 625
Shell model
tional modes can be found (Table 1) [3]. Therefore, from the 18 Raman allowed modes only one is not resolved [3]. Above the phase transition four unusually broad peaks at 240, 390, 510 and 625 cm−1 can be found (inset in Fig. 1). A direct assignment of the 17 modes in the low-temperature phase to the irreducible representations Ag or Bg was not possible. Only 9 modes should be of Ag type. For the (1 1 0)t surface in the monoclinic structure the Bg modes should not be visible with parallel polarization of the light along [0 0 1]t . We assigned modes that show in the perpendicular polarization at least an equal intensity as in the parallel polarization to Bg modes. The result of this assignment is given in Table 1. Based on the Raman results it is possible to develop a simple shell model [12], which ensures the correctness of the assignment (see Table 1).
20 X 10
83 K
Intensity (a.u.)
15
VO2 (110)t surface 1.5
343 K
10
0
200
400
600
5
0
0
200
400
600
800
1000
Raman Shift (cm-1) Fig. 1. Raman spectrum of VO2 at 83 K. The incident light was parallel to [1 1 0]t and its polarization parallel to [0 0 1]t with the polarization of the outgoing light parallel to [0 0 1]t (upper curve) and [1 1 0]t (lower curve) from a specular surface. Fifteen peaks can be identified easily and by close inspection two other peaks at 265 and 395 cm−1 (as a shoulder) can be recognized (enlarged peaks). Inset: Raman spectrum of VO2 at 343 K.
P. Schilbe, D. Maurer / Materials Science and Engineering A 370 (2004) 449–452
Due to symmetry reasons a soft mode associated with lattice distortions from the monoclinic towards the tetragonal rutile structure must be of Ag type. When approaching the metal-insulator transition in VO2 from the low-temperature side, we have found indeed a single Raman mode that shows a pronounced softening in good agreement with the results of Andronenko et al. [10]. It is the lowest mode observed and furthermore shows the correct symmetry of Ag type. All the other modes are proved to be nearly constant and no softening features are detected in their temperature dependence below TMI . Apart from the observation of an optical soft mode, however, the conjecture drawn from the temperature dependence of the Debye temperature calculated from heat capacity data [13] that the whole lattice of the insulating phase becomes increasingly unstable on approaching the metallic phase has been confirmed from our ultrasonic measurements, which indeed show a simultaneous decrease in sound velocity of various independent acoustic modes [2]. In addition, our investigations reveal that the metal-insulator transition in VO2 is associated with strong changes of the elastic anisotropy. Being nearly isotropic in the monoclinic phase, the Rayleigh velocity in the tetragonal phase shows remarkably large anisotropy for surface waves propagating in the (1 1 0)t plane. Quantitatively, the quite different elastic anisotropy of both phases is also nicely reproduced by the shell model based on our Raman data [12] and confirms the high reliability of the given analysis. In Fig. 2 the temperature dependence of the lowest Raman mode is compared with the behavior of the SAW velocity. As can be clearly seen, both optical and acoustical modes show a pronounced softening over the same broad temperature interval of roughly 100 K. In both cases the softening is not complete due to the first-order nature of the phase transition. As can be recognized from a double-logarithmic plot (Fig. 2, lower panel) the vibrational data follow in a wide range of the reduced temperature tred = 1−T/Tc a power law β
x = (x(T) − x(TMI )) ∼ tred
(1)
where x denotes Raman frequency and Rayleigh velocity, respectively. A fit to this power law results in exponents β of 0.15 for the optical phonon and of 0.56 for the sound velocity. The exponent of the acoustic modes is thus several times larger than that of the optical mode. That means that the order parameter coupling of sound waves is clearly of higher order than for the optical mode. In principle, such behavior can be mediated through a secondary order parameter like a lattice constant, whereas the primary order parameter, which couples to the optical phonons, can be regarded as a pseudospin. Most remarkable, the thermal expansion of insulating VO2 reflects in no way the pronounced softening observed in our experiments. Instead the lattice constants depend only slightly on temperature [14] and no anomalous behavior is discernible over the whole range up to TMI . Thus, a simple mechanism of the coupling of the sound waves to the order parameter can be ruled out. It is
451
Fig. 2. Softening of acoustical and optical modes of VO2 . Raman shift of the lowest Raman mode (closed circles: present work, open circles: [10]) and relative sound velocity of Rayleigh modes in the (1 1 0)t plane along [0 0 1]t and [1 1 0]t (squares). The corresponding velocity change amounts to about 500 and 900 m/s, respectively. The solid lines are fits to power laws according to Eq. (1) (upper panel). Double logarithmic plot (lower panel). The optical mode is now also normalized.
