Resistive states in thin films of Y2Ba4Cu8O16−δ

Phystca C 167 (1990) North-Holland

RESISTIVE

348-358

STATES IN THIN FILMS

P. BERGHUIS, Kumerlingh

P.H. KES, B. DAM ‘, G.M. STOLLMAN

Onnes LaboraiorJ:

a Philips Research Laborator?: ’

Katholieke

OF Y2Ba4Cu80,,_G

Leiden

PO Box 80.000,

C’mversrf)~ Ntjmegen.

Recetved 6 December 1989 Revised manuscript received

L’nlversiry.

Toernooiveld.

19 February

a and J. van BENTUM

h

PO Box 9506. 2300 RA Leaden. The ,Yetherland.c

5600 J.4 Eindhoven. 6526 ED Nljmegen.

The h’eihrrland.~ The h’etherlundc

I990

The resistance of a preferentially oriented thin film of Y,Ba,Cu,O,,_, has been measured as a fun&on of temperature and fields up to 20 T oriented parallel to the r-axis. The normal state resistance could bc well fitted by the Bloch-Griineisen theory. Below I-, ( =z80 K) the resistance transitions both in field and temperature could be separated in three regimes. 4 regime where the data can be analysed in terms of a model combining thermally activated flux flow and flux pinning due to dislocation lines. The upper critical field B,,, obtained from this analysis, exhibits an upward curvature at low temperatures, possibly indicating a mixed s-d wave pairing. In the second regime just below Bc2 viscous forces are increasingly important for flux-line motion and the resistance is determined by the flux-flow resistancep,. At fields higher than B,, we find a large contribution ofsuperconducting fluctuations to the conduction.

1. Introduction

The high-temperature oxidic superconductors are characterized by a layered structure of superconducting CuOz planes. This two-dimensional character of the superconductivity is reflected in the properties of the flux-line lattice (FLL) which is brought about by the application of a magnetic field i-I. For instance, for Hllc (perpendicular to the planes) the nonlocal elastic-moduli of the FLL are considerably reduced [ 1 1. The elastic softening favors the development of positional disorder by thermal fluctuations and it has been argued [2,3] that the FLL may melt at temperatures far below the transition line B,,( T). In the presence of pinning centers, however, a very soft FLL can adapt optimally to the random distribution of crystal defects which results in a large critical current density J, at low temperature, and a low energy barrier Cr,, for thermally assisted depinning [4]. Both descriptions lead to non-superconducting behavior in parts of the mixed-state phase diagram. In a novel approach Fisher defined an order parameter analogous to the Edwards-Anderson order parameter for spin-glasses and predicted a real phase transition be0921-4534/90/$03.50 (North-Holland )

0 Elsevier Science Publishers

B.V.

tween a high-temperature liquid FLL and a low-temperature vortex-glass [ 61. FLL melting could not be observed in thin amorphous films [7] well in the regime where it should occur according to theory [ 81. Actually, an onset of a strong peak effect was observed when the local disorder in the FLL induced by collective pinning satisfied the Lindemann criterion [ 9 1. We therefore take the point of view that FLL melting is prevented by flux pinning and that the dissipative behavior should be described in terms of thermal depinning [ IO], or other phase slip processes [ II]. Thermally assisted depinning gives rise to clearly observable effects like “giant” flux creep [ 121 and a constant-field resistivity that follows an Arrhenius law [ 131. Both phenomena are governed by the ratio C’,/kT, so that in principle the height of the activation energy may be determined from creep or resistance measurements. The interpretation of creep experiments is sensitive to a distribution of energy barriers [ 14 1. In addition, the effective barrier height will depend on the flux-density gradient or the current density J [ IO,15 ] which will effect the interpretation of both creep and DC-resistivity experiments. The recently observed [ 161 logarithmic C!(J)

P. Berghuis et al. /Resistive states in thin

behavior is probably a demonstration of the latter effect. We argue that small-amplitude AC-resistivity measurements in zero DC-current trace an average energy barrier if the barrier distribution is flat. Additionally, the small driving-force limit is obeyed, which means that on experimental time scales a uniform motion of the FLL results which was denoted as thermally assisted flux-flow (TAFF) [ 181. Experimentally, uniform FLL motion yields linear IV curves over a range of small current values. However, for large driving forces (or current densities) the flow velocity will be mainly determined by viscous forces on the FLL. This is the viscous-flow (VF) regime in which the resistivity pf follows from the slope of the IV curves; pf is related to the flux-flow viscosity q by the relation pf= B2/q. The theory of flux creep yields for the creep velocity v,, due to a driving force F,=JB [ 17,181 v,,=2u0w exp( - U,/kT)sinh(AW/kT) where v,, is the attempt frequency, w is the distance that a correlated region of the FLL with volume V, [ 41 moves in a thermally activated jump. A W= Fd V,w is the work done to move this volume against the driving force Fd, UP= FPVcrP where F,, is the macroscopic pinning force density and rP is the range of the pinning centers. For overlapping vortices (b=B/ Bcz > 0.2) Kes et al. [ 181 argue that in the amorphous limit (ultimate limit of FLL disorder) w= rPx ao/2 in agreement with Yamafuji et al. [ 19 1. Here ao= 1.075 (&,/B)“* is the FLL spacing. In the TAFF regime sinh( A W/kT) = A W/kT and, since the electric field due to flux creep is given by the Josephson relation E= Bv,,, we obtain pAc=(2u,w2B2VJkT)exp(-UJkT).

