Broadband noise in blue bronze K0.3MoO3

Physica 143B (1986) 108-110 North-Holland, Amsterdam

108

BROADBAND NOISE IN BLUE BRONZE KO.3HoO 3

A. MAEDA, Department

T. FURUYAMA,

K. UCHINOKURA and S. TANAKA

of Applied Physics,

The University

of Tokyo, Hongo, Bunkyo-ku,

Tokyo

113, Japan

L o w - f r e q u e n c y b r o a d b a n d noise was m e a s u r e d in the f r e q u e n c y range between 10 -3 Hz and I MHz in K 0 3Mo03. It was found that the measured noise spectrum cannot be represented only by a simple po~er law, and it is rather rugged. From this result, the energy and its distribution associated with the t r a n s i t i o n among the m e t a s t a b l e states of the c h a r g e - d e n s i t y w a v e in Ko.3MoO 3 were deduced.

Potassium molybdenum oxide K 0 3Mo03 is one of the quasi-one-dimensional c o m p o ~ h d s w h i c h show the n o n l i n e a r c o n d u c t i v i t y and the a s s o c i a t e d p h e n o m e n a due to the s l i d i n g m o t i o n of charged e n s i t y w a v e s (CDW's). I C o m p a r e d with the transition-metal trichalcogenides NbSe 3 and TaS3, one of the most characteristic features of the-physical properties associated with the CDW in K M o O is that the u l t r a l o w f r e q u e n c y responds 3 is ~rominent (especially at low temperatures). The slow phenomena are due to the presence of m e t a s t a b l e states f o r m e d by the l o c a l d e f o r m a t i o n of the CDW's i n t e r a c t i n g with rand o m l y d i s t r i b u t e d i m p u r i t i e s in the crystal. A l t h o u g h these kinds of p h e n o m e n a are common among the materials which have quasi-one-dimensional electrical properties and CDW instabilities, the r e a s o n why the s l o w p h e n o m e n a are prominent especially in K n ~MoO~ is not known. The low-frequency broadband ~oise seems also one of the p h e n o m e n a c l o s e l y r e l a t e d to the p r e s e n c e of m e t a s t a b l e states. The d e t a i l e d m e a s u r e m e n t of it, h o w e v e r , has not been performed in this material. Moreover, it is likely that the a b o v e - m e n t i o n e d characteristic aspect of Ko.3MoO 3 appears in the low-frequency noise. In~hispaper we shall report the results of the measurements of the low-frequency broadband noise in K~ oMoOo in the frequency range between 10 -3 Hz an~'~ M~z. It was found that the measured noise s p e c t r u m cannot be r e p r e s e n t e d by a simple power law, and it is rather rugged. From this r e s u l t we can e s t i m a t e the energy and its d i s t r i b u t i o n a s s o c i a t e d with the t r a n s i t i o n among the metastable states. Noise m e a s u r e m e n t s were p e r f o r m e d by three d i f f e r e n t m e t h o d s c o r r e s p o n d i n g to d i f f e r e n t f r e q u e n c y ranges. B e t w e e n 2 Hz and 110 kHz an o r d i n a r y ac v o l t m e t e r m e t h o d was used. In h i g h e r - f r e q u e n c y range up to I MHz, an a n a l o g s p e c t r u m a n a l y z e r was used. B e l o w 2 Hz the t i m e - s e r i e s data was stored in d i g i t a l memory. The power spectrum was o b t a i n e d by the FastF o u r i e r Transform. An o r d i n a r y bridge circuit was used in order to remove the offset voltage.

0378 - 4363/86/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division) and Yamada Science Foundation

First, the current dependence of the noise in K O 3 M o 0 3 is a l m o s t monotonic. The noise power i n c r e a s e d with i n c r e a s i n g current, after the sudden increase at the threshold field. Figure I shows the noise spectrum of a K O 3 M o 0 3 sample b e t w e e n 10 -3 Hz and I MHz at 77 K.'- A n ~ x a m p l e of the t i m e - s e r i e s data is shown in the inset. Roughly speaking, the so-called I/f noise is observed. At about 20 kHz, a hump is o b s e r v e d , which was confirmed to correspond to the narrowban~ noise. Above it the spectrum falls off as I/f . A huge peak is o b s e r v e d a r o u n d 500 Hz. The frequency where the huge peak exists does

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not change for different current values, which means that the hump does not originate from the narrow-band noise. Figure 2 shows the frequency dependence of the noise in the same sample between 2 Hz and 110 kHz at several temperatures. This figure shows that the huge peak is also observed at other temperatures. The measurement of the noise spectrum in various samples shows that the frequency of the huge peak in the noise spectrum depends on the samples. However, such peaks exist in the measured frequency range in all samples. The origin of the peak will be discussed later. With increasing temperature, the frequencyindependent part grows in the lower frequency range of the noise spectrum. Figure 3 shows the noise spectrum of a K 0 3MoO 3 sample measured by the ac voltmeter met~bd above 77 K. Below a frequency fL' the noise power spectral density becomes almost independent of the frequency. The crossover frequency fL increases with increasing temperature. The temperature dependence of fL can be fitted roughly to the thermally activated form fL=fa'exp(a/kBT),

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with fa=6X105 Hz and A=I080 K, as shown in the inset of Fig. It is generally expected that the low-frequency broadband noise is caused by the nonuniform motion of the CDW domains. Recently it was suggested that the threshold fluctuation due to the local interaction of the CDW condensate and the impurities distributed in the crystal is th~ origin of the nonuniformity in the CDW motion. ~ In the context of this model, the voltage fluctuation <6V2(~)> is represented as 6V2(~)=IR(3R/3V)2"E~'(£/A)'VD'e~'S(~,T),

