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Anomalous profile of amplitude mode in K0.30MoO3 at low temperatures studied by Raman spectroscopy
PERGAMON
Solid State Communications 116 (2000) 7±9
www.elsevier.com/locate/ssc
Anomalous pro®le of amplitude mode in K0.30MoO3 at low temperatures studied by Raman spectroscopy S. Nishio*, M. Kakihana Materials and Structures Laboratory, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama 226-8503, Japan Received 2 May 2000; accepted 29 June 2000 by H. Kamimura
Abstract We precisely reinvestigate the Charge-Density Wave (CDW) amplitude mode in molybdenum blue bronze (K0.30MoO3) by using Raman spectroscopy down to 4 K. The Raman pro®le of the amplitude mode is gradually changing from one harmonic oscillator form to an anomalous asymmetric one like a ª®nº with decreasing temperature. This is probably due to a splitting of the amplitude mode and contrasted with the previous study [Solid State Commun. 45 (1983) 289], where the CDW amplitude mode was analyzed with one harmonic oscillator down to 10 K. This anomaly probably re¯ects a spatial variation of the CDW amplitude in the bulk of the crystal at low temperatures. q 2000 Published by Elsevier Science Ltd. Keywords: A. Quasi-one-dimensional conductor; D. Charge-density wave; D. Phonons; E. Inelastic light scattering PACS: 71.45. Lr; 78.30.-j
Quasi-one-dimensional metals, for instance, molybdenum blue bronze (K0.30MoO3), undergo Peierls transition at low temperature and below the Peierls transition temperature (TP) form a charge-density wave (CDW) state where both the electron-density and the lattice are periodically modulated. In actual CDW state, the modulation of the CDW is distorted (ªpinnedº) to various degree by the potentials of the impurities randomly dispersed in the lattice. The impurity-pinned CDW exhibits unusual physical properties: dynamical collective phenomena (for instance, nonlinear electrical conductivity due to CDW-sliding) and metastability (for instance, strong hysteresis and ªmemory effectº) [1±3]. Extensive theoretical and experimental studies were carried out to understand the physical properties of the CDW. These unusual properties are closely connected with the distortion of the CDW and their deformation in external ®elds. There are two collective excitations in CDWs. One is the phase mode, v 2; the other is the amplitude mode, v 1 [4]. The amplitude mode, v 1, corresponds to a ¯uctuation of amplitude from the equilibrium value. The temperature dependence of the CDW amplitude mode of molybdenum blue bronze, K0.30MoO3, was ®rst reported by Travaglini et * Corresponding author. E-mail address: [email protected] (S. Nishio).
al. [5] by using Raman spectroscopy, where the CDW amplitude mode was well ®tted with one harmonic oscillator [2,5]. In this report we precisely reinvestigate the amplitude mode in molybdenum blue bronze by using Raman spectroscopy and show that the pro®le of the amplitude mode is gradually changing from one harmonic oscillator form to an anomalous asymmetric form like a ª®nº with decreasing temperature, probably due to a splitting of the amplitude mode. This is in contrast to the previous study [5]. The origin of the splitting of the amplitude mode is also discussed. Single crystals of blue bronze, K0.30MoO3, were grown via the electrolysis of K2MoO4 ±MoO3 molten mixture [6]. Blue bronze crystals have a sheet-like structure and easily cleaves parallel to the 201 plane. Samples were cleaved in air just before the measurement. To minimize heating by laser irradiation, the sample was thinned to about 30 mm. An Ar 1 laser with a 514.5 nm line was used for the excitation of the Raman spectra. The spot size and the power of the laser irradiation of the samples was 4 mm in diameter and 0.6 mW, respectively. The Raman spectra were collected with a triple stage Raman spectrometer; Jobin Yvon/Atago Bussan T64000 with microscope optics. A backthinned type CCD detector was chosen for dramatically improving the signal-to-noise ratio of the spectra probably not achievable
0038-1098/00/$ - see front matter q 2000 Published by Elsevier Science Ltd. PII: S 0038-109 8(00)00266-0
8
S. Nishio, M. Kakihana / Solid State Communications 116 (2000) 7±9
Fig. 2. Temperature dependence of the full-width at half-maximum (FWHM) of the amplitude mode. Note that the FWHM of the amplitude mode is slightly increasing with decreasing temperature between 50 and 25 K.