interesting to note that optical experiments simultaneously reveal a strongly temperature dependent infrared absorption [15] right in the same temperature interval where the lattice softening occurs, hinting a change in the electronic structure of the dimerized vanadium ions. Summing up all findings, it seems likely that internal degrees of freedom associated with nearly degenerate local orbital states dominate the lattice dynamics and give rise to an increasing low-energy phonon density of states which is particularly reflected in the peculiar softening of certain phonon modes on approaching the metallic state. The quite unusual behavior of VO2 close to its metal-insulator transition is therefore highly indicative of subtle interplay of both electronic and lattice degrees of freedom, which leads to the formation of an insulating ground state.
Acknowledgements The VO2 crystals were kindly provided by S. Horn and M. Klemm. This work was supported by the Deutsche Forschungsgemeinschaft (Sfb 546 and HO 955/2-2).
452
P. Schilbe, D. Maurer / Materials Science and Engineering A 370 (2004) 449–452
References [1] F.J. Morin, Phys. Rev. Lett. 3 (1959) 34. [2] D. Maurer, A. Leue, R. Heichele, V. Müller, Phys. Rev. B 60 (1999) 13249. [3] P. Schilbe, Physica B 316–317 (2002) 600. [4] G. Andersson, Acta Chem. Scand. 10 (1956) 623. [5] K.B. Burdett, Chemical Bonding in Solids, Oxford University Press, New York, 1995, p. 94. [6] C.N. Berglund, H.J. Guggenheim, Phys. Rev. 185 (1969) 1022. [7] G.U. Chandrashekar, H.L.C. Baroos, J.M. Honig, Mater. Res. Bull. 8 (1973) 369.
[8] A.G. Aronov, D.N. Mirlin, I.I. Reshina, F.A. Chudnovskii, Sov. Phys. Solid State 19 (1977) 110. [9] V.S. Vikhnin, I.N. Goncharuk, V.Y. Davydov, F.A. Chudnovskii, E.B. Shadrin, Phys. Solid State 37 (1995) 1971. [10] R.R. Andronenko, I.N. Goncharuk, V.Y. Davydov, F.A. Chudnovskii, E.B. Shadrin, Phys. Solid State 36 (1994) 1136. [11] R. Srivastava, L.L. Chase, Phys. Rev. Lett. 27 (1971) 727. [12] P. Schilbe, D. Maurer, in preparation. [13] D.B. McWhan, M. Marezio, J.P. Remeika, P.D. Dernier, Phys. Rev. B 10 (1974) 490. [14] D. Kucharczyk, T. Niklewski, J. Appl. Cryst. 12 (1979) 370. [15] P. Merenda, D. Kaplan, C. Sommers, J. Phys. Colloq. (Paris) 37 (1976) C4–C59.
