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Critical fields of Sn in thin films
Solid State CommunicatIons Vol.2, pp. 101-103, 1964. Pergamon Press, Inc. Printed in the United States.
CRITICAL FIELDS OF Sn In THiN FILMS J. P. Burger, G. Deutscher, E. Guyon and A. Martinet
Service de Physique des Solides, Faculté des Sciences, Orsay(S. et 0. )France (Received 4 March 1964 by P. G. de Gennes) Thin hollow cylinders of Sn In alloys (type II superconductors) have been studied in the field range ~c2
second kind superconductor, at fields larger than the Landau limit Hc2, there still remains fields H such that H~
T:2.5K
Z
.w,,
~ ____________________
300
~oo
soc
ooo
w v ~
0.5
A
the parent bulk material. The resulting values are the same within 10 per cent*. This shows that the In concentration in the films can be controlled with reasonable accuracy. The thickness of the films (typically 6000 £) was significantly larger than the expected thickness ~ R~the superconducting sheath ( ~ 1000 A for an 6 per c~n~ In concentration with a K of the order of 1 ‘ ). The critical temperature is approximately that for Sn, as can be expected, and transition occurs within 1/50°K. *Size effects are unimportant for our films with low mean free paths at He temperature (~-= 5 for a 6 per cent alloy). e
0~
300
I 400
500
•
H 600
I~ v Cd)
FIG. 1 (a) Resistive transition in a field perpendicular to Oz. (0) 8 = 90°, (.) 8 = 60°, (‘‘) e = 400 (w) 8 = 20°, (+) 8 = 0°, and in a field along Oz (A). The difference between the two transitions Is due to the size of the contacts in the case (+) (see Fig. 2); (b) schematic representation of the resistive measurement in the case (0); (c) magnetic transition in a longitudinal field; (0) and in a perpendicular one (x); (d) magnetic apparatus.
102
CRITICAL FIELDS OF Sn In THIN FILMS
Vol. 2, No. 4
Hc~ H~
2 1.7
—
j4
TIN KHAM TOMA5CH ~J05EPH
(Turns)
:i
0
10
20
30
40
50
60
70
50
9Q
FIG. 2 Angular dependence of (1) In longitudinal fields (H parallel to the cylinder axis, 8 = 0) there remains a superconducting sheath of uniform thickness around the cylinder up to a field H~3(9O)= Hc3. When H Is below Hc3 we measure no resistance between the points A and B on the cylinder (Fig. 1 b). When H crosses H~3the resistance is abruptly restored~ (Fig. 1 a). The transition is much more accurately defined in our thin films than in bulk samples. ~ Alsq much more easily than with bulk samples, we can detect Hc3 by a magnetic measurement: we superpos~on H a small alternating (600 Hz) field H1 (10 oe) created by a coil A (Fig. 1 d) and we measure the voltage in a 60 turns coil B wound closely around the specimen. The results are represented on Fig. 1 (c): 11. againUp weHhave an abrupt transition at Hsheath = Hc3 admits to = Hc3, the superconducting no flux inside the cylinder~. (2) We now consider the case of a transverse static field H applied along Oy (Fig. 1 b). Along AB the field is normal to the surface specimen; 9 ir/2. It is known1 that, in this case, no superconductivity remains above the Landau limit Hc2. There appears a
strip of normal material along AB and (a) we measure a finite resistance, (b) in the magnetic measurement the flux can penetrate in the cylinder. Thus we measure Hc2 by two Independent means. The experimental results are shown on Fig 1 (a), 1 (c). Again the transitions are unusually sharp* when compared to the usual behavior of superconducting films in perpendicular fields. 4 For our ~i-In 6 per cent sample, the experimental value of (Hc3) / (Hc2) isi1.?~~ 0.05 (the theoretical value being 1. 69, ‘ ‘ For fields H such that Hc2>N N’ in the resistivity measurement, the current flows from A to toNthe andlength N’ andAN. the resistance is proportional Thus, in. principle, the resistance versus field curve should determine the angular dependence of Hc3. In fact, in our experiment AB = 3 cm while N N’- 1 cm and this method would not be accurate. When the field reaches the value Hc3 there is no more a superconducting path along CD, so we see a sharp increase of R/R~for that value and the restoration of full normal resistance.
