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Temperature dependence of the Raman spectra of 1T-TaS2
PERGAMON
Solid State Communications 117 (2001) 361±364
www.elsevier.com/locate/ssc
Temperature dependence of the Raman spectra of 1T-TaS2 T. Hirata a,*, F.S. Ohuchi b b
a National Research Institute for Metals, 1-2-1 Sengen, Tsukuba, Ibraki 305-0047, Japan Department of Materials and Engineering, University of Washington, Box 352120, Seattle, WA 98195-2120, USA
Received 18 August 2000; received in revised form 30 October 2000; accepted 30 October 2000 by F.J. DiSalvo
Abstract The temperature dependence of the unpolarized Raman spectra from 1T-TaS2 has been measured between 297 K and 48 K. The present work demonstrates that the three Raman modes observed above 220 cm 21 (high frequency region) at room temperature exhibit remarkable frequency changes toward low wavenumbers in the vicinity of 200 K, where 1T-TaS2 undergoes a ®rst-order transition of the charge density wave (CDW) from nearly commensurate to a commensurate state. The monotonic line-broadening and intensity reduction with temperature has been identi®ed for these Raman modes. In contrast, the behavior observed in the low frequency region (less than 200 cm 21), suggested that the soft phonons are less likely to be involved in the temperature dependence of the high frequency Raman modes. q 2001 Elsevier Science Ltd. All rights reserved. Keywords: D. Phase transitions; D. Phonons PACS: 63.20.2e; 64.60.2i; 78.30.2j
A transition metal dichalcogenide compound, 1T-TaS2, exhibits a strong charge density wave (CDW) instability [1], which is characterized by two ®rst-order transitions of incommensurate to nearly commensurate and nearly commensurate to commensurate states that are observed at 350 K and 200 K, respectively. At these temperatures, discontinuous changes in the electrical resistivity, magnetic susceptibility and re¯ectivity were observed [2±4]. The CDW instabilities and the effects of cation doping in the transition metal chalcogenides have been studied extensively by electron, X-ray and neutron diffraction techniques, as well as infrared re¯ectivity and Raman scattering [4±16]. Several Raman studies on 1T-TaS2 have shown that there are two Raman Ag modes observed at 81 and 114 cm 21. These low frequency modes behave like soft phonons, and exhibit their frequency shift toward the lower wavenumbers in the vicinity of T 200 K [11,12], as the temperature is raised from a low temperature. The temperature-dependent frequency (v ) of the 82 cm 21 Raman mode, for example, ÿ can be ®tted to a form of v a T0 2 T 0:5 , where a is a constant and T0 is approximately 1040 K is a transition temperature for the soft phonon mode [10]. * Corresponding author. Tel.: 181-298-59-2734; fax: 181-29859-2701. E-mail address: [email protected] (T. Hirata).
There are additional Raman lines present in the 1T-TaS2 Raman spectra when the commensurate CDW state is reached at 200 K. They are explained as the increase in the number of zone center (G -point) phonon modes due to folding of the original Brillouin zone by the formation of a commensurate superlattice [9,11]. These spectral changes are found in the low and/or high frequency region, but no particular attention has been paid to subtle changes in the high frequency region of the Raman spectra from 1T-TaS2, when 1T-TaS2 undergoes the transition from the nearly commensurate to commensurate state at 200 K [11,12]. The present paper reports a new ®nding relating to the spectral changes in the high frequency region (above 2230 cm 21) when the transition from the nearly commensurate to commensurate state takes place in 1T-TaS2. Single crystals of 1T-TaS2 were grown by an iodine vapor transport technique, details of which are given elsewhere [2]. Unpolarized Raman spectra of 1T-TaS2 were collected from 1T-TaS2 at different temperatures ranging from 297 K to 48 K using a Dilor XY spectrometer. Sample temperature was measured by a Au (Fe)-KP thermocouple, and controlled with an accuracy of ^1 K. A 514.5 nm line from the Ar 1 laser was used as the radiation source. Incident laser power was limited to 10 mW in order to minimize a possibility of sample heating. All the Raman spectra from 1T-TaS2 were collected in a backscattering con®guration. A
0038-1098/01/$ - see front matter q 2001 Elsevier Science Ltd. All rights reserved. PII: S 0038-109 8(00)00468-3
362
T. Hirata, F.S. Ohuchi / Solid State Communications 117 (2001) 361±364
Fig. 1. The unpolarized Raman spectra of lT-TaS2 measured at different temperatures between 297K and 48K.
