Probing thermodynamic fluctuations in high temperature superconductors

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0038-1098/88 $3.00 + .00 Pergamon Press plc

Solid State Communications, Vol.66,No.4, pp.421-425, 1988. Printed in Great Britain.

PROBING

THERMODYNAMIC FLUCTUATIONS SUPERCONDUCTORS

Felix Vidal,

J.A.

Veira,

IN

J. Maza,

HIGH

TEMPERATURE

F. Miguelez.

L a b o r a t o r i o de F1sica de M a t e r i a l e s . F a c u l t a d de Flsica. U n i v e r s i d a d de Santiago de Compostela, Spain. E. Moran Departamento Universidad

and M.A.

Alario.

de Qulmica Inorganica. F a c u l t a d de Qulmica. C o m p l u t e n s e de Madrid, 28040 Madrid, Spain.

(Received

29,

D e c e m b er

1987 by E.F.Bertaut)

We probe thermodynamic fluctuations in HTSC by m e a s u r i n g the excess e l e c t r i c a l conductivity, ~a , above T c in single-phase (within 4%) Ba2LnCu307_ 6 compounds, with Ln=Y, Ho and Sm. As expected, the m e a s u r e d relative effect, Aa / a (300 K), is much more important in HTSC than for low-temperature superconductors (at least one order of magnitude). In the r e d u c e d t e m p e r a t u r e region -5< In¢ In[ (T-Tc)/T c ] <-2, ~a may be written as ~a/c(300 K) = A¢ x, where A is a t e m p e r a t u r e - i n d e p e n d e n t amplitude, x is found to be similar for all compounds, with average value =-0.47 ±0.06. This result confirms an universal c r i t i c a l behaviour of A~ in HTSC, and the value of agrees with that p r e d i c t e d by the A s l a m a z o v - L a r k i n (AL) theory for t h r e e - d i m e n s i o n a l BCS s u p e r c o n d u c t i v i t y . However, A shows a normal c o n d u c t i v i t y d e p e n d e n c e which is not a c c o u n t e d for by the AL theory.

There are several reasons for studying thermodynamic fluctuations in "high-temperature" superconductors (HTSC) : i) Thermodynamic fluctuations are e x p e c t e d to play an a p p r e c i a b l ~ role in superconductors if kB~>~n~(T) , where Fsn is the free energy density difference b e t w e e n the normal and the superconducting states, ~(T) is the s u p e r c o n d u c t i n g order p a r a m e t e r correlation length and k B is the Boltzmann constant. 1-5 T c and ~(0) for HTSC are t y p i c a l l y of the order of, respectively, 10 and 10-2times those for "low-temperature" c o n v e n t i o n a l s u p e r c o n d u c t o r s . ~,7 So, one may expect a much more important role of f l u c t u a t i o n s in HTSC, and their effects will be d e t e c t a b l e at much more easily a c c e s s i b l e temperatures, than in conventional superconductors, ii) Therm o d y n a m i c f l u c t u a t i o n s will affect most of the static and dynamic p r o p e r t i e s of s u p e r c o n d u c t o r s a r o u n d T c .1-5 However , as the normal e l e c t r i c a l c o n d u c t i v i t y of HTSC above T c is small, the relative excess c o n d u c t i v i t y due to f l u c t u a t i o n s will be v e r y i m p o r t a n t for these materials. So, in HTSC it s h o u l d be p o s s i b l e to probe f l u c t u a t i o n s by studying an e a s i l y a c c e s s i b l e m a g n i t u d e as it is the

