SCALING BEHAVIOUR OF RESISTIVE SUPERCONDUCTING TRANSITIONS IN THIN FILMS

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SCALING BEHAVIOUR OF RESISTIVE

SUPERCONDUCTING TRANSITIONS IN THIN

FILMS

N. Ya Fogel, A. Sidorenko

To cite this version:

JOURNAL DE PHYSIQUE

Colloque C6, supplPment au

no

8, Tome

39, aoirf

1978,

page

C6-498

SCALING BEHAVIOUR OF RESISTIVE SUPERCONDUCTING TRANSITIONS IN THIN FILMS

N.Ya Fogel and A.S. Sidorenko

physico-TechnicaZ I n s t i t u t e of Low Temperatures, Ukr SSR Academy of Sciences, 47, Lenin Prospect, Kharkov, 310164, USSR

R6sumd.- On a ddcouvert des lois d'dchelle pour les transitions rdsistives de couches supraconductri- ces, dues

B

une variation de tempdrature, de courant et de champ magndtique extdrieur. On peut expli- quer les rdsultats obtenus B l'aide de la thdorie gsndrale des fluctuations de transformations de phase de second ordre.

Abstract.- Scaling laws for resistive transitions in superconducting films caused by temperature, transport current and applied magnetic field changes have been found. The results obtained may be explained in terms of the general fluctuational theory of second order phase transitions.

We studied resistive transitions to the super- conducting state occurring at temperature T and ap-

D

plied magnetic field H variations on 300-400 A thick vanadium films produced by vacuum condensation onto glass substrates heated to 400°C. It was found that, in the transition region, in wide ranges of T and H, the excess conductivity a' changes exponentially with temperature and field.

Fig. 1 shows temperature dependences of Rn (an/u') for different measuring currents I. As it can be seen, the resistive transition is divided

Fig. 1

into two different temperature regions. Restricting the discussion to T < Tc for the time (Tc is deter- mined by the midpoint of transition where &n(on/O')

= 0), we can describe the results for a fixed current

as follows :

on/at = exp

1-A(I)

(I-t))

and for different currents, an/a' = exp 1-y (I-jn)(l-t)]

where a is the normal state conductivity, j = I/I,, n

t = TITc, y > 0 is a constant for the particular sample n < 1.

Investigations of the resistive transitions in perpendicular and parallel magnetic fields sho- wed that the excess conductivity obeys the law :

an/o' = exp {-y'(l-h)(l-t)} (2)

where h = H/H for perpendicular field H and

c l

l

h = H/HcII for parallel field He/,. The values of Hcl and H were determined from the midpoint of

c//

the transition, y ' is a constant close to y.

Thus, for all the three independent parame- ters involved, i.e. T, H, and I, and for any magne- tic field orientation, the scaling laws are obser- ved, that is to say,

0'1%

can be described by a certain universal function of reduced variables t, h, and j.

It should be noted that in case of H//, vor- tices do not penetrate into the film because the film thickness is less than the critical thickness, dc, whereas, in case of H1

,

there are vortices in the film. Since the resistive behaviours in fields H and H// are identical, as follows from Eq.(2),

l

then it is appropriate to conclude that the resis- tive state in the perpendicular field is not con- nected with vortex motion.

In our opinion, the behaviour found may be

interpreted as being due to fluctuation effects ap- pearing in the vicinity of second order phase tran- sitions. The exponential dependence of u'/un on reduced parameters, t, h and j, at T < Tc and the identical forms of functions ur(t,h) in two quali- tatively different situations (perpendicular and parallel magnetic fields) seem to give sufficient evidence that the superconducting transition is governed by fluctuations. On the other hand, the universality of the dependences relating U', t, h,

and j suggests that the transitions in question

conform to the general fluctuation theory of second order phase transitions (see e.g. Ref. /l/).

Thus, for the first time we managed to show the scaling behaviour of, the superconducting tran- sitions ; the resistive phenomena in the transition region are controlled not by the character of the post-transition superconducting ordering (viz., a uniform state for H vortex state for H ) but just

l / '

l

by the fact of proximity of the critical point. The exponential dependence of U' on tempera- ture at T < Tc in the form of Eq. (l), in the limit j -t 0 has been obtained in terms of critical fluctua- tions in the calculations of Ref. 121. When using the literature-available vanadium electronic spectrum parameters, then the experimental value of A in Eq-

(1) agrees well with the prediction of Ref. /2/.

The data obtained suggest that in many cases, the large superconducting transition width may be explained without recourse to superconductor struc- tural inhomogeneities.

References

/I/ Patashinski, A.Z. and Pokrovski, V.L., Fluktuat- sionnaya teoriya fazovykh perekhodov, Nauka Publishers, Moscow (1975