curve ®tting program GRAMS/32 (Galactic Ltd.) was used for analysis. Shown in Fig. 1 is a set of unpolarized Raman spectra measured from 1T-TaS2 at different temperatures from 297 K to 48 K. Whole features of the Raman spectra at
Fig. 2. A deconvolution of the Raman spectrum of 1T-TaS2 at 48 K; X: experimental data; Ð: composed; ´´´: resolved lines with numbers.
each temperature were in good agreement with the results previously reported [7,9,11,12]. There are four observed at approximately 100, 243, 306 and 381 cm 21 in the nearly commensurate CDW state at 297 K. As the temperature is decreased, these peaks are intensi®ed, and split into several well-de®ned peaks. Previous studies [7,9,11,12] from 1TTaS2 have shown that the Raman modes below 100 cm 21 become intense signi®cantly while other modes appear when the nearly commensurate±commensurate transition takes place at T 200 K. Additional lines that appeared in the commensurate CDW state are due to folding of the G -point modes from originalp non-zero wave vector points in a thep p 13a 0 £ 13a0 £ 13c0 superlattice formed at 200 K [9,11]. The structure of this superlattice is triclinic belonging to space group Ci1 with 13 formula units per unit cell, totalling 39 atoms. Hence, 114 optical phonon modes are expected, in which 57 are Raman active and the rest are infrared active [9,11]. The modes above 220 cm 21 are derived from the optical phonon branches, in which the sulfur atoms are involved in the atomic vibrations, whereas the modes observed below 100 cm 21 are from acoustical phonon branches in which the tantalum atoms take part in the vibrations. To bring out any spectral changes while cooling, each spectrum was deconvoluted into several peaks using a Gaussian line ®tting. Shown in Fig. 2 is the spectrum obtained at 48 K, in which the results from peak deconvolution are superposed. The deconvoluted peaks were then numbered as shown in Fig. 2, and compared with published data [9,12] (Table 1). While the constituent phonon modes resolved at 48 K in the present study are at least consistent with those observed previously, careful examination of each spectrum would reveal that three Raman modes observed at 243, 306 and 381 cm 21 at 297 K undergo systematic changes in frequency, linewidth and intensity as the temperature decreases. The frequencies of these modes are therefore plotted as a function of temperature in Fig. 3. Here, peaks 5, 8 and 11 were used to represent the changes. Note that the temperature dependences of the modes' frequencies are somewhat different. The 381 cm 21 mode represents the most traditional temperature dependence associated with a phase transition, exhibiting a tremendous frequency change in the vicinity of T 200 K, at which the nearly commensurate to commensurate transition occurs; besides, it appears that the frequency change of this mode with temperature is characteristic of a second-order rather than ®rst-order transition. In contrast, the 306 cm 21 and 243 cm 21 modes show no obvious anomaly near 200 K, whilst the former reveals a unique stiffening below 100 K and the latter stiffens ordinarily with cooling. An attempt was madeÿ to ®t the frequency data of these peaks to a form of v a T0 2 T b . However, no proper ®tting could be achieved with reasonable values of T0 and/or b , even for peak 11 that shows the most typical frequency change with
T. Hirata, F.S. Ohuchi / Solid State Communications 117 (2001) 361±364
363
Table 1 The frequency and intensity of each constituent line obtained by resolving the Raman spectrum of 1T-TaS2 at 48 K as shown in Fig. 2, as compared with available frequency data of 1T-TaS2 [9,12] Peak No.
Frequency (cm 21)
Intensity a
Ref. [9] (121K)
Ref. [12] (24K)
1 2 3 4 5 6 7 8 9 10 11
101 115 130 231 246 266 286 309 329 368 390
vs s s w s w m s w w s
56 62 68 72 80 89 100 106 115 121 129 134 229 243 266 282 300 306 322 329 366 390
62 67 81 100 114 128 229 234 255 262 275 282 286 300 306 324 334 368 390
a
vs: very strong; s: strong; m: medium; w: weak; vw: very weak.
temperature. However, the 82 cm 21 mode that appears below 200 K in 1T-TaS2 can be ®tted to the above functional form [10]. The 81 cm 21 and 114 cm 21 modes would appear below 200 K in 1T-TaS2 and behave like the soft phonons [11,12]. When we compare the temperature dependences of these two modes with those of the high frequency modes as shown in Fig. 3, we notice that there are some dissimilarities between them. Thus, the present work indicates that the high frequency modes in the spectra of 1T-TaS2 do not behave as the soft phonons. However, there exist some remarkable frequency changes with temperature for the high frequency modes.