e l e c t r i c a l resistivity, p(T), above T ciii) From a t h e o r e t i c a l point of view, the influence of f l u c t u a t i o n s on p(T) is now very well e s t a b l i s h e d for c o n v e n t i o nal low-temperature superconductors on the grounds of the BCS theory. In addition, the i n f l u e n c e of the system dimensionality, always very important on fluctuations, is also very well charact e r i z e d in this theory. So, r e s i s t i v i t y measurements of fluctuations in HTSC open an unique p o s s i b i l i t y to probe both the a p p l i c a b i l i t y of BCS s u p e r c o n d u c t i vity and its d i m e n s i o n a l i t y in these materials, iv) Two of the b a s i c ingredients of some of the most p r o m i s i n g new t h e o r e t i c a l d e v e l o p m e n t s of HTSC are the p r e s e n c e of t h e r m o d y n a m i c fluctuations, 9 and r e d u c e d d i m e n s i o n a l i t y . 10 As noted before, both aspects may be, in principle, d i r e c t l y p r o b e d by m e a s u r i n g the excess c o n d u c t i v i t y above T cThe p o s s i b l e p r e s e n c e of f l u c t u a t i o n s effects on p ( T ) in HTSC was already s u g g e s t e d by Bednorz and M u l l e r in their seminal work, II although no detailed a n a l y s e s were then presented. Recently, quantitative m e a s u r e m e n t s of the resist i v i t y b e h a v i o u r above T c in HTSC and an analysis in terms of the Aslamazov421

.422

PROBING THERMODYNAMIC FLUCTUATIONS

Larkin (AL) theory were published by Freitas, Tsuei and Plaskett. 12 They found good quantitative agreement between their e x p e r i m e n t a l results and the t h r e e - d i m e n s i o n a l AL result. However, all their data were o b t a i n e d from the same type of HTSC (Ba2Y Cu 3 0 9 _ ~ , with 6~2). Moreover, all the different samples used by these authors had almost the same e l e c t r i c a l c o n d u c t i v i t y in the normal state (at room temperature), a l t h o u g h it is well known from previous results in " l o w - t e m p e r a t u r e " superconductors t h a t the normal state p r o p e r t i e s play a s u b s t a n t i a l role on fluctuations effects on resistivity. 4,5,8

and may be w r i t t e n

A(3D) = (e2/32 ~)(P~/~ (0)) A(2D)=(e2/16 ~) (PB/d)

changes

characteristic

AT c is the from

Ho

(I)

Sm Ho

(II)

p(lO0

of the samples

interval

for which

Transition

temperature

(K)

K)

p(T)

(2/5)p(Tc).

( n cm)xlO 3

p(300 K) Y

parameters

temperature

(8/5)p(T c) to

Resistivity Sample

;

x=-i/2 x=-i

(3) (4)

Four series of samples were cut from four sintered pellets of nominal composition Ba 2 H ° C u 3 0 7 (I and II), B a 2 Y C u 3 7 0 and Ba2SmCu370 . The pellets were p r e p a r e d by m i x l n g the appropiate amounts of coper nitrate, b a r i u m carbonate and yttrium, s a m a r i u m or holmium oxides (Merk R.A.), following a ceramic method similar to that used by us previously.13,14 The general characteristics of these samples, including their structural, stoichiometric and m a g n e t i c p r o p e r t i e s were p r e s e n t e d else-

where o(T) ~ I/p(T), and ~B(T) is the background (normal) conductivity, i.e. the c o n d u c t i v i t y the sample w o u l d have in the absence of s u p e r c o n d u c t i n g transition. As very often in critical dynamics, p _ ( T ) may be ~estimated by extrapolatin~ to T c the behaviour of p(T) well above T c. In the AL approach, A~(T) is due to s u p e r c o n d u c t i n g e l e c t r o n pairs c r e a t e d by thermal fluctuations

studied.

;

where ~(0) is the amplitude (zerotemperature ) of the superconducting correlation length and d is a characteristic length of the two-dimensional system. It is now well established, both e x p e r i m e n t a l l y (in the "low-temperature" s u p e r c o n d u c t o r s ) and theoretically, that the above results may be strongly affected by Cooper-pairs interaction with normal electrons and by pair breaking mechanisms.4However, Eqs.(1) to (4) a l l o w a basic i n s p e c t i o n of fluctuation effects in HTSC on the grounds of BCS s u p e r c o n d u c t i v i t y .