Fig. 1. Temperature dependent Raman spectra of the amplitude mode of molybdenum blue bronze, K0.30MoO3, with open circles between 4 and 100 K. Note, the symmetric Raman pro®le of the amplitude mode at 100 K turns into an unusual asymmetric shape like a ª®nº with decreasing temperature down to 4 K. As indicated by arrows, we can see that the lower frequency side of the top of the peak is slightly ªchopped offº. Fittings with harmonic oscillators are also made tentatively. The thin solid line denotes the individual oscillator pro®les and the baseline; the thick solid line denotes the synthesized pro®les from the individual ones; the broken line denotes the residuals. Note that one harmonic oscillator ®t was not satisfactory below 75 K due to the asymmetry of the amplitude mode.
in the previous reports. The spectral resolution in the vicinity of the amplitude mode was about 2 cm 21. x~ con®guration, where All the spectra were taken p in x yy x and y correspond to 1= 5201 and y 010; respectively [5]; incommensurate CDW is formed along [010] below TP 180 K [7]. The temperature dependent Raman spectra of the amplitude mode of molybdenum blue bronze between 4 and 100 K are shown in Fig. 1. The amplitude mode has a symmetric pro®le at 100 K, as was observed in the previous study [5]. Surprisingly enough, the Raman pro®le of the amplitude mode is no longer symmetric below 75 K; we can see that the lower frequency side of the top of the peak is slightly ªchopped offº. This asymmetry is enhanced
with further cooling. At 4 K, the Raman pro®le of the amplitude mode takes an anomalous shape like a ª®nº. See also Ref. [5] for comparison. Although it is well known that the asymmetric line shape can be seen in the solids with electron±phonon interaction (Fano interference effect), the asymmetry observed in the amplitude mode is different from that with the Fano interference effect. Therefore, it is likely that the single amplitude mode in molybdenum blue bronze splits into several modes below 75 K. Fittings with harmonic oscillators were also made tentatively to clarify the asymmetry and the peak splitting. While the Raman pro®le of the amplitude mode was well ®tted with one harmonic oscillator at 100 K, this one harmonic oscillator ®t was not satisfactory below 75 K due to the asymmetry of the amplitude mode. The number of harmonic oscillators necessary to ®t the amplitude mode increased with decreasing temperature. Even the ®tting with three harmonic oscillators were not satisfactory below 25 K. The presence of the peak splitting of the amplitude mode at low temperature is also supported by the temperature dependence of the full-width at half-maximum (FWHM) of the amplitude mode (Fig. 2). The FWHM of the amplitude mode showed normal temperature dependence Ð the FWHM was decreasing with decreasing temperature down to 50 K. However, the FWHM of the amplitude mode was slightly increasing with decreasing temperature between 50 and 25 K. To the best of our knowledge, the theory dealing with the shape of the amplitude mode is absent. Based on the principle of vibrational spectroscopy, the origin of the asymmetry of the amplitude mode can be explained as given below: Since the amplitude mode, v 1 corresponds to a ¯uctuation of amplitude from the equilibrium value as mentioned above, it is natural to assume that the strength of the force constant for the amplitude mode is dependent on magnitude
S. Nishio, M. Kakihana / Solid State Communications 116 (2000) 7±9
of the amplitude of the CDW modulation. It can allow NOT a single amplitude mode under spatial variation of the CDW amplitude. Therefore, it is reasonable to attribute the asymmetry of the amplitude mode due to splitting below 75 K to a spatial variation of the CDW amplitude. The question is then why the spatial variation of the CDW amplitude is temperature dependent. This can be explained by taking into account the screening of impurity potentials by normal electrons as follows: The amplitude as well as the phase of the CDW can be perturbed by impurity potentials. At low temperatures like 4 K, the presence of thermally excited normal electrons are negligible. Therefore the CDW amplitude can be strongly perturbed by ªrawº impurity potentials; spatial variation of the CDW amplitude can