Bose-glass transition in irradiated Bi2Sr2Ca1-xYxCu2O8 crystals

PHYSlCA ELSEVIER

Bose-glass

Physica C 341-348 (2000)1339-1340

www.elsevier.nl/Iocate/physc

transition in irradiated Bi2Sr2Cal-xYxCu208 c r y s t a l s

R. De Sousa a , L.Ammor a" , J.C.Soret a, V.Ta Phuoc a, A.Ruyter a, A.Wahl b, E.Olive a aLaboratoire d'Electrodynamique des Mat6riaux Avanc6s Universit6 F.Rabelais - UFR Sciences - Parc de Grandmont. 37200 Tours - France bLaboratoire CRIMAT, CNRS URA 1318, 6 Bd Marechal Juin, 14050 Caen cedex, France Current-voltage characteristics are investigated in Bi2Sr2Cai_xYxCu2Oscrystals irradiated parallel to the c-axis with 5.8 GeV Pb ions. Over a wide range of filling fractions 0.026 < f < l, I-V isotherm curves near the superconducting transition are consistent with the Bose-glass scaling theory. The Bose glass line, derived from scaling analysis, is well described by the Lindemann criterion which accounts for the contribution of correlated disorder. Two characteristic temperatures to~0.72 (f~0.8) and try0.83 (f~l/3), beyond which the vortex system is increasingly dominated by vortex-vortex interactions or thermal fluctuations, respectively, are identified. It has been clearly demonstrated in many experimental studies that, in irradiated hightemperature superconductors (HTS) and for fields below the matching field B,, the resulting Boseglass (BG) transition line TBG(B) separating vortex liquid and glassy state is shifted to higher temperatures from the melting line of an unirradiated sample. Nevertheless, the behaviour of TBG(B) line, extracted by different experimental techniques (peak in the ac susceptibility )(', onset of the third harmonic in ac measurements, etc.), and its comparison with theoretical predictions in different fields regions, is still a widely discussed topic in HTS. In this study, we report on the BG line extracted from BG scaling analysis [1] which describes correctly our experimental data. In particular, the universal behaviour is evidenced and the critical exponents are derived. We studied three Bi2Sr2YxCat.xCuzOs crystals with x=0 (samples 1 and 2) and x=0.36 (sample 3) whose zero-field critical temperature Tc are 80.0, 89.5 and 91.2K, respectively. The samples with typical dimensions of lxlx0.03 mm 3 have been irradiated with 5.8 Gev Pb ions at Ganil (Caen, France). Irradiation doses expressed in terms of a matching field B, were 0.75T (samples land 3) and 1.5T (sample 2). Columnar tracks of diameter 2Co ~ 90A ± 10 A were created along the c-axis. Isothermal I-V characteristics were obtained by using a d.c. four probe method with a voltage resolution of 10l°V and a temperature stability better than 5 mK. Currents up to 100mA were used

without heating effects detected from the temperature controller. The magnetic field was parallel to the columnar defects, i.e. to the c-axis. We have examined the behaviour of I-V curves, in the vicinity of the glass transition [R- limt-~o V/I=0]. For f=B/B~
(EIJ)I

t v(,'-2) =

F±(JITt 3v)

(1)

where v' and z' are the critical exponents governing the size and time relaxation of fluctuations, respectively. F+ and E are scaling functions defined in the flux liquid state (T>TBG) and localized fluxline state (T
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R. De Sousa et aL/Physica C 341 348 (2000) 1339-1340

1340

dependence in the exponents z' and v' provides a demonstration of an universal behaviour as expected in the Bose-glass to liquid transition. The only field dependent fitting parameter in insert of Fig. 1 is TB~, in such a way that TB~(B) defines the BG line transition in B-T phase diagram. 101

'

I

~

[

I

'

'

I

l

'

I

'

I

'

"~(B)

all samples

'

I

I

'

II

]

,

0.8

o.s

'

TO T1

m

.30+0.05 i!

I -4-3-2-1

10_ 2

t

l

0.0 0.1

,

v'=1.1

0 I

0.2

,

1 2 I

0.3

3

li~all

4 i

0.4

3

± 0.1 5 I

6 ,

o.s

7 I

0.6

,

I

0.7

,

1.0

tBG=(TBJTc)

Fig. 1 : Schematic B-T phase diagram of Bi2Sr2Cal_xYxCu208 compound over a wide range of filling fractions 0.026 < f _< 1 (open symbols: O samplel, A sample 2 and [2sample 3). The solid line represents the fit from Eq. (2) to the data with defect diameter 2C0 .= 90A. The filled symbols represent the data determined by using a low ohmic resistivity c r i t e r i o n Refit ~ 1~t~. The insert shows the universal scaling laws F+ and F_ according to Eq. (1). The experimental B-T phase diagram, extracted from scaling analysis, including the BG line of each sample, is shown in Fig. 1. As may be seen in this figure, the BG lines are well described by the expression (solid line in Fig. 1)

T . ~ ( B ) = F T . , ( B ) + (I - F ) T c

I-

.

calculated using the Lindemann criterion which accounts for the contribution of correlated disorder [1]. This analytic expression is only valid below the accommodation field B*(T) which separates singlevortex strong pinning from collective weak pinning regime. The disorder-related parameter F and the first-order melting line Tm(B) expression are given in ref. [1].

The solid line shown in Fig. 1, represents the diameter Co of defects as the only fitting parameter. The theoretical TBG(B) line (Eq. 2), using the typical average experimentally found values of the other parameters are tab = 18A, Xab = 1850A, ~' = 50 and CLz 0.28. Theoretical curves and experimental data quantitatively agree over a magnetic field range 0.3B,
[1] D.R. Nelson and V.M.Vinokur, Phys. Rev. B 48 (1993) 13060. [2] V. Ta Phuoc, A.Ruyter, L. Ammor, A. Whal, J. C. Soret, Phys. Rev. B 56 (1997) 122. [3] R. C. Budhani, W. L. Holstein, and M. Suenaga, Phys. Rev. Lett. 72 (1994) 566.