(i)

I. Some

(2)

where o ° is the normal c o n d u c t i v i t y at room t~mperature (300 K) , A is a temperature-independent amplitude coefficient, ~-(T-Tc)/Tc is the reduced temperature and x is the "critical" exponent. In this model, both A and x strongly depend on the s u p e r c o n d u c t i n g dimensionality. For three (3D) and two (2D) d i m e n s i o n s :

The central magnitude studied in this work is, therefore, the excess electrical conductivity Ao above Tc d e f i n e d by

TABLE

as5

Ao/o~ = Ac x

In this c o m m u n i c a t i o n we present precise m e a s u r e m e n t s of the excess conductivity A~T) above Tc in three different types of well-characterized single-phase (within 4%) HTSC. For one of the compounds, we were able to synthesize two d i f f e r e n t samples of the same Tc (see Table I) but with very different normal conductivities. This allowed us to p e r f o r m an important check of the i n f l u e n c e of the normal state p r o p e r t i e s on Aa.

AoH~(T)-OB(T)

Vol. 66, No. 4

Tc

ATc

9.80

7.00

91.3

1.4

5.10

2.80

92.1

0.9

2.60

1.45

92.6

1.6

1.70

0.85

92.1

1.3

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PROBING THERMODYNAMIC

where. 13-15 Let us i n d i c a t e here, however : i) We have i n t r o d u c e d small diff erenc e s in the final part of the s i n t e r i n g p r o c e s s of the holmium-based samples. In one case (I), the final slow c o o l i n g ( ~ 40 K/hour) in the furnace was performed under 1 atm oxygen, whereas for p e l l e t II the c o o l i n g was performed in air. As a consequence, important d i f f e r e n c e s are o b s e r v e d in sample I and II, both in their m e c h a n i c a l hardness and their e l e c t r i c a l resistivity. The soft p e l l e t may be cut off with a razor blade and the e l e c t r i c a l r e s i s t i v i t y of the samples so o b t a i n e d (I) are about three times higher at room temperature than those o b t a i n e d from the hard pellet (II), which must be cut with a saw. In contrast, the s u p e r c o n d u c t i n g t r a n s i t i o n t e m p e r a t u r e of all samples I and II are very similar (Table I). ii) x-ray powder diffraction p a t t e r n s indicate, in all cases, an o r t h o r h o m b i c cell, with small d i f f e r e n c e s in lattice p a r a m e t e r s in the two h o l m i u m - b a s e d samples. ~J The structure is indeed the w e l l - k n o w n "oxygendeficient" triple-layered perovskite~ v and all samples are s i n g l e - p h a s e (within 4 %). Electrical ac and dc resistivity m e a s u r e m e n t s were made with a four-probe method, by using c o a x i a l leads m o u n t e d in such a way as to m i n i m i z e inductive p i c k u p in the ac case. Parallelepipedic s h a p e d samples (typical d i m e n s i o n s 6 x 2 x 1 mm J ) were cut from the sintered pellets. To minimize the electrical lead-sample resistance, contacts were made by p r e s s i n g copper leads suitably s h a p e d and then using also silver paste. In this way, the lead c o n t a c t s resistance was of the order of 5 n or less. we used in these m e a s u r e m e n t s current d e n s i t i e s about 1 A / c m 2 (less than 30 m A through the sample) and our dc measureme n t system was able to detect changes of r e s i s t i v i t y of 1 part in 104 . However, due to the u n c e r t a i n t y in the voltage c o n t a c t s s e p a r a t i o n and sample geometry, the absolute resistivity error is of the order of 10%. Special care was taken to control the sample temperature s t a b i l i t y and homogeneity, and r e l a t i v e t e m p e r a t u r e v a r i a t i o n s were resolved to better than 3 0 mK using c a l i b r a t e d Pt-100 sensors. A b s o l u t e temperatures around T c are measured to b e t t e r than 0.I K. A typical example of temperature dependence of dc e l e c t r i c a l r e s i s t i v i t y is shown in Fig.l. Very often, Tc is defined as the t e m p e r a t u r e for which ~T) is 1/2 of the normal r e s i s t i v i t y "near" the transition. As such a definition may i n t r o d u c e here some ambiguity, in this work T_ is d e f i n e d as the temp e r a t u r e at w h i c h 0(T) has its i n f l e x i o n point, as can be seen in the inset in Fig.l. In any case, we must stress that these definitions give Tc'S differing

12

10 0

423

FLUCTUATIONS I

i

i

i

i

Ba2Y Cu307_~

8

x

o

!

