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Submitted on 1 Jan 1978
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THERMALLY GENERATED MAGNETIC FLUX IN
SUPERCONDUCTING LOOPS
A. Guénault, K. Webster
To cite this version:
JOURNAL DE PHYSIQUE
Colloque C6, supplkment au
no
8, Tome 39, aolic 1978, page
C6-539
THERMALLY GENERATED MAGNETIC F L U X I N SUPERCONDUCTING LOOPS A.M. Gudnault and K.A. Webster
Physics Department, University o f Lancaster, Lancaster LA1 4YB, U.K.
Rdsum6.- Nous avons mesurd les changements du flux magndtique relie B un SQUID lorsque on chauffe une partie du cercle supraconducteur. Ces changements qui concernent la profondeur de pdngtration dans le supraconducteur se trouvent tr6s fortement influencds par la condition superficielle du fil d'gtain. Ce rd- sultat pourrait avoir des implications pour les expsriences concernant le flux thermo6lectrique produit par le cercle supraconducteur bimgtallique.
Abstract.- We have measured the changes in magnetic flux coupled into a SQUID from a superconducting loop which occur when part of the loop is heated. These changes, related to penetration-depth changes, are found to be very strongly influenced by the surface condition of the tin wire. This resultcould have com- plications in experiments concerning the thermoelectric flux generated in a bimetallic superconducting loop.
INTRODUCTION.- There has been considerable interest in the past few years arising from the prediction /1,2/ that a small non-quantised magnetic flux should be produced when a temperature gradient is applied to a bimetallic all-superconducting loop. All experimental results so far reported 13-6/ seem to give fluxes several orders of magnitude larger than expected, a source of considerable in- terest. However, before one can be sure that the explanation lies in the fundamental properties of the normal current/supercurrent counterflow there are a number of experimental pitfalls which must be avoided. One of these problems is that magnetic flux movements can be induced by thermally-produced changes in the superconducting penetration depth when part of the loop is heated, an effect which has been described in detail elsewhere 171. Briefly the effect arises in our experiments as follows. A change in temperature (just below T ) in part of a superconducting loop causes a change in the super- conducting penetration depth X of that portion of the loop, and hence in its self-inductance. The self-inductance change then causes a slight redis- tribution of the residual magnetic flux trapped in the loop, and since only a part of the loop is coupled into the SQUID a change in the flux measu- red by the SQUID is observed. Theoretical estima- tes and direct measurements of this effect (with different amounts of residual magnetic flux trap- ped in the loop) have demonstrated 171 that we could at best only set an upper limit on the ma- gnitude of the true thermoelectric effect /1,2/in
our experiments on Pb-Sn loops. This was in spite of our best efforts to minimise the residual trap- ped flux in our loops by superconducting and U- metal shielding (typical residual fields IO-~T).
EXPERIMENTAL.- We have recently performed experi- ments using basically the same apparatus as Pegrum /7,8/ but using loops made entirely of a single superconductor, tin. In these experiments therefo- re the true thermoelectric effect should be absent.
Our loops are fabricated from 99.99 % tin wire, 0.5 mm diameter. The loop is arranged in the
form of two 4 mm diameter, two-turn end coils joi- ned by a 45 mm straight section. The straight section had two copper thermal anchoring posts, one of which was in good thermal contact with a controlled pumped helium bath, and the other of which could be heated. In this way, the two end
loops were arranged to have no temperature gradient but one (which was coupled by a flux transformer
to the SQUID) was at fixed temperature, whilst the other could be heated; temperature gradients were restricted to the small region between the thermal anchors. A flux injecting coil used for trapping different amounts offlux in the loop was inducti- vely coupled into the loop; and current leads were attached to the loop near the thermal anchors, in order to be able to check the coupling between the SQUID and the loop. Fuller details are found elsewhere 181.
The experiment was performed as follows. A given amount of flux was trapped in the loop (in
addition to any residual background flux) by coo- ling the loop through T with a known current through the flux injecting coil; this current was then turned off, and the SQUID locked on with the temperature of the whole loop about 30 mK below Tc. The SQUID output was then plotted as the hea- ted portion of the loop had its temperature rai- sed to within about 3 mK of Tc. The SQUID output was reversibly dependent on temperature over this range. Changes of several flux quanta occured for a persistent loop current (I) of about 2 mA.
RESULTS.- All our results gave changes in SQUID flux which (I) depend linearly in magnitude and sign on the trapped flux in the loop, verifying that one is seeing a thermal modulation of this
1
flux; (2) vary almost linearly with (I-t4)-7 over the range indicated (t = TIT ) , showing the cor- rect temperature-dependence for a penetration depth effect.
These two features seem to indicate the essential correctness of the approach in 171, but one should also be able to make a quantitative estimate. The change in SQUID flux A+s is given by
M I A L M I a A A
,
A+s = - = L-
Lwhere M is the mutual inductance between the loop and the SQUID (about 0.4 nH), I the loop current, L the self-inductance of the loop, and AL the small self-inductance change generated by a penetration depth change AA. M and I were determined experimen- tally from the changes in $I when currents were passed down the external current leads and through the flux-injecting coil. L was calculated roughly to be about 0.17 pH, and ci = AL/AA was estimated (on a ctude model) to be about 90 u~m-'. If finally
1
we use A(t) = ~~(1-t4)-2, the experimental results give a value of .A equal to (9t2). 10-~m, a result far in excess of the true penetration depth of tin (%6 X 10-~m).
In view of this unexpected discrepancy, we repeated the experiment with a loop made from electropolished wire, but otherwise identical. This second loop gave almost identical responses to external currents (so, for example, M was the same); but the magnitudes of A+ observed were reduced dramatically, to give values of
.
A
of about (1824) x 10-%I within a factor of 3 of the expected value.induced by changing the temperature of part of a superconducting loop. These flux movements are con- sistent with being driven by penetration-depth changes in that (I) they depend linearly on the background flux present and (2) they have the ex- pected temperature dependence.
However, although the magnitude is reasona- ble in an electropolished loop; we find that the effect is of order 200 times larger than expected in a drawn wire. Although this wire has deeply crazed surface, the factor 200 seems too big to be accounted for by geometrical effects alone
-
for instance Laurmann and Shoenberg found similar enhancements of about three due to increasing the perimeter /10/. Perhaps flux concentration at the surface due to magnetic impurities might be par- tially responsible? In any case this work indica- tes that penetration depth effects as discussed in /7/ can be particularly damaging to the thermoelec- tric experiment, but that they can perhaps be re- duced by electropolishing the relevant surfaces.
References
/l/ Garland, J.C. and Van Harlingen, D.J., Phys. Lett.
5
(1974) 423./2/ Gal'Perin, Y.M. and Gurevich, V.L., JETP
39
(1974) 680./3/ Pegrum, C.M., Guenault, A.M. and Pickett, G.R. Proceedings of LT14,
2
(1975) 513./4/ Falco, C.M., Solid State Commun
2
(1976) 623. 151 Garland, J.C. and Van Harlingen, D.J. PrivateCommunication (1977) and to be published. 161 Zavaritskii, N.V., JETP. Lett.
19
(1974) 26. /7/ Pegrum, C.M. and Guenault, A.M., Phys. Lett.59A (1976) 393.
/8/ Pegrum, C.M., Ph. D. Thesis, University of Lancaster (I 976).
191 Webster, K.A., M. Sc. Thesis, University of Lancaster ( 1 977)
.
/10/ Laurmann, E. and Shoenberg, D., Proc. Soc. A198 (1947) 560.