(1)

As pointed out independently by Malozemoff et al. [ 201 and Yamafuji et al. [ 191 the appropriate attempt frequency for the motion of a FLL is the one derived by Kramers [ 2 1 ] in the overdamped limit. It can be expressed as v,,=~y/2rcr1, where (I! is proportional to the curvature of UP. It can be identified as the Labusch parameter (Yez F,/r,, [ 19 1. For a sinusoidal pin potential U= U,, [ 1 -cos 2xX/r,] we get ac,=4n2U,Jlfcr~ and after substitution of the parameters in eq. ( 1) we obtain:

films

of YzBalCu80,6_-6

349

With UP= 2 U, the constant c, is of order 2x. The behavior of pf with T and B has recently been reviewed [ 221 and is for conventional superconductors in good agreement with experiment [ 231. A plot of In@,,) versus T-l seems appropriate to determine UP. However, if U, is the pin potential, then it must be a function of temperature and field, generally obeying scaling laws in t( = T/T,) and b( =B/B,,) [24]. In particular, U,CC(1 -b), since the pinning force couples linearly to the average of the Ginzburg-Landau order parameter which itself is proportional to (l-b) [ 251. Thus, Bc2 must be known for a proper analysis of flux-creep or flux-flow data in terms of c$( T, B). Unfortunately, Bc2( T) cannot be accurately determined from resistivity measurements [ 26 1, so we must treat it as a fit parameter. Such a fit procedure can only be attempted if i) the predominant pin mechanism is known and ii) an expression for its UP is available. In case of caxis oriented thin films of YBa2Cu,0, such a procedure has been carried out assuming twin-plane pinning as the predominant pin mechanism [ 27 1. A value for dBc2/dT] Tc = 1.2 T/K resulted, slightly smaller than the magnetically detected value for bulk single crystals of 1.9 T/K [ 28 1. This may be related to the larger purity of the films [ 291, but may also be caused by the approximations that have to be made in the procedures of obtaining Bc2. E.g., theoretical expressions for F, which are strictly valid close to Bc2, were used at much smaller fields, B 5 0.5 Bc2.

In this paper we show that pinning by dislocation lines is the predominant pin mechanism in a c-axis oriented thin film of Y2Ba4Cug0,6 (Y: 248). From the analysis of the pAC( B) curves it follows that the TAFF regime is followed by a VF regime, both below a knee in the p(B) curves. Above the knee the resistivity is still far below the normal state resistivity pn as obtained from a Bloch-Grtineisen fit. It is assumed that in this regime the conductivity is determined by superconducting fluctuations. A preliminary comparison with theory [30,31] shows qualitative agreement.

2. Experimental PAC

=W+W(

-

UplW

.

(2)

A series of amorphous

films were codeposited

on

350

P. Berghuhuls et al. /Resistive States in thrn,films o_fYzBa4C‘usOr6_a

( 100) SrTi03 in an UHV triple e-gun system, using copper, yttrium and BaF, [32] as evaporants. The deposition rates of the individual sources were monitored by three quartz crystals. During deposition the substrate was sprayed by oxygen giving a background oxygen pressure of lo-‘mbar. After deposition the Cu-rich samples were annealed ex situ at 800°C in wet oxygen. X-ray diffraction experiments revealed both Y: 123 and Y: 248 diffraction lines. The resistivity of the mixed phase samples decreased with increasing Y: 248 concentration. For the investigations described in this paper we used the best sample with the lowest resistivity and no observable diffraction lines from the Y : 123 structure. Only Y : 248 OOL lines (demonstrating the preferential orientation of the c-axis) were found. Furthermore, a very high critical current j,= 2.5 x 10” ( 1 -t)A/m2 was measured in zero field. Laser patterning was used to define the dimensions (400x 10 pm’) for the resistance measurements. The film thickness was 250 nm. A four-probe AC technique at frequency of 72 1 Hz was used to detect pAC with a sensitivity of 5 x lo-l3 am. All transitions, determined in magnetic fields up to 7.5 T applied perpendicular to the layer, were measured using current amplitudes ranging between 10 and 500 PA. At small enough currents, typically I< 100 uA, the voltage depends linearly on the current. We only considered data obtained in this linear IV regime. Experiments up to 20 T were carried out at the highfield facility in Nijmegen. In this case the DC resistance was measured using a current of 50 PA. The results coincided with overlapping measurements in Leiden. First reports on the structural and electrical transport properties of the Y: 248 were published by Zandbergen and Thomas [ 33 ] and Kapitulnik [ 34 1. The unit cell consists of two building blocks of Y: 123 with the upper block shifted over (0, b/2, 0) with respect to the lower block. The shift is located between the two adjacent CuO-chain planes. Intergrowth of Y: 123 and Y: 123.5 layers is quite general [ 33,341, but a small volume fraction of this intergrowth cannot be detected by XRD experiments. The structure is not densely twinned, so that pinning by twin boundaries is not considered to be an important mechanism. In the course of this work we considered dislocation-lines and dislocation-loops and

point pins, e.g. oxygen vacancies, as other possibilities of pinning centers. The results (see below) show that the pinning in the Y: 248 is related to the intergrowth in the form of stacking faults [ 331. Stacking faults give rise to dislocation lines and/or dislocation loops. The pin interaction arises from the coupling of the dislocation strain-field to the modulation of the order parameter, either via the larger density of the normal core (AV-effect ) or via the larger elastic moduli in the core (A&effect) [ 351. For the former to be effective it is required that T, depends on pressure. Recently, a large pressure dependence (dTJd,=0.55 K/kbar) has been reported for the Y: 248 [ 361 in support of our assumption of dislocation-line pinning.