This is largely contrasted with the previous works [11,12] where no such changes were identi®ed. As for the changes in linewidth and relative intensity of the Raman peaks observed at the high frequency region, no unusual behavior was observed. In Fig. 4, the changes in the linewidth and the relative intensity for the Raman peaks 5, 8 and 11 are plotted as a function of temperature. Each peak is monotonously sharpened and intensi®ed as the temperature decreases. Such monotonous line-broadening and intensity reduction with temperature have been observed for the 82 cm 21 Ag Raman mode of 2H-TaSe2, which also exhibits the CDW instability [17].
Fig. 3. The frequencies of the three Raman modes at 243 cm 21, 306 cm 21 and 381 cm 21 (at 297 K) observed in the Raman spectra of 1T-TaS2 are plotted as a function of temperature. Note that the lines are only a visual guide, and each curve is numbered corresponding to one of the resolved Raman lines as shown in Fig. 2.
364
T. Hirata, F.S. Ohuchi / Solid State Communications 117 (2001) 361±364
for Promotion of Materials Science and Technology of Japan) for variable-temperature Raman scattering.
References
Fig. 4. Changes in linewidth (a) and relative intensity (b) of the three Raman modes at 243 cm 21, 306 cm 21 and 381 cm 21 (at 297 K) as a function of temperature. Each number attached on the curve represents a resolved line of the Raman spectrum of 1T-TaS2 at 48 K as shown in Fig. 2.
This short communication presents new ®ndings about the temperature dependence of the unpolarized spectra of 1T-TaS2 measured in the range between 297 K and 48 K. It is highlighted that the three Raman modes observed above 220 cm 21 exhibit remarkable frequency changes toward the low wavenumbers in the vicinity of T 200 K, where 1T-TaS2 undergoes a ®rst-order transition from a nearly commensurate to a commensurate CDW state. A monotonic line broadening and an intensity reduction with temperature was found for these Raman modes. In contrast, the behavior observed in the low frequency region (less than 200 cm 21), suggested that the soft phonons are less likely to be involved in the temperature dependence of the high frequency Raman modes. Acknowledgements We would like to thank F. Fujishima of MST (Foundation
[1] N. Nagaosa, E. Hanamura, Phys. Rev. B29 (1984) 2060. [2] A.H. Thompson, F.R. Gamble, J.F. Revelli, Sol. Stat. Commun. 9 (1971) 981. [3] F.J. Di Salvo, J.E. Graebner, Sol. Stat. Commun. 23 (1977) 825. [4] P. Fazekas, E. Tosatti, Phil. Mag. B39 (1979) 229. [5] F.J. Di Salvo, J.A. Wilson, B.G. Bagley, J.V. Waszczak, Phys. Rev. B12 (1975) 2220. [6] G. Lucovsky, W.Y. Liang, R.M. White, K.R. Pisharody, Sol. Stat. Commun. 19 (1976) 303. [7] J.E. Smith Jr, J.C. Tsang, M.W. Shafer, Sol. Stat. Commun. 19 (1976) 283. [8] A.S. Barker Jr, J.A. Ditzenberger, F.J. Di Salvo, Phys. Rev. B12 (1975) 2049. [9] J.R. Duffey, R.D. Kirby, R.V. Coleman, Sol. Stat. Commun. 20 (1976) 617. [10] G.A. Sai-Halasz, P.B. Perry, Sol. Stat. Commun. 21 (1977) 995. [11] S. Uchida, S. Sugai, Physica 105B (1981) 393. [12] S. Sugai, K. Murase, S. Uchida, S. Tanaka, Physica 105B (1981) 405. [13] C.B. Scruby, P.M. Williams, G.S. Parry, Phil. Mag. 31 (1975) 255. [14] D.E. Moncton, J.D. Axe, F.J. Di Salvo, Phys. Rev. Lett. 34 (1975) 734. [15] D.R. Karecki, B.P. Clayman, Sol. Stat. Commun. 19 (1976) 479. [16] D.R. Kurecki, B.P. Clayman, Phys. Rev. B19 (1979) 6367. [17] J.C. Tsang, J.E. Smith Jr, M.W. Shafer, S.F. Meyer, Phys. Rev. B16 (1977) 4239.