Lattice dynamics in VO2 near the metal-insulator transition P. Schilbe a,∗ , D. Maurer b b
a Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany Institut für Physik, Chemische Physik und Materialwissenschaften, Universität Augsburg, 86135 Augsburg, Germany
Received 12 July 2002
Abstract We present a comprehensive experimental study of the lattice dynamics in the vicinity of the metal-insulator transition in VO2 by means of combined use of Raman spectroscopy and ultrasonic microscopy. Single crystalline samples of high quality particularly allow quite a complete determination of all Raman modes in the insulating phase at the -point and the observation of an optical soft mode. In addition, the elastic behavior has been successfully investigated by measuring the propagation velocity of ultrasonic surface waves microscopically excited in various crystal directions. Our study reveals a striking coincidence of strong lattice softening attributable to certain acoustic branches and the occurrence of the optical soft mode, which precedes the metal-insulator transition over more than 100 K on approaching the critical temperature. © 2003 Elsevier B.V. All rights reserved. Keywords: Metal-insulator transition; Soft mode; Raman scattering; Ultrasonic microscopy
1. Introduction Among the transition metal oxides the vanadium oxides are of great current interest due to their potential applications and wealth of interesting physical properties. One of the most interesting problems is the metal-insulator transition in VO2 near ambient temperature [1–3] with a conductivity jump of up to five orders in magnitude. The microscopic origin and the mechanism stabilizing the low-temperature structural order is still a matter of debate. At TMI = 339 K the structure changes on cooling from a metallic tetragonal rutile structure to an insulting distorted rutile structure with monoclinic symmetry [4]. The cations form dimers in the insulating phase, which can be understood from simple tight binding arguments [5] although strong electronic correlation is also present. The metal-insulator transition is of first-order and the transformation entropy derived from latent heat data varies between 12.6 J mol−1 K−1 [6] and 13.8 J mol−1 K−1 [7], which is about five times larger than that what is expected from band-structure calculations due to electron localization. Hence, a realistic description must take into account changes in lattice entropy and for ∗ Corresponding author. Tel.: +49-30-838-56113; fax: +49-30-838-51355. E-mail address: [email protected] (P. Schilbe).
0921-5093/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2003.08.114
that detailed information on the lattice vibrations in VO2 is indispensable. Unfortunately, the vanadium ion has a large incoherent neutron scattering length so that inelastic neutron measurements are difficult to perform. Therefore, inelastic light scattering and ultrasonic investigations are the two main possibilities in order to study the vibrational behavior near the phase transition. 14 , In the low-temperature phase, with a space group D4h nine Ag and nine Bg modes are Raman allowed and in 5 , four the high-temperature phase, with a space group C2h modes: A1g , B1g , B2g and Eg . Former Raman studies on VO2 [8–11] were not able to detect the full spectrum in the low-temperature phase and to give a consistent assignment to the irreducible representations. In one investigation [10] a softening of the lowest Raman mode was observed, which was not observed in other investigations. In the high-temperature phase only broad structures in the Raman spectra remain, the origin of which is not understood.
2. Experimental set up The single crystals, used for the present investigation, were grown in the group of Prof. Horn in Augsburg by chemical vapor transport. The crystals were approximately
450
P. Schilbe, D. Maurer / Materials Science and Engineering A 370 (2004) 449–452
2 mm × 2 mm × 1 mm in size and had a specular (1 1 0)t surface from the growth process (all directions are given with respect to the tetragonal rutile unit cell of the high-temperature phase). The Raman spectra were taken with a double monochromator with a spectral resolution of <2 cm−1 and were excited by 0.1 W of the 514.5 nm line of an argon ion laser. All Raman measurements were done with a microprobe Raman facility in backscattering geometry. A high resolution ultrasonic microscope was used to excite Rayleigh-type surface acoustic waves (SAW) in small crystalline samples. Due to the high quality of the optically flat crystal surfaces the ultrasonic investigations could be performed at a high sound frequency of 1 GHz. The sound velocity was determined for various crystal directions from the interference pattern usually appearing close to the smooth crystal edges. Crystallites for investigation were chosen to be small enough so that we were able to pass through the phase transition without irreversible changes because cracking due to thermal cycling is a severe problem of larger VO2 single crystals, in particular. The diameter of the laser spot of the Raman system was approximately 5 m whereas the ultrasonic investigations probes a length scale of a few wave lengths (≈20 m). Thus, the investigated length scales in both methods are similar.