3. Pin potential As will be pointed out below one can distinguish between pinning by dislocations and point defects via the field dependence of the pinning force. The elementary interaction f, of a dislocation with the FLLis&3c(GA/A)Hft-‘(l-b)I/,,,H,isthethermodynamic critical field, 5 the Ginzburg-Landau (G-L) coherence length, and Vdefthe defect volume, e.g. line length times bg for dislocation lines, or D2bs for loops. Here D is the diameter of the loop and 6, the Burgers vector. For the 6I’-effect 6A/ AxB,-‘(dB,/dp), with p the pressure. The factor dB,/dp weakly depends on temperature [ 7 1. The pinning strength is defined by W= np fi/2, where n, is the concentration of pinning centers, For dislocation lines in the overlapping vortex limit, W can be written as W=Cb( 1 -h)’ [7] where C depends on the properties of the defects, i.e. concentration. size and coupling to the FLL. Note that for oxygen vacancies [ 37 ] W= Cb3 ( 1 - b)2 which provides a way to discriminate between vacancies and dislocations and to determine which is the predominant pinning center. To derive Up we assumed the theory of collective pinning to be valid, so that U,= ( WVc)“2r,. In addition, we assumed that the amorphous limit of the CP theory was applicable which means that the correlated volume V,ra& Here L, is the correlation length of the FLL in the field direction. Starting from the expression for the tilt modulus cd4 of a layered

P. Berghuis et al. /Resistive

351

States in thin films of YzBa4Cu8016-d

superconductor [ 11, it was shown [ 371 that the relevant tilt modulus in the amorphous limit is given by c44= $

c,,(O)k;& r

(3)

where ~~~(0) = B2/po is the uniform-tilt modulus, kz = ( 1 -b) /A*, 1 the penetration depth, and r= m, / m is the ratio of the effective masses of the Cooper pairs in anisotropic superconductors. Writing down the extra free energy per unit volume related to the elastic deformation and the work done by the pins [51

Af=4c44

($(g’2rp

(4)

0

0

50

100

150

200

250

300

T(K)

Fig. 1. Temperature dependence of the resistance of the YZBa4CuS0,6_6thin film. The solid line represents the fit by the Bloch-Gtineisen theory.

and minimizing with respect to L, we obtain

r3&‘Z(O)ki

“3

r*W

(5)

and Upx0.52(r~a~C4,(0)k~

WIlJ’r3.

(6)

Substitution of the parameters for pinning by dislocations leads to

U,=G(T)

(&2-B) p,,B2/3

.

The temperature dependence of the parameter C, arises from the factor (dB,/dp)2’3rc-4’3, where K is the G-L parameter. It is expected that cdK (1 +At) or (1+At2) with ]A] a constant of order one [7]. The parameter r can be obtained from r= (S,,/S, )* /dT] =,. The subscripts denote wtth S,,,, = bd&,,,l the field orientations with respect to the CuO, layers. An estimate for rfollows from the resistive transitions (see below). Finally, it should be noted that pinning by vacancies or precipitates would give rise . . to an additional factor (B/B,,) *I3 on the right-hand side in eq. (7), which arises from the different form of w.

4. Results and discussion The normal state resistivity of our 248 film is very small: 2 x 10M8Qm at 100 K, see fig. 1. After reduc-

ing the width to 4.5 pm we measured the same p value, demonstrating that the patterning process did not deteriorate the properties at the film edges. We stress that the low resistivity cannot come from free Cu, because of the post anneal in oxygen at 800°C. The p,, ( T) data clearly show a positive curvature setting in below 200 K. As pointed out by Martin et al. [ 381 the Bloch-Griineisen (BG) theory fits the data above a temperature where fluctuation effects are negligible. The drawn line represents p(T) =pO+ C,, ( T/tl*,)*g, ( t?*,/T) fitted to the data between 290 and 1lOK. We obtained po=1.35x10-8Qm, e;- -627K and Cno= 142x 10-8Qm (Martin et al. [38] reported 19>=50OK and po=14.0x10-8Qm for their film) Bedell [ 391 pointed out that Fermiliquid theory would also show a positive curvature. A T2 behavior has been recently reported by Tsuei et al. for Nd CeCuO films [ 401. Here we merely use the computed p,(T) curve to demonstrate that below T,=79.6 K, it lies well above the pAC(T) data measured in fields up to 20 T (fig. 2 (a) ). In fig. 2b the results of p,&B) measurements at various constant temperatures are shown. The corresponding p,, ( T) data are indicated as well. The data in both figures display the following characteristic behavior of both pAc( T) and pAc(B): an exponential increase with T or B below O.OSp,, an almost linear increase up to a knee which eventually turns over into a much slower increase above the knee.