Solid State Communications 117 (2001) 361±364
www.elsevier.com/locate/ssc
Temperature dependence of the Raman spectra of 1T-TaS2 T. Hirata a,*, F.S. Ohuchi b b
a National Research Institute for Metals, 1-2-1 Sengen, Tsukuba, Ibraki 305-0047, Japan Department of Materials and Engineering, University of Washington, Box 352120, Seattle, WA 98195-2120, USA
Received 18 August 2000; received in revised form 30 October 2000; accepted 30 October 2000 by F.J. DiSalvo
Abstract The temperature dependence of the unpolarized Raman spectra from 1T-TaS2 has been measured between 297 K and 48 K. The present work demonstrates that the three Raman modes observed above 220 cm 21 (high frequency region) at room temperature exhibit remarkable frequency changes toward low wavenumbers in the vicinity of 200 K, where 1T-TaS2 undergoes a ®rst-order transition of the charge density wave (CDW) from nearly commensurate to a commensurate state. The monotonic line-broadening and intensity reduction with temperature has been identi®ed for these Raman modes. In contrast, the behavior observed in the low frequency region (less than 200 cm 21), suggested that the soft phonons are less likely to be involved in the temperature dependence of the high frequency Raman modes. q 2001 Elsevier Science Ltd. All rights reserved. Keywords: D. Phase transitions; D. Phonons PACS: 63.20.2e; 64.60.2i; 78.30.2j
A transition metal dichalcogenide compound, 1T-TaS2, exhibits a strong charge density wave (CDW) instability [1], which is characterized by two ®rst-order transitions of incommensurate to nearly commensurate and nearly commensurate to commensurate states that are observed at 350 K and 200 K, respectively. At these temperatures, discontinuous changes in the electrical resistivity, magnetic susceptibility and re¯ectivity were observed [2±4]. The CDW instabilities and the effects of cation doping in the transition metal chalcogenides have been studied extensively by electron, X-ray and neutron diffraction techniques, as well as infrared re¯ectivity and Raman scattering [4±16]. Several Raman studies on 1T-TaS2 have shown that there are two Raman Ag modes observed at 81 and 114 cm 21. These low frequency modes behave like soft phonons, and exhibit their frequency shift toward the lower wavenumbers in the vicinity of T 200 K [11,12], as the temperature is raised from a low temperature. The temperature-dependent frequency (v ) of the 82 cm 21 Raman mode, for example, ÿ can be ®tted to a form of v a T0 2 T 0:5 , where a is a constant and T0 is approximately 1040 K is a transition temperature for the soft phonon mode [10]. * Corresponding author. Tel.: 181-298-59-2734; fax: 181-29859-2701. E-mail address: [email protected] (T. Hirata).
There are additional Raman lines present in the 1T-TaS2 Raman spectra when the commensurate CDW state is reached at 200 K. They are explained as the increase in the number of zone center (G -point) phonon modes due to folding of the original Brillouin zone by the formation of a commensurate superlattice [9,11]. These spectral changes are found in the low and/or high frequency region, but no particular attention has been paid to subtle changes in the high frequency region of the Raman spectra from 1T-TaS2, when 1T-TaS2 undergoes the transition from the nearly commensurate to commensurate state at 200 K [11,12]. The present paper reports a new ®nding relating to the spectral changes in the high frequency region (above 2230 cm 21) when the transition from the nearly commensurate to commensurate state takes place in 1T-TaS2. Single crystals of 1T-TaS2 were grown by an iodine vapor transport technique, details of which are given elsewhere [2]. Unpolarized Raman spectra of 1T-TaS2 were collected from 1T-TaS2 at different temperatures ranging from 297 K to 48 K using a Dilor XY spectrometer. Sample temperature was measured by a Au (Fe)-KP thermocouple, and controlled with an accuracy of ^1 K. A 514.5 nm line from the Ar 1 laser was used as the radiation source. Incident laser power was limited to 10 mW in order to minimize a possibility of sample heating. All the Raman spectra from 1T-TaS2 were collected in a backscattering con®guration. A
0038-1098/01/$ - see front matter q 2001 Elsevier Science Ltd. All rights reserved. PII: S 0038-109 8(00)00468-3
362
T. Hirata, F.S. Ohuchi / Solid State Communications 117 (2001) 361±364
Fig. 1. The unpolarized Raman spectra of lT-TaS2 measured at different temperatures between 297K and 48K.