' ;oi..2-t

I

o~-~, o,11 o14

4

v o_

2

0~

50

,

100

150

200

250

,

300

T (K)

Fig.l. A typical e x a m p l e of t e m p e r a t u r e d e p e n d e n c e of the dc c o n d u c t i v i t y in one of the samples s t u d i e d in this work. The solid line is the background normal resistivity obtained as explained in text. In the inset the c h a r a c t e r i z a t i o n of T c is shown.

in less than 0.2%. Also, we have checked the influence of the possible uncertainty in T_ : An error as big as 0.5 K in T c woul~ hav~ no appreciable effects on the e x t r a c t i o n of ~a(T) for ¢> 5 x l ~ 3 . As can be seen in Fig.l, 0(T) shows a linear temperature dependence from at least 2T_ to room temperature. All samples s t u d i e d here had similar behaviour. So, we may suppose that the deviations from metalic behaviour observed at lower t e m p e r a t u r e s are due to critical phenomena associated with the presence of the superconducting transition. In other words, the experimental c r i t i c a l excess c o n d u c t i v i t y is defined as the d i f f e r e n c e between the measured resistivity and the b a c k g r o u n d one, this last b e i n g the resistivity linearly extrapolated from the data above 2Tc (the s t r a i g h t line in Fig.l). The measured excess conductivity for two of our samples is p r e s e n t e d in Fig.2 where, to f a c i l i t a t e the comparison with the AL theory and with p r e v i o u s results in HTSC and in l o w - t e m p e r a t u r e s u p e r c o n d u c t o r s , we p l o t t e d in(ao/0~) as a f u n c t i o n of inc. The general b e h a v i o u r of the data in this figure is very similar to that o b s e r v e d in 3D lowtemperature superconductors, although the excess c o n d u c t i v i t y a m p l i t u d e is, as expected (see c o m m e n t s in the introduction), much more i m p o r t a n t for all our HTSC compounds, even when compared with data obtained in very dirty amorphous s u p e r c o n d u c t o r s (an order of m a g n i t u d e bigger). I n the r e d u c e d temperature range -5
424

PROBING '

I

'

I

'

I

I

THERMODYNAMIC

Vol. 66, No. 4

FLUCTUATIONS \ I

I

\ \\\/~(30)

12 30 AL SlopQ N

o

B

>"

I -0, 6

"L o

-0.4

X^L(3D) x .(

0

b <~

4

-0. 2

x w LJ }-

-2

I

200

I

-5

,

I

-4

J

I 600

o o

,

I 400

O'~(.Qc,51

Be 2Ln Cu 307_6 -6

Q ---6

,

I

-a

II

Ho

,

I

-2

o-

,

I

-i

L n [(T-Tc)/Tc]

Fig.2. L o g a r i t h m of the n o r m a l i z e d (to ~B at 300 K) excess c o n d u c t i v i t y as a function of the l o g a r i t h m of the reduced temperature. The solid lines were obtained by fitting the data in the range -5
above i n d i c a t e d t e m p e r a t u r e range) the data for each sample to Eq.(2), but leaving both A and x as free parameters. The dashed line in this figure just give the slope c o r r e s p o n d i n g to the AL theory for 3D (x=-i/2) s u p e r c o n d u c t i v i t y (the ordenates are arbitrary). The agreement b e t w e e n this p r e d i c t e d slope and the o b s e r v e d one in the above indic ated temperature range is excellent. This result for x was already found by Freitas and coworkers for Y-based compounds. Finally, and although not plotted in that figure, we must note here that close to T c (for in~<-5) we observe for all samples studied an increase of the slope of ao/a~ which could indicate a change of ~ r i t i c a l region. In Fig.3 we represent the excess c o n d u c t i v i t y amplitude A (full circles) and the c r i t i c a l exponent x (open circles) o b t a i n e d as e x p l a i n e d for each of the four c o m p o u n d s studied as a function of their normal conductivity. The experimental uncertainties (due, in particular to the treatment of the b a c k g r o u n d resistivity, ~ ) are for both A and x less than 15%. The dashed line c o r r e s p o n d s to A from Eq.(3) (with ~(0)=20 A) and the solid line to x=-i/2. A first important result is that, w i t h i n the e x p e r i m e n t a l uncertainties, the cri-