(2)

where I, V, R, A and I are the current, the voltage, the resistance, the cross section and the length of the sample, respectively, E T is the threshold field of nonlinear conduction, V D is the coherent volume of the moving CDW, gt is the relative fluctuation of the threshold field of each segment, and S(~,T) is the spectral density. By the application of the well-known idea of the thermally activated process with the distribution of the activation energy D(E) for S(~,T), 3 the threshold fluctuation model tried to explain the I/f noise in the sliding CDW systems. We have a different idea for the f-a spectrum observed for wide range of parameters in the CDW transport problems rather than the distribution of the activation energy, which is discussed in another paper.4 However, we believe that the

1 10

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rugged feature observed in Ko.3MoO 3 is explained by the thermally activated m d d e l ~ i t h the distribution of the activation energy, and we estimate this distribution of the activation energy from the e x p e r i m e n t a l results, f o l l o w i n g th~ Dutta et al.'s a n a l y s i s in the n o r m a l metals. ~ According to them, with the assumption that the width of D(E) is much larger than kBT , the power spectral density is represented as S(~,T)=(kBT/~)'D(E),

(3)

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where ~ is the a n g u l a r f r e q u e n c y and ~O is the relaxation time in the high t e m p e r a t u r e limit. By c o m b i n i n g eqs. (2) and (3), we obtain

6V2(w)=(kBT/~)I2(~R/3V)2E~(£/A)'(VD'E~'D(~)}.

(5)

U s i n ~ eqs. (4) a n d (5) we h a v e c a l c u l a t e d VD'E~'D(~) as a f u n c t i o n of ~ from the r e s u l t s o f the noise-power measurement for various temperatures and frequencies. Then the four curves in Fig. 2 are unified into a s i n g l e c u r v e as shown in Fig. 4, which reflects the distribution of the a c t i v a t i o n energies. The p a r a m e t e r ~0 was assumed to be 10 - ~ sec, c o n s i d e r i n g the temperature dependence of the crossover frequency as g i v e n in eq. (I). The r e s u l t in Fig. 4 shows that the d i s t r i b u t i o n of the a c t i v a t i o n

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energy has two sharp peaks around EI=30 m@V and E2=60 meV in this sample. Note that the ordinate is in the log scale. The obtained v a l u e of Ei(i=1,2,...) is comparable with the value.estimated from other measurements in K OqMoO~. 6 The large peaks in the noise spectrum ~s no$ found to originate from the peaks in the energy distribution, which is d i f f e r e n t among samples. C o n s i d e r i n g that the b r o a d b a n d noise in monoclinic T ~ 3 and NbSe 3 does not show such rugged features,~-the large-peaks in the energy distribution around 50 meV is c h a r a c t e r i s t i c to K0.3Mo03, and is probably connected to the prominence of the slow phenomena in K0.3MoO 3. It s h o u l d be noted that the energy for th~ formation of solitons is comparable to our E iMoreover, the energy distribution is different among samples. Then, the n o n u n i f o r m i t y in the velocity of the CDW segment in K 0 3Mo03 likely comes from the thermal activation'bf the loca2 d e f o r m a t i o n of the CDW (as soliton), which occurs randomly through the interaction with the impurities. The origin of the metastability in K 0.3 MoO 3 may be a s c r i b e d to the defects of the crystal structural origin. F i n a l l y , we w o u l d comment s h o r t l y on the d y n a m i c a l coherent v o l u m e V D. The fact that four c u r v e s in Fig. 2 are u n i f i e d into a s i n g l e curve means that V D does not change so much in the t e m p e r a t u r e range measured. If we assume Eta0.1 , then we obtain V D > I O - 8 cm 3. So, as in NbSe 3 and TaS3, the motion of the CDW is a l s o cohegent o v e r the m a c r o s c o p i c l e n g t h s c a l e in Ko.3Mo03, in w h i c h the d i s o r d e r e d feature is more prominent. We would like to thank T. Arima and Y. lijima for their collaboration. REFERENCES

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FIGURE 4 The distribution of the activation energy estimated from the broadband-noise measurement shown in Fig. 2. D i f f e r e n t marks r e p r e s e n t the data at d i f f e r e n t temperatures. The s o l i d line is only the guide for the eye.

I. See for instance, Charge Density W a v e s in Solids, eds. Gy. H u t i r a y and J. Solyom, Lecture Notes in Physics, vol. 27 (SpringerVerlag, Berlin, 1985). 2. S. Bhattacharya, J.P. Stokes, M.O. Robbins and R.A. Klemm, Phys. Rev. 54 (1985) 2453. 3. F.K. du Pre, Phys. Rev. 78 (1950) 615. 4. A. Maeda, K. U c h i n o k u r a and S. Tanaka, to be published in Proc. ICSM 1986, Synth. Metals. 5. P. Dutta, P. Dimon and P.M. Horn, Phys. Rev. Lett. 43 (1979) 646. 6. R.J. Cava, R.M. Fleming, P. Littlewood, E.A. Rietman, L.F. S c h n e e m e y e r and R.G. Dunn, Phys. Rev. B30 (1984) 3228. 7. A. Maeda, M. Naito and S. Tanaka, J. Phys. Soc. Jpn. 54 (1985) 1912. 8. G. T r a v a g l i n i and P. Wachter, S o l i d State Commun. 37 (1981) 599 and Phys. Rev. B30

(1984) 1971.