be formed. With increasing temperature the impurity potentials can be weakened by thermally excited normal electrons; the spatial variation of the CDW amplitude can be gradually suppressed and vanishes at some temperature. In most theoretical treatments of dynamical collective phenomena of the CDW in the bulk of the crystal, only the dynamics of the phase is considered, where it is assumed that the amplitude of the CDW is not perturbed by an interaction between the CDW and the impurity potential [1,2]. However, our result suggests that spatial variation of the CDW amplitude, i.e. a deviation from the ªmajor premiseº in the bulk CDW physics is present below 75 K in molybdenum blue bronze. In conclusion, we reinvestigated the CDW amplitude
9
mode in molybdenum blue bronze (K0.30MoO3) by using Raman spectroscopy down to 4 K and found that the Raman pro®le of the amplitude mode is gradually changing from one harmonic oscillator form to an anomalous asymmetric form like a ª®nº with decreasing temperature. This is probably due to the splitting of the CDW amplitude mode; it is likely that the CDW amplitude is NOT spatially uniform below 75 K. Acknowledgements We appreciate V.V. Petrykin for his continuous interest on this subject. References [1] G. GruÈner, Rev. Mod. Phys. 60 (1988) 1129. [2] G. GruÈner, Density Waves in Solids, Addison-Wesley, Reading, MA, 1994. [3] J. Dumas, C. Schlenker, Int. J. Mod. Phys. B 7 (1993) 4045. [4] P.A. Lee, T.M. Rice, P.W. Anderson, Solid State Commun. 14 (1974) 1974. [5] G. Travaglini, I. MoÈrke, P. Wachter, Solid State Commun. 45 (1983) 289. [6] A. Wold, W. Kunnmann, R.J. Arnott, A. Feretti, Inorg. Chem. 3 (1964) 545. [7] G. Travaglini, P. Wachter, J. Marcus, C. Schlenker, Solid State Commun. 37 (1981) 599.
Solid State Communications 116 (2000) 7±9
www.elsevier.com/locate/ssc
Anomalous pro®le of amplitude mode in K0.30MoO3 at low temperatures studied by Raman spectroscopy S. Nishio*, M. Kakihana Materials and Structures Laboratory, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama 226-8503, Japan Received 2 May 2000; accepted 29 June 2000 by H. Kamimura
Abstract We precisely reinvestigate the Charge-Density Wave (CDW) amplitude mode in molybdenum blue bronze (K0.30MoO3) by using Raman spectroscopy down to 4 K. The Raman pro®le of the amplitude mode is gradually changing from one harmonic oscillator form to an anomalous asymmetric one like a ª®nº with decreasing temperature. This is probably due to a splitting of the amplitude mode and contrasted with the previous study [Solid State Commun. 45 (1983) 289], where the CDW amplitude mode was analyzed with one harmonic oscillator down to 10 K. This anomaly probably re¯ects a spatial variation of the CDW amplitude in the bulk of the crystal at low temperatures. q 2000 Published by Elsevier Science Ltd. Keywords: A. Quasi-one-dimensional conductor; D. Charge-density wave; D. Phonons; E. Inelastic light scattering PACS: 71.45. Lr; 78.30.-j
Quasi-one-dimensional metals, for instance, molybdenum blue bronze (K0.30MoO3), undergo Peierls transition at low temperature and below the Peierls transition temperature (TP) form a charge-density wave (CDW) state where both the electron-density and the lattice are periodically modulated. In actual CDW state, the modulation of the CDW is distorted (ªpinnedº) to various degree by the potentials of the impurities randomly dispersed in the lattice. The impurity-pinned CDW exhibits unusual physical properties: dynamical collective phenomena (for instance, nonlinear electrical conductivity due to CDW-sliding) and metastability (for instance, strong hysteresis and ªmemory effectº) [1±3]. Extensive theoretical and experimental studies were carried out to understand the physical properties of the CDW. These unusual properties are closely connected with the distortion of the CDW and their deformation in external ®elds. There are two collective excitations in CDWs. One is the phase mode, v 2; the other is the amplitude mode, v 1 [4]. The amplitude mode, v 1, corresponds to a ¯uctuation of amplitude from the equilibrium value. The temperature dependence of the CDW amplitude mode of molybdenum blue bronze, K0.30MoO3, was ®rst reported by Travaglini et * Corresponding author. E-mail address: [email protected] (S. Nishio).