-

different pinning models. .-\ detailed discussion 01. our analysis will be given In an appendix. The final results for the pin cnergq i’,(H) at constant tcmpcraturr are shown in fig. 3. The (~p( 11) data arc compared with the prediction for dislocation pinning eq. ( 7 1 (drawn lines ). Good agrccmcnt is ohtained in the entire temperature and field range. On the other hand no consistent results could be obtained assuming vacancy or precipitate pinning. The pinning parameter C’:,( 7‘) ( = (i/r”“) and the upper critical field H,,( 7‘) were determined and plotted in fig. 4(a) and 4(b). C’i,(T) agrees reasonabl! with the prediction C‘:,f 7’) I ( I +.I/‘). Extrapolating eq. ( 7 ) to IOU temperatures an c\timation for the maxlmum pinning barrier can bc with made using (‘,,(O.O) 2 ~‘,,(O.R=02B,.,) /I,2(0)z40T and (‘;,(0)=llmeV/‘/” ‘. W’c get l’,,( 0, 0 ) z 100 meV. The same approximation used in the case of twin-boundary pinning in 1’: I23 films yields a maximum barrier of 0.3 eV replacing the earlier reported I cV 1271. Bq measuring the resistance transition with thl field parallel to the substrate and perpendicular to the current. B,,,, and from that I’could be estimated. We obtained I’= 40. From this value and the data in

Fig. 2. (a) AC(Bs6T) and DC(B>6T) resistance transitions of YzBa4Cug016_6 as function of temperature m constant fields applied l/c. The symbols refer to B(in Tesla)=O(O). ?( + ). 4(A).6(:).8(0), 12(x). 16(X)and20(H). 7i2(8) values are indicated by solid symbols. The normal state resistance isgiven by the solid line. (b) Field (applied 11~)dependence ofthc transition at constant temperature. AC measurements up to 7.5 T al 7‘(in Kelvin)=73.4( +), 65.7( x), 59.1(O) and 53.3(x ). DC resistance at 7‘(in Kelvin) =62.4( A ). 52.4( 0 ). 43.1 (* ). 35.5 (#) and 25.5( 0). The corresponding normal-state reststances are marked by the same symbols (dashed). The solid symbols give the Bc2( T) values obtained by the TAFF analysis.

I i

4. I. TA FF reginw

We first discuss the exponential regime which we believe is the TAFF regime where p is described by eq. (2). We determined C’JkTfrom the data so that WCcould compare UP( 7; B) with the predictions for

I-lg. 3. The field dependence ol.the pin potential. the pm potential calculated from the p(n) data symbols as m fig. 7( b ). The field dependence of pinning evaluated at corresponding temperatures solid lines.

The plot shoa\ wng the Same dislocation llnr IS shown by rhc

P. Berghuis et al. /Resistive states in thin films of YZBa&u8016_a

o/L’ 0

60

40

20

80

T(K)

bI

0

20

40

60

80

100

T(K) Fig. 4 (a) Temperature dependence of Cd. The triangles and the circles arc obtained from the p(T) and p(B) data, respectively. The solid line r ( 1 +A?) is a guide to the eye only. (b) Phase diagram of YZBa4Cug016_-6. The upper critical field Bc2given by the open and solid circles was obtained from the p( T) and p(B) data, respectively. The triangles, at which Cl,/kT=4, indicate the transition from the TAFF regime to the viscous flow regime (the dashed line is a guide to the eye only). The solid lines represent B,, ( T) for conventional s-wave pairing in the 2D (thin line) and 3D (thick line) case. The short-dashed line represents the prediction for mixed s-d wave pairing (see text). fig. 4(a) the parameter C,( T) may be computed. Although it is well known that Bcz is not reliably determined from p( T), it has been reported by several authors [ 41-431 that the Bc2 anisotropy can be reasonably estimated from resistivity curves measured close to T, and a resistivity criterion p/p, = constant. The agreement with direct determination of the anisotropy from torque measurements becomes better

353

when a 90% criterion is chosen. In our estimate we used a 50% criterion. The result rz 40 lies between the values 29 for Y: 123 [44] and 3000 for Bi:2212 [ 45 1. We think two effects are important in determining the anisotropy, in the first place the distance between the superconducting CuOz planes. This is 0.83nm, l.Onm and 1.2nm for Y: 123, Y:248 and Bi : 22 12, respectively. In the second place it seems reasonable to assume that the extra CuO chain plane facilitates the charge transfer in the c-direction between the CuOz planes. This is supported by the resistivity anisotropy measured in the normal state which is much larger for Bi: 22 12 [ 461 than for Y: 123 [47]. As far as we know the resistance ratio is not measured in Y: 248, but in view of the above considerations we do not expect a much larger anisotropy for Y: 248, because the larger separation is caused by the inclusion of an extra CuO chain plane, which probably reduces the effect of the larger separation. Knowing the parameters of the pin model and r it is now possible to determine the longitudinal dimension L, of the correlated region in the amorphous limit. Taking rp=ao/2 and using for the penetration depth a= 140( 1 -t4)-“2nm as obtained for Y, Ba2Cu307 _-6 [ 48 ] we have calculated L, as given by eq. (5). LJd,, with d,= 1.0 nm the spacing between two CuO, planes in this compound [ 33,34,36], ranges between 20 and 4 being almost temperature independent but decreasing monotonously with increasing field. So, the FLL is indeed highly disordered in the c-direction with a correlation length that only extends over a few unit cells of the crystal lattice. In fig. 4(b) B,,(T) is compared with the theory for conventional s-wave superconductors. Both the three-dimensional [49] (3D) and the 2D theory [ 291 are displayed. The slope of B,, at T, is - 0.33 T/ K which is about a factor 6 smaller [ 281 than has been reported for Y : 123. The smaller value of dBc2/ dT is reasonable, if one takes into consideration the very small pn of our film. Tewordt et al. [29] computed Hc2 as a function of impurity-scattering rate for quasi-2D superconductors with several pairing states. Their predictions are in qualitative agreement with our result. The most remarkable feature of fig. 4 (b) is the upward deviation of Bc2 from both curves for s-wave pairing at low temperatures. Such behavior is predicted by Rieck et al. [ 3 1 ] for mixed s- and