§ The advantage of the cylindrical films is to suppres~all edge effects that broaden the resistive transition in flat films in a longitudinal magnetic field. ¶ This behavior is strikingly different from what is observed on bulk samples of such alloys where we see a partial flux penetration well below ~ + We take the determination of the critical field as the field where the penetration is complete and that corresponds to the beginning of the resistive transition. The restoration of the full normal resistance, which is a more drastic condition, occurs at a slightly higher field. ~ The resistive and magnetic transitions in longitudinal and transverse fields are reversible. ‘~
Vol. 2, No. 4
CRITICAL FIELDS OF SnIn THIN FILMS
(3) A better determination of H~3(8)can be obtained by rotating the field H in the x y plane and detecting the onset of a resistance along AB when the normal strip reaches the probes. The resulting curve for H~~(8) is represented on Fig. 2 and compared to the results of Tomasch and Josephb, obtained by torque measurements on films. They are roughly in agreement except at low angles. This is not very surprising since our accuracy in the determination of 8 is limited by the finite size (— 1/2 mm) of the probes AB. 7 predicts a curve for H due to A simple physical argument, Tinkham 03(8) which
103
is rather close to the Tomasch result and Is also represented on Fig. 2. We conclude that thin hollow cylinders are particularly well suited for studies of the superficial superconducting layer since both Hc2 and Hc3 can be simultaneously measured by resistive and magnetic measurements with unusually sharp transitions. It is a pleasure to thank P. G. de Gennes and P. Pêrio for numerous discussions all along this work. We are grateful to M. Tinkham for giving us his paper on angular dependence of Hc3(8) prior to Its publication.
References 1. SAINT-JAMES D. and DE GENNES P. G., Phys. Letters 7, 306 (1963). 2. See for example: DOIDGE P.R., Phil. Trans. Roy. Soc. A 248, 553 (1956). 3. BON MARDION G., GOODMAN B. B. and LACAZE A. Phys. Letters 8,15 (1964). 4. GUYON E., CAROLI C. and MARTINET A., J. Phys. Rad. to be published. 5. For experimental evidence and determinations see: SERAPHIM D. P. in Superconductors (Edited by M. TAVENBAUM and W. V. WRIGHT) p.28; GYGAX S., OLSEN J. L. and KROPSCHOT R. H., Phys. Letters 8, 228 (1964) and to appear; HEMPSTEAND C. P. and KIM Y. B., Phys. Rev. Letters 12, 195 (1964); ROSENBAUM, Phys. Letters to appear; HART and SWARTZ, private coñTinunication. 6. TOMASCH W.J. and JOSEPH A.S., Phys. Rev. Letters 12,148 (1964). 7. TINKHAM M., Phyè. Letters to be published. De minces cylindres crewc d’alllages Sn In (supraconducteurs de deuxibme espèce) ont été étudlês pour des champs Hc2 < H < Hc3 oü la supraconductivit~ est limitée a une couche superficielle. Pour ces cylindres, a la fois Hc2 et H~3ont êté d~termlnésindêpendamznent par des mesures résistives et magnétiques. Les transitions sont beaucoup plus raides que dans les ~chantillons masslfs correspondants. Le rapport Hc3/Hc2 qu’on en dédult est en hon accord avec la valeur thêorique. Des résultats préliminaires sur la dépendance angulaire du champ critique supérieur ont aussi ét4 obtenus.
CRITICAL FIELDS OF Sn In THiN FILMS J. P. Burger, G. Deutscher, E. Guyon and A. Martinet
Service de Physique des Solides, Faculté des Sciences, Orsay(S. et 0. )France (Received 4 March 1964 by P. G. de Gennes) Thin hollow cylinders of Sn In alloys (type II superconductors) have been studied in the field range ~c2
second kind superconductor, at fields larger than the Landau limit Hc2, there still remains fields H such that H~
T:2.5K
Z
.w,,
~ ____________________
300
~oo
soc
ooo
w v ~
0.5
A
the parent bulk material. The resulting values are the same within 10 per cent*. This shows that the In concentration in the films can be controlled with reasonable accuracy. The thickness of the films (typically 6000 £) was significantly larger than the expected thickness ~ R~the superconducting sheath ( ~ 1000 A for an 6 per c~n~ In concentration with a K of the order of 1 ‘ ). The critical temperature is approximately that for Sn, as can be expected, and transition occurs within 1/50°K. *Size effects are unimportant for our films with low mean free paths at He temperature (~-= 5 for a 6 per cent alloy). e
0~
300
I 400
500
•
H 600
I~ v Cd)
FIG. 1 (a) Resistive transition in a field perpendicular to Oz. (0) 8 = 90°, (.) 8 = 60°, (‘‘) e = 400 (w) 8 = 20°, (+) 8 = 0°, and in a field along Oz (A). The difference between the two transitions Is due to the size of the contacts in the case (+) (see Fig. 2); (b) schematic representation of the resistive measurement in the case (0); (c) magnetic transition in a longitudinal field; (0) and in a perpendicular one (x); (d) magnetic apparatus.