curve ®tting program GRAMS/32 (Galactic Ltd.) was used for analysis. Shown in Fig. 1 is a set of unpolarized Raman spectra measured from 1T-TaS2 at different temperatures from 297 K to 48 K. Whole features of the Raman spectra at
Fig. 2. A deconvolution of the Raman spectrum of 1T-TaS2 at 48 K; X: experimental data; Ð: composed; ´´´: resolved lines with numbers.
each temperature were in good agreement with the results previously reported [7,9,11,12]. There are four observed at approximately 100, 243, 306 and 381 cm 21 in the nearly commensurate CDW state at 297 K. As the temperature is decreased, these peaks are intensi®ed, and split into several well-de®ned peaks. Previous studies [7,9,11,12] from 1TTaS2 have shown that the Raman modes below 100 cm 21 become intense signi®cantly while other modes appear when the nearly commensurate±commensurate transition takes place at T 200 K. Additional lines that appeared in the commensurate CDW state are due to folding of the G -point modes from originalp non-zero wave vector points in a thep p 13a 0 £ 13a0 £ 13c0 superlattice formed at 200 K [9,11]. The structure of this superlattice is triclinic belonging to space group Ci1 with 13 formula units per unit cell, totalling 39 atoms. Hence, 114 optical phonon modes are expected, in which 57 are Raman active and the rest are infrared active [9,11]. The modes above 220 cm 21 are derived from the optical phonon branches, in which the sulfur atoms are involved in the atomic vibrations, whereas the modes observed below 100 cm 21 are from acoustical phonon branches in which the tantalum atoms take part in the vibrations. To bring out any spectral changes while cooling, each spectrum was deconvoluted into several peaks using a Gaussian line ®tting. Shown in Fig. 2 is the spectrum obtained at 48 K, in which the results from peak deconvolution are superposed. The deconvoluted peaks were then numbered as shown in Fig. 2, and compared with published data [9,12] (Table 1). While the constituent phonon modes resolved at 48 K in the present study are at least consistent with those observed previously, careful examination of each spectrum would reveal that three Raman modes observed at 243, 306 and 381 cm 21 at 297 K undergo systematic changes in frequency, linewidth and intensity as the temperature decreases. The frequencies of these modes are therefore plotted as a function of temperature in Fig. 3. Here, peaks 5, 8 and 11 were used to represent the changes. Note that the temperature dependences of the modes' frequencies are somewhat different. The 381 cm 21 mode represents the most traditional temperature dependence associated with a phase transition, exhibiting a tremendous frequency change in the vicinity of T 200 K, at which the nearly commensurate to commensurate transition occurs; besides, it appears that the frequency change of this mode with temperature is characteristic of a second-order rather than ®rst-order transition. In contrast, the 306 cm 21 and 243 cm 21 modes show no obvious anomaly near 200 K, whilst the former reveals a unique stiffening below 100 K and the latter stiffens ordinarily with cooling. An attempt was madeÿ to ®t the frequency data of these peaks to a form of v a T0 2 T b . However, no proper ®tting could be achieved with reasonable values of T0 and/or b , even for peak 11 that shows the most typical frequency change with
T. Hirata, F.S. Ohuchi / Solid State Communications 117 (2001) 361±364
363
Table 1 The frequency and intensity of each constituent line obtained by resolving the Raman spectrum of 1T-TaS2 at 48 K as shown in Fig. 2, as compared with available frequency data of 1T-TaS2 [9,12] Peak No.
Frequency (cm 21)
Intensity a
Ref. [9] (121K)
Ref. [12] (24K)
1 2 3 4 5 6 7 8 9 10 11
101 115 130 231 246 266 286 309 329 368 390
vs s s w s w m s w w s
56 62 68 72 80 89 100 106 115 121 129 134 229 243 266 282 300 306 322 329 366 390
62 67 81 100 114 128 229 234 255 262 275 282 286 300 306 324 334 368 390
a
vs: very strong; s: strong; m: medium; w: weak; vw: very weak.
temperature. However, the 82 cm 21 mode that appears below 200 K in 1T-TaS2 can be ®tted to the above functional form [10]. The 81 cm 21 and 114 cm 21 modes would appear below 200 K in 1T-TaS2 and behave like the soft phonons [11,12]. When we compare the temperature dependences of these two modes with those of the high frequency modes as shown in Fig. 3, we notice that there are some dissimilarities between them. Thus, the present work indicates that the high frequency modes in the spectra of 1T-TaS2 do not behave as the soft phonons. However, there exist some remarkable frequency changes with temperature for the high frequency modes.