al. [5] by using Raman spectroscopy, where the CDW amplitude mode was well ®tted with one harmonic oscillator [2,5]. In this report we precisely reinvestigate the amplitude mode in molybdenum blue bronze by using Raman spectroscopy and show that the pro®le of the amplitude mode is gradually changing from one harmonic oscillator form to an anomalous asymmetric form like a ª®nº with decreasing temperature, probably due to a splitting of the amplitude mode. This is in contrast to the previous study [5]. The origin of the splitting of the amplitude mode is also discussed. Single crystals of blue bronze, K0.30MoO3, were grown via the electrolysis of K2MoO4 ±MoO3 molten mixture [6]. Blue bronze crystals have a sheet-like structure and easily cleaves parallel to the 201 plane. Samples were cleaved in air just before the measurement. To minimize heating by laser irradiation, the sample was thinned to about 30 mm. An Ar 1 laser with a 514.5 nm line was used for the excitation of the Raman spectra. The spot size and the power of the laser irradiation of the samples was 4 mm in diameter and 0.6 mW, respectively. The Raman spectra were collected with a triple stage Raman spectrometer; Jobin Yvon/Atago Bussan T64000 with microscope optics. A backthinned type CCD detector was chosen for dramatically improving the signal-to-noise ratio of the spectra probably not achievable
0038-1098/00/$ - see front matter q 2000 Published by Elsevier Science Ltd. PII: S 0038-109 8(00)00266-0
8
S. Nishio, M. Kakihana / Solid State Communications 116 (2000) 7±9
Fig. 2. Temperature dependence of the full-width at half-maximum (FWHM) of the amplitude mode. Note that the FWHM of the amplitude mode is slightly increasing with decreasing temperature between 50 and 25 K.
Fig. 1. Temperature dependent Raman spectra of the amplitude mode of molybdenum blue bronze, K0.30MoO3, with open circles between 4 and 100 K. Note, the symmetric Raman pro®le of the amplitude mode at 100 K turns into an unusual asymmetric shape like a ª®nº with decreasing temperature down to 4 K. As indicated by arrows, we can see that the lower frequency side of the top of the peak is slightly ªchopped offº. Fittings with harmonic oscillators are also made tentatively. The thin solid line denotes the individual oscillator pro®les and the baseline; the thick solid line denotes the synthesized pro®les from the individual ones; the broken line denotes the residuals. Note that one harmonic oscillator ®t was not satisfactory below 75 K due to the asymmetry of the amplitude mode.