Fig.3. Measured excess conductivity amplitude A (solid circles and critical exponent x (open circles) as functions of the normal conductivity at room temperature (300 K) for the four compounds studied. The solid line is x = ~ / 2 and the dashed line is A p r e d i c t e d by the 3D-AL theory. tical exponent is found to be similar for all the d i f f e r e n t samples of our four d i f f e r e n t compounds. The average critical e x p o n e n t is =-0.47 ± 0.06, in e x c e l l e n t agreement with that predicted by the 3D AL theory (x=-i/2). It is also clear from Fig.3 that the observed normal conductivity d e p e n d e n c e of the excess c o n d u c t i v i t y amplitude, A, strongly differs from that p r e d i c t e d by the AL theory (dashed line). (Notice that the amplitude coefficient measured and predicted does not differ very much at about 600 ( n cm)-~ which are precisely the normal c o n d u c t i v i t y of the samples used by Freitas et el. 12 ). A further c o n f i r m a t i o n of this d i s a g r e e m e n t for A is p r o v i d e d by the two H o - b a s e d samples. From c o n v e n t i o n a l BCS t h e o r y for dirty superconductors, the relation between the a m p l i t u d e c o r r e l a t i o n length in both samples (I and II) is e x p e c t e d to be ~(0)/ ~(0)=[a~T/O~IT]I~ When combined with E~.(3), %he ~ i s a g r e e m e n t for A between theory and experiments still worsens. These d i f f e r e n c e s for A in the more resistive samples may perhaps be due to p a i r - b r e a k i n g mechanisms, as in the case of low-temperature superconductors, which are not included in the AL theory. Inspection of these effects is now under way. We must also note here that these results are not affected by c h a n g i n g as much as 50% the electrical current density. A l t h o u g h we are now preparing new experimental tests, these results seem to indicate no important influence of percolative or inhomogeneity effects on the measured excess conductivity. M o r e o v e r , t h e strong a n i s o t r o p y of these H T S ~ 8 c ~ p o u n d s , now very well e s t a b l i s h e d , ' may have an influence not only on A but also on x. However, the measured interplanar

Vol. 66, No. 4

PROBING THERMODYNAMIC FLUCTUATIONS

c o h e r e n c e length ~II is of the order of 7 ~ (Ref. 18) or 8 A (Ref. 19), whereas the Cu-O layer spacing is of the order of 4 ~ or less. So, we believe that s u p e r c o n d u c t i v i t y in the HTSC c o m p o u n d s studied in the present work is essentially 3D. In summary, our e x p e r i m e n t a l results confirm that the o b s e r v e d excess electrical c o n d u c t i v i t y aa above T in HTSC is p r o b a b l y due to thermal fluctuations. In particular, our results strongly suggest that up to in ¢ > -5 the reduced temperature critical ~exponent x is universal and its average value = -0.47 ± 0.06 agrees very well with the prediction of A s l a m a z o v - L a r k i n theory based on BCS s u p e r c o n d u c t i v i t y in three dimensions. However our results indicate, for the first time, that for HTSC the excess c o n d u c t i v i t y amplitude

425

highly depends on the normal conductivity. This o b s e r v e d b e h a v i o u r is not accounted for by the AL theory. More e x p e r i m e n t a l work is needed, specially to clear up the role of the system intrinsic anisotropy, inhomogeneities, percolative effects and p a i r - b r e a k i n g effects. We w o u l d like to thank P r o f e s s o r J. Sordo, for his support at the time he was Vicerrector of Research of the U n i v e r s i t y of Santiago de C o m p o s t e l a and also to acknowledge expert and i n d i s p e n s a b l e technical a s s i s t a n c e from J. Ponte. Even though this work was not e x p l i c i t l y s u p p o r t e d by CAICYT, we have used financial support from the project PR 84-620. We a c k n o w l e d g e useful remarks of P r o f e s s o r E.F. Bertaut to the manuscript.

REFERENCES

I. 2.

3.

4.

5.

6.

7.

8.

9.