3. Experimental results and discussion In Fig. 1 Raman spectra from the (1 1 0)t surface are shown for polarizations perpendicular and parallel to the [0 0 1]t direction at 83 K. One can clearly distinguish 15 peaks and by close inspection two well reproducible addi-
Table 1 Optical phonon modes in the insulating and metallic phase from the Raman spectrum of Fig. 1 compared with the results from a shell model calculation for the monoclinic structure (cm−1 )
Raman data
Ag
149 225 392 503 618
199 313 453 595
254 225 420 500 732
201 303 451 586
Bg
259 339 444 670 830
265 395 489
185 331 451 682 829
244 405 487 722
>TMI
240 510
390 625
Shell model
tional modes can be found (Table 1) [3]. Therefore, from the 18 Raman allowed modes only one is not resolved [3]. Above the phase transition four unusually broad peaks at 240, 390, 510 and 625 cm−1 can be found (inset in Fig. 1). A direct assignment of the 17 modes in the low-temperature phase to the irreducible representations Ag or Bg was not possible. Only 9 modes should be of Ag type. For the (1 1 0)t surface in the monoclinic structure the Bg modes should not be visible with parallel polarization of the light along [0 0 1]t . We assigned modes that show in the perpendicular polarization at least an equal intensity as in the parallel polarization to Bg modes. The result of this assignment is given in Table 1. Based on the Raman results it is possible to develop a simple shell model [12], which ensures the correctness of the assignment (see Table 1).
20 X 10
83 K
Intensity (a.u.)
15
VO2 (110)t surface 1.5
343 K
10
0
200
400
600
5
0
0
200
400
600
800
1000
Raman Shift (cm-1) Fig. 1. Raman spectrum of VO2 at 83 K. The incident light was parallel to [1 1 0]t and its polarization parallel to [0 0 1]t with the polarization of the outgoing light parallel to [0 0 1]t (upper curve) and [1 1 0]t (lower curve) from a specular surface. Fifteen peaks can be identified easily and by close inspection two other peaks at 265 and 395 cm−1 (as a shoulder) can be recognized (enlarged peaks). Inset: Raman spectrum of VO2 at 343 K.
P. Schilbe, D. Maurer / Materials Science and Engineering A 370 (2004) 449–452
Due to symmetry reasons a soft mode associated with lattice distortions from the monoclinic towards the tetragonal rutile structure must be of Ag type. When approaching the metal-insulator transition in VO2 from the low-temperature side, we have found indeed a single Raman mode that shows a pronounced softening in good agreement with the results of Andronenko et al. [10]. It is the lowest mode observed and furthermore shows the correct symmetry of Ag type. All the other modes are proved to be nearly constant and no softening features are detected in their temperature dependence below TMI . Apart from the observation of an optical soft mode, however, the conjecture drawn from the temperature dependence of the Debye temperature calculated from heat capacity data [13] that the whole lattice of the insulating phase becomes increasingly unstable on approaching the metallic phase has been confirmed from our ultrasonic measurements, which indeed show a simultaneous decrease in sound velocity of various independent acoustic modes [2]. In addition, our investigations reveal that the metal-insulator transition in VO2 is associated with strong changes of the elastic anisotropy. Being nearly isotropic in the monoclinic phase, the Rayleigh velocity in the tetragonal phase shows remarkably large anisotropy for surface waves propagating in the (1 1 0)t plane. Quantitatively, the quite different elastic anisotropy of both phases is also nicely reproduced by the shell model based on our Raman data [12] and confirms the high reliability of the given analysis. In Fig. 2 the temperature dependence of the lowest Raman mode is compared with the behavior of the SAW velocity. As can be clearly seen, both optical and acoustical modes show a pronounced softening over the same broad temperature interval of roughly 100 K. In both cases the softening is not complete due to the first-order nature of the phase transition. As can be recognized from a double-logarithmic plot (Fig. 2, lower panel) the vibrational data follow in a wide range of the reduced temperature tred = 1−T/Tc a power law β