354

P. Berghuis et al. / Kesrsrrvr states rn rh~n,films q/‘Y2BarC‘~i80,n~_,,

d-wave pairing and a quasi-2D tight-binding model for the description of the wave functions [ 501. The data points are in qualitative agreement with the theoretical curves given in fig. 1 of ref. [ 3 11. Case ( 3 ) is reproduced in fig. 4(b). The values of Br2( 7) and T,,(B) (the temperature at which the transition line is intersected in a constant field) are indicated in figs. 2 (a) and 2 (b ) by the solid symbols. A striking coincidence is found with the fields and temperatures at which a kink in the p( T,B) curves is observed. Such a coincidence is not seen in the Y: 123 where the magnetically determined Bcz lies well above the knee in the resistance transition [28]. In that case the resistance curves between the kink and Bc2 could be reasonably described by a flux-flow resistivity model as has been demonstrated by Malozemoff et al. [ 201. In section 4.2 we will show that the present data cannot be interpreted in such a way. According to eq. (7) the pin potential goes to zero when B approaches B,,. In conventional superconductors this only leads to measurable thermally assisted depinning effects very close to the transition field [ 5 1 1. In the high-temperature superconductors the depinning regime is much larger and well-accessible to experiments. In fig. 5, where log(p/p”) has been plotted versus U,/kT, the TAFF regime is characterised by the condition C’JkT> 4 for all fields WC investigated. The data almost coincide on one line, which means that such an Arrhenius plot hardly de-

Fig. 5. Arrhenius plot ofthep( T)/p, data m constant field vs. C;/ kT for all fields measured. The same symbols are used as in fig. 2(b).

pends on the prefactor in eq. (2). Palstra et al. [ 131 observed this behavior for the first time for the TAFF regime of a Bi: 2212 single crystal. In determining the prefactor one has to be aware of the factor ( Bc2- B) in the expression for the pin potential. This factor can be expressed as ( Bc2 - B) = S( B) ( Tc, - 7.) in the temperature range of an experiment. S(B) denotes the slope of the transition line at a field B. Substituting this into eqs. (3 ) and (7 ) we obtain for B> O.?B,,:

Here,f’=pr/pn. and N is an exponent of order one depending on the pin mechanism, e.g. a= i for dislocations. Putting in some reasonable numbers:,f’& 0.1. I,/kTz 10C’(T)/B’Y~ IO-10 S(B) =0.5-l T/K. meV the prefactor of the Arrhenius law ( 8) ranges between 1O”p, and 1OsJy,. a value mentioned in ref. [ 131. More interesting is the field dependence of the exponential factor on the right of eq. (8 ). Considering that S(B)Tcz(B)~Bc2(0) and C’(7-) almost constant, the main factor determining the field dependence is B-“. Such a behavior is indeed found by Palstra et al. [ I 3 1. Another point worth discussing is the temperature dependence of the pin potential according to eq. ( 7 ). LTp(T) for different B with C&( T) and B,,( 7‘) substituted has been plotted in fig. 6. It follows from

Fig. 6. Pin potential for pinning by dislocation lines as functton of temperature in constant fields 11~.The symbols refer to E( in Tesla)=4(A),8(0). 12(x), 16(x),20(n).

P. Berghuis et al. /Resistive states in thin films of Y2Ba+Cus016_a

these graphs that U,,(T) is always increasing with decreasing temperature, as it should when the TAFF behavior is governed by flux pinning. Potentials which are determined from flux-creep measurements, always show a maximum as a function of T [ 521 which can be explained by assuming a distribution of energy barriers [ 141. We argue that resistance measurements cannot probe such a distribution, because they sense the average motion of all flux lines between the voltage contacts. (Note that partial motion of the vortex lattice leads to ua Tfa ce6,with rf the flow stress and ce6 the shear modulus. Since c66a (1 - b)2 this would give a quite different field dependence of pAC). Only magnetization experiments under T, B conditions were p is too small to be measured [ 531 are sufficiently sensitive to investigate flux creep (a simple magnetization set-up can be easily three orders of magnitude more sensitive than an AC-resistance measurement). This kind of flux creep typically is a slow hopping process in that part of the FLL where the energy barrier is of the order kT. In addition, the interpretation of creep experiments depends on the time window of the set up and the sequence in which the experiments are performed. Therefore, at high temperatures, it is impossible to probe the small barriers, because the corresponding relaxation times are too short. In this respect AC-susceptibility experiments are much more appropriate and comparable to resistance measurements. At low temperatures those barriers are observed for which the effective height V,,a (J, -J) is of order kT (depending on the time window via ln( vat) ). If because of the experimental procedure the starting condition for the creep measurements is such that (J,-J) /J, -=x1, than the small barriers will not be observable. Probably, this is the reason for the log-normal distribution observed in this kind of experiment [ 141. 4.2. Viscous flow and fluctuation

regime

The TAFF behavior breaks down below V,IkT= 4. In the preceding section it has been shown that this is related to the proximity of the transition line: T+T,,(B) or B-+BC2(T). For V,/kT=4, eq. (2) leads to pAc=O. lp, Clearly, for smaller V,,/kT, pAC quickly approaches pf, which means that the pinning barriers are entirely overruled by the thermal depin-

355

ning. In fig. 4(b) we draw a line corresponding to the condition V,=4kT. Below this line lies the TAFF regime where pinning still affects the flux flow. Above the line the resistivity is mainly determined by the viscosity of the FLL. Close to the transition line the flux-flow resistivity in the dirty limit is given by [ 221 pf/p,={l+cy(T)(l-b)}-‘zl--(T)(l-b).