This is largely contrasted with the previous works [11,12] where no such changes were identi®ed. As for the changes in linewidth and relative intensity of the Raman peaks observed at the high frequency region, no unusual behavior was observed. In Fig. 4, the changes in the linewidth and the relative intensity for the Raman peaks 5, 8 and 11 are plotted as a function of temperature. Each peak is monotonously sharpened and intensi®ed as the temperature decreases. Such monotonous line-broadening and intensity reduction with temperature have been observed for the 82 cm 21 Ag Raman mode of 2H-TaSe2, which also exhibits the CDW instability [17].
Fig. 3. The frequencies of the three Raman modes at 243 cm 21, 306 cm 21 and 381 cm 21 (at 297 K) observed in the Raman spectra of 1T-TaS2 are plotted as a function of temperature. Note that the lines are only a visual guide, and each curve is numbered corresponding to one of the resolved Raman lines as shown in Fig. 2.
364
T. Hirata, F.S. Ohuchi / Solid State Communications 117 (2001) 361±364
for Promotion of Materials Science and Technology of Japan) for variable-temperature Raman scattering.
References
Fig. 4. Changes in linewidth (a) and relative intensity (b) of the three Raman modes at 243 cm 21, 306 cm 21 and 381 cm 21 (at 297 K) as a function of temperature. Each number attached on the curve represents a resolved line of the Raman spectrum of 1T-TaS2 at 48 K as shown in Fig. 2.
This short communication presents new ®ndings about the temperature dependence of the unpolarized spectra of 1T-TaS2 measured in the range between 297 K and 48 K. It is highlighted that the three Raman modes observed above 220 cm 21 exhibit remarkable frequency changes toward the low wavenumbers in the vicinity of T 200 K, where 1T-TaS2 undergoes a ®rst-order transition from a nearly commensurate to a commensurate CDW state. A monotonic line broadening and an intensity reduction with temperature was found for these Raman modes. In contrast, the behavior observed in the low frequency region (less than 200 cm 21), suggested that the soft phonons are less likely to be involved in the temperature dependence of the high frequency Raman modes. Acknowledgements We would like to thank F. Fujishima of MST (Foundation
[1] N. Nagaosa, E. Hanamura, Phys. Rev. B29 (1984) 2060. [2] A.H. Thompson, F.R. Gamble, J.F. Revelli, Sol. Stat. Commun. 9 (1971) 981. [3] F.J. Di Salvo, J.E. Graebner, Sol. Stat. Commun. 23 (1977) 825. [4] P. Fazekas, E. Tosatti, Phil. Mag. B39 (1979) 229. [5] F.J. Di Salvo, J.A. Wilson, B.G. Bagley, J.V. Waszczak, Phys. Rev. B12 (1975) 2220. [6] G. Lucovsky, W.Y. Liang, R.M. White, K.R. Pisharody, Sol. Stat. Commun. 19 (1976) 303. [7] J.E. Smith Jr, J.C. Tsang, M.W. Shafer, Sol. Stat. Commun. 19 (1976) 283. [8] A.S. Barker Jr, J.A. Ditzenberger, F.J. Di Salvo, Phys. Rev. B12 (1975) 2049. [9] J.R. Duffey, R.D. Kirby, R.V. Coleman, Sol. Stat. Commun. 20 (1976) 617. [10] G.A. Sai-Halasz, P.B. Perry, Sol. Stat. Commun. 21 (1977) 995. [11] S. Uchida, S. Sugai, Physica 105B (1981) 393. [12] S. Sugai, K. Murase, S. Uchida, S. Tanaka, Physica 105B (1981) 405. [13] C.B. Scruby, P.M. Williams, G.S. Parry, Phil. Mag. 31 (1975) 255. [14] D.E. Moncton, J.D. Axe, F.J. Di Salvo, Phys. Rev. Lett. 34 (1975) 734. [15] D.R. Karecki, B.P. Clayman, Sol. Stat. Commun. 19 (1976) 479. [16] D.R. Kurecki, B.P. Clayman, Phys. Rev. B19 (1979) 6367. [17] J.C. Tsang, J.E. Smith Jr, M.W. Shafer, S.F. Meyer, Phys. Rev. B16 (1977) 4239.