HOW THE STATISTICS OF PINNING CENTRES INFLUENCE ON V-I CHARACTERISTICS OF SUPERCONDUCTORS

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HOW THE STATISTICS OF PINNING CENTRES

INFLUENCE ON V-I CHARACTERISTICS OF

SUPERCONDUCTORS

Yu. Krasnov, L. Matushkina, V. Shukhman

To cite this version:

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JOURNAL DE PHYSIQUE

_{Colloque C6, s~pplkment au no 8, Tome 39, aofit 1978, page C6-631}

HOW THE STATISTICS OF PINNING CENTRES INFLUENCE ON

V-I

CHARACTERISTICS OF SUPERCONDUCTORS

YU.K: Krasnov, L .V. Matushkina and V.A. Shukhman

I n s t i t u t e of Physics, Georgian Academy of Sciences, TbiZissi, U. S. S . R.

RQsumi5.- On montre coment les formes des caract~risti~ues courant-tension des supraconducteurs de type I1 dans 1'Qtat intermddiaire peuvent Stre relides 2 la distribution des centres de "pinning" par les forces de leur interaction avec les vortex.

Abstract.- It is shown how the shape of volt-current characteristics of the I1 kind superconductors in the mixed state can be connected with the distribution of pinning centers by the forces of their interaction with vortices.

The behaviour of volt-current characteristics (VCC) of real superconductors in the mixed state is determined by the interaction of vortex lines with crystal-lattice defects. The comon trait, which unites VCC of the real specimens, is the existence of the threshold critical current I and nonlinear region after I > Ic

.

While current is increased VCC tends to exhibit linear conduction. It is assumed that the existence of such a linear conduction signifies that asymptotically VCC corresponds to the "dry friction" model, which leads to the dependence V = rf(I-I ) , From this point of view the nonlinea-

P

rity in VCC reflects the smooth transition to such anasymptotic regime. There is no simple explanation of such a nonlinearity at the present time. The most direct explanation is based on the idea, that only part of vortexes can move in the presence of the pinning contribution to the voltage /I/. This model may bejustified when pinning forces surpass the

interaction between vortexes. In this case the vortex system is inclined to exhibit rather liquid properties than crystal one. Such a "melted" vortex lattice was observed

121.

There are reasons to be- lieve that the similar properties must be manifested in thin films 131 and specimens with Ginsburg-Landau parameter

g-

I / I / . The consistent application of the "melted" vortex lattice idea in order to explain the nonlinearity of VCC permits, to connect this nonlinearity with the distribution function of pinning centres by their interaction with vortexes. This possibility was first outlined in / I / and 141. Accor- ding to Baixeras and Fournet

v(I)

-

rf jl(I-Ip)f(I)dI

0

where rf

-

the resistance in the mixed state in the

absence of pinning, and £(I) = 0 when I & Ic in order to fulfil the experimental result : V = 0 when I s Ic.

Meanwhile there is no need to put such a ri- gid terms on the distribution function, which may be naturally assumed to be a Gaussian one, if pinning centres are randomly distributed according to their interaction with vortexes and excluding any correlations between space and energetical distri- butions of these centres. Since only a part a of

vortexes is depinned from the pinning centres at the given current I and only these vortexes contribute to voltage, the right side of (1) must be multiplied by

a.

The value of a can be received as follows. Let us divide our specimen into cellls pi6rceing it along the direction of the external magnetic field (the minimal dimension of each cell is determined by the pinning interaction mean radius of pinning centres contained in the cell). Each cell exhibits the possible "pinning-site" of vortex. If no

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the total density of such "pinning-sites" in which a vortex is affected by any finite force, n(1)

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the density of pinning sites from which a vortex is depinned under the influence of the current I, then n(I)/no determines the probability that current I will de- pin a vortex and f(1) -the corresponding probability density. m i l e current is increased the redis- tribution of vortexes from "weak" sites to "strong" ones. When I = Imax the number of sites which can still pin vortexes at this value of current is equal to B/$~K, where B/$o

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the density of vortexes and K

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the mean number of vortexes, which in average are pinned by the same pinning-site. When I > Imax the stationary movement of vortexes begins since there is no sites at all to pin them down. So,

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19786284

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I- is the same what we usually call critical current Ic and, as it follows from the former,

It should be noted that generally speaking

K

depends on magnetic induction B. The density n of the mo

-

m

ving vortexes will be determined by the number of pinning sites, which can't pin vortexes at the given current, that is

From (2) and (2'), we receive

m

The substitution a Gaussian distribution in (4) leads to :

1 P = a

+

'

[ a x exp

[

-

$1

/[

I+

3 m

(here 4t)

-

the probability integral).

The comparison of (5) with experimental data comes to the determination of parameters a,

u

and rf at which (5) describes experimental data with accuracy as high as possible. Experiments were per- formed on In-2.5 ai.I Bi specimens

(x=

1.3) in the temperature and magnetic field range of (0.93-0.83) Tc and (0.35-0.9) Hc2 correspondingly

.

The computor program was developed and the values of a, (3 and rf were found at which the mean squire departure of (5) from experimental curves reached its minimum. The analysis of the whole data in aggregate shows, that if we require the accuracy within the line width of graph-recorder as a criterium of agreement between theory and experiment (that is 0.3% at high currents and

-

10% in the vicinity of Ic), then the obtained parameters a,

u

and rf behave regularly as functions of magnetic field and temperature and can be determined with accuracy of several percents.

Such accuracy in agreement between theoretical and experiment was reached in magnetic fields not higher than (0.5-0.7)xHc2 usually. As temperature was lawered this interval extended towards higher values of fields. The centre of distribution (a) falls linearely as field increases and its behaviour is described by empirical dependences :

where

D(t) =(14.5 f 0.5)-(12.2 f 0.5)t (t = TITc). The dispersion o does not reveal any nobiceable dependence neither temperature nor magnetic field. The ratio rf/rn (r -the resistance in the normal

n

state) as a function of the reduced magnetic field h is well described in the whole temperature range by a sngle curve, which lies lower than relation rf/rn = h

,

confirming theoretical and experimental data on resistive state.

Ratio V/I r in the whole range of tempera- P f

ture and fields appears to be a universal function of 111 which coincides with the results of (5) in-

P

dicating that in this point too our approach provi- des non-conductive results.

It is interesting to note that a definite relation between a, (3 and rf, is observed, being

reveal in the fact

[I

+ $

[?]][~+a(;]]

=

rf(1)dI = A = const. Constant A has a weak tendency to increase with the decrease of temperature. From (2) it fo.1- lows that mean number of vortices pinned at one and the same site has a linear dependence on B. In con- clusion the following should be noted : The above approach corresponds to the "melted" vortex lattice when pinning dominates over the inter vortex interaction. Tn the bulk specimen it is most probably justified in comparatively weak fields.

References

/I/ Hudson, W.R., Jirberg, R.J., Solid State Commuii. 7 (1969) 429

-

/ 2 / Trauble, H., Essmann,

U.,

J. Appl.Phys.

2

(1968) 4052

/3/ Ogushi, T., Shibuya, Y., J.Phys.Soc.Jpn,

2

(1972) 400

141 Baixeras, J., Fournet, G., J.Phys.Chem. Solids 28 (1967) 1541

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