102
CRITICAL FIELDS OF Sn In THIN FILMS
Vol. 2, No. 4
Hc~ H~
2 1.7
—
j4
TIN KHAM TOMA5CH ~J05EPH
(Turns)
:i
0
10
20
30
40
50
60
70
50
9Q
FIG. 2 Angular dependence of (1) In longitudinal fields (H parallel to the cylinder axis, 8 = 0) there remains a superconducting sheath of uniform thickness around the cylinder up to a field H~3(9O)= Hc3. When H Is below Hc3 we measure no resistance between the points A and B on the cylinder (Fig. 1 b). When H crosses H~3the resistance is abruptly restored~ (Fig. 1 a). The transition is much more accurately defined in our thin films than in bulk samples. ~ Alsq much more easily than with bulk samples, we can detect Hc3 by a magnetic measurement: we superpos~on H a small alternating (600 Hz) field H1 (10 oe) created by a coil A (Fig. 1 d) and we measure the voltage in a 60 turns coil B wound closely around the specimen. The results are represented on Fig. 1 (c): 11. againUp weHhave an abrupt transition at Hsheath = Hc3 admits to = Hc3, the superconducting no flux inside the cylinder~. (2) We now consider the case of a transverse static field H applied along Oy (Fig. 1 b). Along AB the field is normal to the surface specimen; 9 ir/2. It is known1 that, in this case, no superconductivity remains above the Landau limit Hc2. There appears a
strip of normal material along AB and (a) we measure a finite resistance, (b) in the magnetic measurement the flux can penetrate in the cylinder. Thus we measure Hc2 by two Independent means. The experimental results are shown on Fig 1 (a), 1 (c). Again the transitions are unusually sharp* when compared to the usual behavior of superconducting films in perpendicular fields. 4 For our ~i-In 6 per cent sample, the experimental value of (Hc3) / (Hc2) isi1.?~~ 0.05 (the theoretical value being 1. 69, ‘ ‘ For fields H such that Hc2
§ The advantage of the cylindrical films is to suppres~all edge effects that broaden the resistive transition in flat films in a longitudinal magnetic field. ¶ This behavior is strikingly different from what is observed on bulk samples of such alloys where we see a partial flux penetration well below ~ + We take the determination of the critical field as the field where the penetration is complete and that corresponds to the beginning of the resistive transition. The restoration of the full normal resistance, which is a more drastic condition, occurs at a slightly higher field. ~ The resistive and magnetic transitions in longitudinal and transverse fields are reversible. ‘~
Vol. 2, No. 4
CRITICAL FIELDS OF SnIn THIN FILMS
(3) A better determination of H~3(8)can be obtained by rotating the field H in the x y plane and detecting the onset of a resistance along AB when the normal strip reaches the probes. The resulting curve for H~~(8) is represented on Fig. 2 and compared to the results of Tomasch and Josephb, obtained by torque measurements on films. They are roughly in agreement except at low angles. This is not very surprising since our accuracy in the determination of 8 is limited by the finite size (— 1/2 mm) of the probes AB. 7 predicts a curve for H due to A simple physical argument, Tinkham 03(8) which
103
is rather close to the Tomasch result and Is also represented on Fig. 2. We conclude that thin hollow cylinders are particularly well suited for studies of the superficial superconducting layer since both Hc2 and Hc3 can be simultaneously measured by resistive and magnetic measurements with unusually sharp transitions. It is a pleasure to thank P. G. de Gennes and P. Pêrio for numerous discussions all along this work. We are grateful to M. Tinkham for giving us his paper on angular dependence of Hc3(8) prior to Its publication.
References 1. SAINT-JAMES D. and DE GENNES P. G., Phys. Letters 7, 306 (1963). 2. See for example: DOIDGE P.R., Phil. Trans. Roy. Soc. A 248, 553 (1956). 3. BON MARDION G., GOODMAN B. B. and LACAZE A. Phys. Letters 8,15 (1964). 4. GUYON E., CAROLI C. and MARTINET A., J. Phys. Rad. to be published. 5. For experimental evidence and determinations see: SERAPHIM D. P. in Superconductors (Edited by M. TAVENBAUM and W. V. WRIGHT) p.28; GYGAX S., OLSEN J. L. and KROPSCHOT R. H., Phys. Letters 8, 228 (1964) and to appear; HEMPSTEAND C. P. and KIM Y. B., Phys. Rev. Letters 12, 195 (1964); ROSENBAUM, Phys. Letters to appear; HART and SWARTZ, private coñTinunication. 6. TOMASCH W.J. and JOSEPH A.S., Phys. Rev. Letters 12,148 (1964). 7. TINKHAM M., Phyè. Letters to be published. De minces cylindres crewc d’alllages Sn In (supraconducteurs de deuxibme espèce) ont été étudlês pour des champs Hc2 < H < Hc3 oü la supraconductivit~ est limitée a une couche superficielle. Pour ces cylindres, a la fois Hc2 et H~3ont êté d~termlnésindêpendamznent par des mesures résistives et magnétiques. Les transitions sont beaucoup plus raides que dans les ~chantillons masslfs correspondants. Le rapport Hc3/Hc2 qu’on en dédult est en hon accord avec la valeur thêorique. Des résultats préliminaires sur la dépendance angulaire du champ critique supérieur ont aussi ét4 obtenus.