(9)

The parameter a! ( T) = B,,p; ’ dp/dB is given in fig. 1 of ref. [ 221. It depends weakly on temperature, ranging between 2 and 4. It also depends on the inelastic scattering time. Equation (9) predicts a linear behavior of pf(B) for B+B,,. This behavior is observed in conventional superconductors, e.g. amorphous Nb3Ge [ 23 1. Although the dirty limit may not be applicable to our Y :248 film, it still seems reasonable to compare eq. (9 ) with the linear behavior observed in fig. 2 (b) for pAC (B) just below the knee. From the slopes and the values of pn and Bc2 ( T) determined from the preceding analysis, we obtained a(T) = 1.3 fO.3 between t=0.3 and 0.9. This result is only a factor two below the theoretical prediction. However, it should be expected that a! ( T) is systematically smaller. The reason is that the experimental pf( B) curves do not go to pn at Bcz, probably because the resistivity is suppressed by superconducting fluctuations in the region above Bc2 (see below). Taking this into account we conclude that the linear behavior below the knee in fig. 2 displays the viscous flow of the FLL. We like to point out that the shape of the p(B) curve in fig. 2(b) above the knee excludes an interpretation in terms of flux flow resistivity. The resistivity above the knee extrapolates to p( B= 0) > 0. In addition, p depends weakly on field: p; ’ dp/ dB= 2 x 1O-* T-‘. However, theory predicts pf to go to zero for low fields according to pf/p,, = 1.1B/B,, (0) [ 221 and on approaching Bc2 an upward curvature of pf( B) occurs until close to Bc2 eq. (9) holds. Both features are in good agreement with experiments on conventional superconductors [ 23 1, but disagree with the behavior we observe in fig. 2(b) above the knee. For fields and temperatures above the knee the resistance still increases staying well below the normal state value following from the Bloch-Grtineisen tit. We think that p
in the normal state. It is well-known that such fluctuations are enhanced in a magnetic field [ 541. The effect of thermally activated depinning below the knee and superconducting fluctuations above the knee leads to the disappearance of the phase transition in a field, as has been argued on general grounds by De Jongh [ 55 1. .A comparison with the theory for the fluctuationcontribution to the conduction in layered superconductors [30,31.54] in a field jJc is only appropriate far above the transition line determined from the TAFF analysis. This is obvious, since the fluctuation theory would give rise toy= 0 and an infinitely large dp/dTor dp/dRat 7,,(B) or&(T). A preliminary analysis of our data at 20 T shows good qualitative agreement with the theory but more data at higher fields and temperatures are needed for a reliable analysis. In summary. we have performed AC-resistivity measurements on a very low-resistivity thin film of Y1Ba4Cu8016_,+ The normal-state resistivity agrees well with a Bloch-Griineisen behavior. In the superconducting state the p( 7: B) data below 2 0. Ip,, have been analysed in terms of a model for thermally assisted flux flow over energy barriers. These pinning barriers are caused by dislocation lines which are related to stacking faults and intergrowth of other phases. Good agreement is observed indicating that I?,,( 7‘) or T,?(R) coincides with the knee in p( 7: 8) curves. Most remarkable is the deviation of Bc2( 7.) from the conventional BCS behavior. possibly indicating a mixed s-d wave pairing mechanism. An analysis of the data below the knee in terms of fluxflow resistivity supports this view. The regime above the knee is supposed to be determined by superconducting fluctuations in a field perpendicular to the superconducting layers. The phase transition at R,, is smeared out.

Appendix

To determine Lb( T. U) we first analysed our/)(B) data using eq. (2). To obtain L;/k7‘the constant L; and the flux-flow resistivity p+-should be known. For /),-//I, we substituted a polynomial in h obtained from a best fit to experimental data of amorphous NbtGe at r=0.6 [23] which agreed well with the existing

theory [ 221. Note, that we actually should know U,: to determine [1((B). So. we first estimated H, from /)(I?,,) =0.5/l, and used an iterative proccdurc to improve the f+(H) values. It turned out that the itcration was not always necessar), because the final rcsuits did not sensitively depend on 11,. So the set of data points is reduced to a set p( 7: H) /pl-( 7: B) which according to eq. (7) has to be compared with the expression 1,/y, = c,,.f( .I-)