B.A. Pippard, Proc. Roy. Soc. (London) A203, 210(1950). V.L. Ginzburg, Fiz. Tverd. Tela, 2, 2031(1960) [English transl. Soviet. Phys. Solid State, 2, 1824(1960)]. For a very nice i n t r o d u c t o r y r e v i e w of early d e v e l o p m e n t s of fluctuations in s u p e r c o n d u c t o r s see, P.C. Hohenberg, in F l u c t u a t i o n s in Superconductors, Edited by W.S. Gore and F. Chilton, S t a n f o r d R e s e a r s c h Inst., Menlo Park, Ca. (1968). p.305. For an i n t r o d u c t o r y r e v i e w of more recents d e v e l o p m e n t s of fluctuations near s u p e r c o n d u c t i n g phase transitions see, M. Tinkham, I n t r o d u c t i o n t_~o s u p e r c o n d u c t i v i t y (Mc Graw-Hill, New York, 1975) chap.7; see also, W.J. Skocpol and M. Tinkham, Rep. Prog. Phys. 38, 1049(1975). L.G. Aslamazov and A.I. Larkin, Phys. Lett. 26A, 238(1968); Fiz. Tverd. Tela i0, 1104(1968) [Engl. trans. Sov. Phys. Solid St. 10, 875(1968)]. R.J. Cava, B. Batlogg, R.B. van Dover, D.W. Murphy, S. Sunshine, T. Siegrist, J.R. Remika, E.A. Rietman, S. Zahurak and G.P. Espinosa, Phys. Rev. Lett. 56, 1676(1987); see also M . B . S a l o m o n and J. Bardeen, Phys. Rev. Lett.59, 2615(1987); B. BatIogg,R.J. Cava and R.B. van Dover, Phys. Rev. Lett. 59, 2616(1987). U. Gottwick, R. Held, G. Sparn, F. Steglich, H. Rietschel, D. Ewert, B. Renker, W. Bouhofer, S. von Molnar, M. W i l h e l m and H.E. Hoenig, Europhys. Lett. 4, 1183(1987). See, for instance, W.L. Johnson, C.C. Tsuei and P. Choudhari, Phys. Rev. 17, 2884(1978) and references herein. See, for instance, P.W. Anderson, Science 235, 1196(1987); P.W. Ander-

i0.

ii. 12. 13.

14.

15.

16.

17. 18. 19

son, G. Baskaran, Z. Zon and T. Hsu. Phys. Rev. Lett. 58, 2790(1987). J. Labbe and J. Bok, Europhysics Letters, 3, 1225(1987), J. Bok and J. Labbe, C.R.Ac. Sc. (Paris), to appear. J.G. Bednorz and K.A. Muller, Z. Phys. B6_4, 189(1986). P.P. Freitas, C.C. Tsuei and T.S. Plaskett, Phys. Rev. B36, 833(1987). F. Garcia Alvarado, E. Moran, M. Vallet, J.M. Gonzalez Calvet, M.A. Alario, M.T. P e r e z - M i c h e l and M.C. Asensio, Sol.St.Comm. 63, 507(1987). M.A. Alario, E. Moran, R. SaenzPuche, F. Garcia Alvarado, V. Amador, B. Barahona, F. Fernandez, M.T. P e r e z - F r l a s and J.L. Vicent, Materials Research Bulletin (to appear). J.A. Veira, G. Domarco, C. Torron, F. Miguelez, J. Maza, F.Vidal, F. Garcia Alvarado, E.Moran, M. Vallet, J.M. Gonzalez Calbet, R. Saenz Puche and M.A. Alario, in P r o c e e d i n g o f the European Workshop on High T Superconductors and Potential Applications, Genova, Italy (1987), p.407; J.A. Veira, J. Maza, F. Miguelez, J.J. Ponte, C. Torron, F. Vidal, F. Garcia-Alvarado, E. Moran and M. A. Alario, J. Phys. D: Appl. Phys. 21, 378(1988). R.J. Cava, R.B. van Dover, B. Batlogg, and E.A. Rietman, Phys. Rev. Lett. 58, 408(1987). R.A. Croven, G.A. Thomas and R.D. Parks, Phys. Rev. B4, 2185(1973). T. K. W o r t h i n g t o n 7 W.J. Gallagher and T.R. Dinger, Phys. Rev. Lett. 59, 10(1987). ~. No~l, P. Gougeon, Y Padiu, Y.C. Levet, M. Potel, O. Laborde and P. Monceau, Sol. St. Comm. 63, 915 (1987).