in the previous reports. The spectral resolution in the vicinity of the amplitude mode was about 2 cm 21. x~ con®guration, where All the spectra were taken p in x yy x and y correspond to 1= 5201 and y 010; respectively [5]; incommensurate CDW is formed along [010] below TP 180 K [7]. The temperature dependent Raman spectra of the amplitude mode of molybdenum blue bronze between 4 and 100 K are shown in Fig. 1. The amplitude mode has a symmetric pro®le at 100 K, as was observed in the previous study [5]. Surprisingly enough, the Raman pro®le of the amplitude mode is no longer symmetric below 75 K; we can see that the lower frequency side of the top of the peak is slightly ªchopped offº. This asymmetry is enhanced
with further cooling. At 4 K, the Raman pro®le of the amplitude mode takes an anomalous shape like a ª®nº. See also Ref. [5] for comparison. Although it is well known that the asymmetric line shape can be seen in the solids with electron±phonon interaction (Fano interference effect), the asymmetry observed in the amplitude mode is different from that with the Fano interference effect. Therefore, it is likely that the single amplitude mode in molybdenum blue bronze splits into several modes below 75 K. Fittings with harmonic oscillators were also made tentatively to clarify the asymmetry and the peak splitting. While the Raman pro®le of the amplitude mode was well ®tted with one harmonic oscillator at 100 K, this one harmonic oscillator ®t was not satisfactory below 75 K due to the asymmetry of the amplitude mode. The number of harmonic oscillators necessary to ®t the amplitude mode increased with decreasing temperature. Even the ®tting with three harmonic oscillators were not satisfactory below 25 K. The presence of the peak splitting of the amplitude mode at low temperature is also supported by the temperature dependence of the full-width at half-maximum (FWHM) of the amplitude mode (Fig. 2). The FWHM of the amplitude mode showed normal temperature dependence Ð the FWHM was decreasing with decreasing temperature down to 50 K. However, the FWHM of the amplitude mode was slightly increasing with decreasing temperature between 50 and 25 K. To the best of our knowledge, the theory dealing with the shape of the amplitude mode is absent. Based on the principle of vibrational spectroscopy, the origin of the asymmetry of the amplitude mode can be explained as given below: Since the amplitude mode, v 1 corresponds to a ¯uctuation of amplitude from the equilibrium value as mentioned above, it is natural to assume that the strength of the force constant for the amplitude mode is dependent on magnitude
S. Nishio, M. Kakihana / Solid State Communications 116 (2000) 7±9
of the amplitude of the CDW modulation. It can allow NOT a single amplitude mode under spatial variation of the CDW amplitude. Therefore, it is reasonable to attribute the asymmetry of the amplitude mode due to splitting below 75 K to a spatial variation of the CDW amplitude. The question is then why the spatial variation of the CDW amplitude is temperature dependent. This can be explained by taking into account the screening of impurity potentials by normal electrons as follows: The amplitude as well as the phase of the CDW can be perturbed by impurity potentials. At low temperatures like 4 K, the presence of thermally excited normal electrons are negligible. Therefore the CDW amplitude can be strongly perturbed by ªrawº impurity potentials; spatial variation of the CDW amplitude can be formed. With increasing temperature the impurity potentials can be weakened by thermally excited normal electrons; the spatial variation of the CDW amplitude can be gradually suppressed and vanishes at some temperature. In most theoretical treatments of dynamical collective phenomena of the CDW in the bulk of the crystal, only the dynamics of the phase is considered, where it is assumed that the amplitude of the CDW is not perturbed by an interaction between the CDW and the impurity potential [1,2]. However, our result suggests that spatial variation of the CDW amplitude, i.e. a deviation from the ªmajor premiseº in the bulk CDW physics is present below 75 K in molybdenum blue bronze. In conclusion, we reinvestigated the CDW amplitude
9
mode in molybdenum blue bronze (K0.30MoO3) by using Raman spectroscopy down to 4 K and found that the Raman pro®le of the amplitude mode is gradually changing from one harmonic oscillator form to an anomalous asymmetric form like a ª®nº with decreasing temperature. This is probably due to the splitting of the CDW amplitude mode; it is likely that the CDW amplitude is NOT spatially uniform below 75 K. Acknowledgements We appreciate V.V. Petrykin for his continuous interest on this subject. References [1] G. GruÈner, Rev. Mod. Phys. 60 (1988) 1129. [2] G. GruÈner, Density Waves in Solids, Addison-Wesley, Reading, MA, 1994. [3] J. Dumas, C. Schlenker, Int. J. Mod. Phys. B 7 (1993) 4045. [4] P.A. Lee, T.M. Rice, P.W. Anderson, Solid State Commun. 14 (1974) 1974. [5] G. Travaglini, I. MoÈrke, P. Wachter, Solid State Commun. 45 (1983) 289. [6] A. Wold, W. Kunnmann, R.J. Arnott, A. Feretti, Inorg. Chem. 3 (1964) 545. [7] G. Travaglini, P. Wachter, J. Marcus, C. Schlenker, Solid State Commun. 37 (1981) 599.