(IO)

with ,/‘(.x) =.\-ep ’ and .\-= I ,,/1\7’> I. The value of (‘, should not depend on temperature and field, but will still depend on the actual curvature of I ‘,, (section 1 ). Therefore. (‘, should be a constant somewhere in the range between ~/3 and 2~. In principle. (‘,. R, and (‘:1 can be obtained from a least squares fit to the /I( R)//>,(U) data. However. the shape of the curves only depends weakly on c’,. Therefore. we also used another method in which C,,(B) was computed for several o, values bctwecn rt/2 and 2~. For all (.,‘s the .!‘,,(U) data demonstrated a ver\’ clear upward curvature with decreasing h in accord with the bchavior expected for dislocation pinning (cy. ( 7 ) ). but in disagreement with the linear dependence one should observe for pinning bq point defects. Thercfore. the only mechanism further investigated was pinning by dislocations. Bc2( 7‘) and (‘& ( 7‘) were dctermined by a least squares lit of cq. ( 7 ) to the ( ‘I,( B 1 data. For (‘,< 5 the determined Bc2 tends to a nonlinear temperature dependence close to 7;. and for c,> 5 H,,( 7’) does not extrapolate to zero at 7,. Therefore. we decided that (‘\= 5( -t 1 ) is the optimal value. The corresponding <‘;( 7‘) values arc given in fig. 4( a ) (circles) and in fig. 4(b) the B,,( T) values are represented by the solid circles. The B,,( 7‘) values turn out to coincide nicely with the values obtained from the criterion /I( lj,? ) =0.4/j,, (fig. 2 (b ) ). Further. using (‘,=_5 in cq. ( IO), WC determined I ,,( 7‘) from the p( 7.) data at different fields. Suhsequently, the quantity (‘i,( B,, -B) was plotted versus temperature for each value of B. ht an) temperature 7;, the separation between two C‘:,( BC7- B) curves (c.g. at B, and B2 ) equals C’; ( 7;) ) AR. where AR= B, - B7. The resulting C’:,( 7’) and B,?( I-) values have been plotted in fig. 4(a) and fig. 4( b j. respectively.

P. Berghuis et al. /Resistive

states in thin films of Y2Ba4Cu80,6_a

Acknowledgements We appreciate the experimental assistance of A. van der Slot. P.H. Kes likes to thank K. Bedell and the Los Alamos National Laboratory for their hospitality during the period that part of this manuscript was prepared. This work was partially supported by the stichting voor Fundamenteel Onderzoek der Materie (FOM).

[ 191 K. Yamafuji, T. Fujiyoshi, K. Toko and T. Matsushita, Physica C 159 (1989) 743. [ 201 A.P. Malozemoff, T.K. Worthington, E. Zeldov, N.C. Yeh, M.W. McElfresh and F. Holtzberg, Springer Series in Physics, vol. 89 (Springer, Heidelberg, 1989) p. 349. [211H.A. Kramers, Physica 7 ( 1940) 284. (22 A.I. Larkin and Yu. N. Ovchinnikov, Non Equilibrium Superconductivity (North-Holland, Amsterdam, 1986) p. 493. P.H. Kes and E. van der Drift, Physica C ~23 A. Pruijmboom, 165 (1990) 179. [ 241 E.J. Kramer, J. Appl. Phys. 44 ( 1973) 1360. [25] E.H. Brandt, Phys. Status Solidi B 51 (1972)

References [ 1 ] A. Houghton, R.A. Pelcovits and A. Sudb$, Phys. Rev. B 40 (1989) 6763. [2] D.R. Nelson, Phys. Rev. Lett. 60 (1988) 1973. [3] P.L. Gammel, L.T. Schneemeyer, J.V. Waszczak and J. Bishop, Phys. Rev. I&t. 61 (1988) 1666; S. Gregory, C.T. Rogers, T. Venkatesan, X.D. Wu, A. Inam and B. Dutta, Phys. Rev. Lett. 62 ( 1989) 1548. In terms of collective pinning [ 51 F,= JJl= ( W/V,) “’ and U,x ( WVc)“2rp, where F,, is the pinning force density, B the flux-line density, W measures the pinning strength, V, is the volume of a correlated region and rp the range of the pin potential U,. The elastic softening greatly reduces V,, leading to a large Fp, but a small tTp ‘I A.I. Larkin and Yu. N. Ovchinnikov, J. Low Temp. Phys. 34 (1979) 409. [6] M. Fisher, Phys. Rev. Lett. 62 (1989) 1415. [7]P.H.KesandC.C.Tsuei,Phys.Rev.B28(1983)5126. [ 8 ] D. Fisher, Phys. Rev. B 22 ( 1980) 1190. [9] P.H. Kes, R. Wijrdenweber and C.C. Tsuei, Proc. 17th Int. Conf. on Low Temperature Physics, Karlsruhe, 1984, eds. U. Eckern, A. Schmid, W. Weber and H. Wiihl (NorthHolland, Amsterdam, 1984) p. 457. [lo] M.V. Feigelman and V.M. Vinokur, Phys. Rev. B, to be published; M.V. Feigelman, V.B. Geshkenbein, A.I. Larkin and V.M. Vinokur, Phys. Rev. Lett. 63 (1989) 2303. [ 111 M. Tinkham, Phys. Rev. Lett. 61 (1988) 1658. [ 121 Y. Yeshurun, A.P. Malozemoff, Phys. Rev. Lett. 60 (1988) 2202. [ 13lT.T.M. Palstra, B. Batlogg, L.F. Schneemeyer and J.V. Waszczak, Phys. Rev. Lett. 61 ( 1988) 1662. [ 141 C.W. Hagen and R. Griessen, Phys. Rev. Lett. 62 (1989) 2857. [ 15 ] Y. Xu, M. Suenaga, A.R. Moodenbaugh and D.O. Welch, Phys. Rev. B 40 (1989) 10882. [ 161 E. Zeldov, N.M. Amer, G. Koren, A. Gupta, R.J. Gambino and M.W. McElfresh, Phys. Rev. Lett. 62 (1989) 3093. [ 171 M. Tinkham, Introduction to Superconductivity (McGrawHill, New York). [ 18 ] P.H. Kes, J. Aarts, J. van den Berg, C.J. van der Beek and J.A. Mydosh, Supercond. Sci. Technol. 1 ( 1989) 242.