x = (x(T) − x(TMI )) ∼ tred
(1)
where x denotes Raman frequency and Rayleigh velocity, respectively. A fit to this power law results in exponents β of 0.15 for the optical phonon and of 0.56 for the sound velocity. The exponent of the acoustic modes is thus several times larger than that of the optical mode. That means that the order parameter coupling of sound waves is clearly of higher order than for the optical mode. In principle, such behavior can be mediated through a secondary order parameter like a lattice constant, whereas the primary order parameter, which couples to the optical phonons, can be regarded as a pseudospin. Most remarkable, the thermal expansion of insulating VO2 reflects in no way the pronounced softening observed in our experiments. Instead the lattice constants depend only slightly on temperature [14] and no anomalous behavior is discernible over the whole range up to TMI . Thus, a simple mechanism of the coupling of the sound waves to the order parameter can be ruled out. It is
451
Fig. 2. Softening of acoustical and optical modes of VO2 . Raman shift of the lowest Raman mode (closed circles: present work, open circles: [10]) and relative sound velocity of Rayleigh modes in the (1 1 0)t plane along [0 0 1]t and [1 1 0]t (squares). The corresponding velocity change amounts to about 500 and 900 m/s, respectively. The solid lines are fits to power laws according to Eq. (1) (upper panel). Double logarithmic plot (lower panel). The optical mode is now also normalized.
interesting to note that optical experiments simultaneously reveal a strongly temperature dependent infrared absorption [15] right in the same temperature interval where the lattice softening occurs, hinting a change in the electronic structure of the dimerized vanadium ions. Summing up all findings, it seems likely that internal degrees of freedom associated with nearly degenerate local orbital states dominate the lattice dynamics and give rise to an increasing low-energy phonon density of states which is particularly reflected in the peculiar softening of certain phonon modes on approaching the metallic state. The quite unusual behavior of VO2 close to its metal-insulator transition is therefore highly indicative of subtle interplay of both electronic and lattice degrees of freedom, which leads to the formation of an insulating ground state.
Acknowledgements The VO2 crystals were kindly provided by S. Horn and M. Klemm. This work was supported by the Deutsche Forschungsgemeinschaft (Sfb 546 and HO 955/2-2).
452
P. Schilbe, D. Maurer / Materials Science and Engineering A 370 (2004) 449–452
References [1] F.J. Morin, Phys. Rev. Lett. 3 (1959) 34. [2] D. Maurer, A. Leue, R. Heichele, V. Müller, Phys. Rev. B 60 (1999) 13249. [3] P. Schilbe, Physica B 316–317 (2002) 600. [4] G. Andersson, Acta Chem. Scand. 10 (1956) 623. [5] K.B. Burdett, Chemical Bonding in Solids, Oxford University Press, New York, 1995, p. 94. [6] C.N. Berglund, H.J. Guggenheim, Phys. Rev. 185 (1969) 1022. [7] G.U. Chandrashekar, H.L.C. Baroos, J.M. Honig, Mater. Res. Bull. 8 (1973) 369.
[8] A.G. Aronov, D.N. Mirlin, I.I. Reshina, F.A. Chudnovskii, Sov. Phys. Solid State 19 (1977) 110. [9] V.S. Vikhnin, I.N. Goncharuk, V.Y. Davydov, F.A. Chudnovskii, E.B. Shadrin, Phys. Solid State 37 (1995) 1971. [10] R.R. Andronenko, I.N. Goncharuk, V.Y. Davydov, F.A. Chudnovskii, E.B. Shadrin, Phys. Solid State 36 (1994) 1136. [11] R. Srivastava, L.L. Chase, Phys. Rev. Lett. 27 (1971) 727. [12] P. Schilbe, D. Maurer, in preparation. [13] D.B. McWhan, M. Marezio, J.P. Remeika, P.D. Dernier, Phys. Rev. B 10 (1974) 490. [14] D. Kucharczyk, T. Niklewski, J. Appl. Cryst. 12 (1979) 370. [15] P. Merenda, D. Kaplan, C. Sommers, J. Phys. Colloq. (Paris) 37 (1976) C4–C59.