357

345.

[26] A.P. Malozemoff, T.K. Worthington, Y. Yeshurun, F. Holzberg and P.H. Kes, Phys. Rev. B 38 ( 1988) 7203. [27]P.H. Kes, P. Berghuis, S.Q. Guo, B. Dam and G.M. Stollman, J. Less Comm. Met. 151 ( 1989) 325. [28] U. Welp, W.K. Kwok, G.W. Crabtree, K.G. Vandervoort and I.Z. Liu, Phys. Rev. Lett. 62 ( 1989) 1908. [29] L. Tewordt, D. Fay and Th. WGlkhausen, Solid State Commun. 67 (1988) 301. [30] R.A. Klemm, J. Low Temp. Phys. 16 (1974) 381. D. Fay and L. Tewordt, Phys. Rev. B 39 (1989) 278. [32] P.M. Mankiewich, J.H. Scofield, W.J. Skorpol, R.E. Howard and A.H. Dayem, Appl. Phys. Lett. 51 (1987) 1753. [ 331 H.W. Zandbergen and G. Thomas, Phys. Status. Solidi A 107 (1988) 825. [34] A. Kapitulnik, PhysicaC 153-155 (1988) 520.

[ 3 1 ] CT. Rieck, Th. Wiilkhausen,

[35]E. Schneider, J. Low Temp. Phys. 31 (1978) 357 and reference cited therein. 13611E. Kaldis, P. Fischer, A.W. Hewat, E.A. Hewat, J. Karpinski and S. Rusiecki, Physica C 159 (1989) 668. 137‘1 P.H. Kes and J. van den Berg, to appear in: Studies of High Temperature Superconductors, ed. A. Narlikar (NOVA Science Publ., New York). C.E. Rice, A.F. Hebard, P.L. 13881S. Martin, M. Gurvitch. Gammer, R.M. Fleming and A.T. Fiory, Phys. Rev. B 39 (1989)9611. [39] K.S. Bedell, in: NATO AS1 Series vol. B, Interacting Electrons in Reduced Dimensions, to be published. [40] C.C. Tsuei, A. Gupta and G. Koren, Physica C 161 ( 1989) 415. [41] T.T.M. Palstra, B. Batlogg, L.F. Schneemeyer, R.B. van Dover and J.V. Waszczak, Phys. Rev. B 38 (1988) 5102. [42]M.J. Naughton, R.C. Yu, P.K. Davies, J.E. Fischer, R.V. Chamberlin, Z.Z. Wang, T.W. Jing, N.P. Ong and P.M. Chaikin, Phys. Rev. B 38 (1988) 9280. [43] J.Y. Juang, J.A. Cutro, R.A. Rudman, R.B. van Dover, L.F. Schneemeyer and J.V. Waszczak, Phys. Rev. B 38 (1988) 7045. [ 44 ] D.E. Farrell, C.M. Williams, S.A. Wolf, N.P. Bansal and V.G. Kogan, Phys. Rev. Lett. 6 1 ( 1988) 2805. [45] D.E. Farrell, S. Bonham, I. Foster, Y.C. Chang, P.Z. Jiang, K.G. Vandervoort, D.I. Lam and V.G. Kogan, Phys. Rev. Lett. 63 (1989) 782.

[46] S. Martin. A.T. Fiery. R.M. Fleming, G.P. Espinosa and AS. Cooper. Appl. Phys. Lett. 54 ( 1989) 72. [ 47 ] S.W. Tozer. A. W. Kleinsasser, T. Penney, D. Kaiser and F. Holzberg. Phys. Rev. Lett. 59 ( 1987) 1768: Y. Iye, Int. J. Mod. Phys. B (1989) 367: S.J. Hagen, T.W. Jing. Z.Z. Wang, J. Hot-vath and N.P. Ong. Phys. Rev. B 37 ( 1988) 7928. [48] L. Krusin-Elbaum, R.L. Greene, F. Holtzberg. 4.1’. Malozemoff and Y. Yeshurun. Phys. Rev. Lett. 62 ( I988 ) 217. [49] N.R. Werthamer, E. Helfland and P.C. Hohenberg, Phys. Rev. 147 (1966) 295.

[50] V.J. Emery. Phys. Rev. Lett. 58 ( 1987) 2794. [ 5 I ] P. Berghuis, A. van dcr Slot and P.H. Kes. to be published. [521 Y. Yeshurun and A.P. Malozemoff. Phys. Rev. Lett. 60 ( 1988) 2202: C. Rossel and P. Chaudhan, Physcra C 153-l 55 ( I988 ) 306: M. Tmkham. Helv. Phys. Acta 61 ( 1988) 443. [ 531 M.R. Beasley. R. Labush and W.W. Webb. Phys. Rev. 18 I (1969) 682. [ 541 R. Ikeda. T. Ohmi and Isuneto, J. Phys. Sot. Jpn. 58 ( 1989) 1377. [ 551L.J. de Jongh. Solid State C‘ommun. 70 ( 1989) Y55.