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Superheating in pure superconducting niobium
PHYSICS
Volume 24A. number 10
and (4) that if W(=l/K) is the thermal resistance, the change in W produced by the magnetic field is given by AW=-
8% c2’!n
Sl-+hSZ dw I. s O-AD lw
(5)
Thus, under these circumstances, measurement of the change in conductivity yields information about the phonon-spin interaction, rather than about the phonon interactions in the absence of the magnetic field. The reason for this is that if there are a large number of N-processes, as we are at present postulating, energy flux is rapidly transferred from one phonon mode to another. Thus if energy is abstracted from a narrow band of modes due to the spin-phonon interaction, this is ‘felt’ by all the other modes, and thus leads to a net change in conductivity depending on the magnitude of this spin-phonon interaction.
LETTERS
8 May 1967
The above calculation is, of course, strictly valid only if the scatter due to N-processes is much larger than other scattering mechanisms. However, the qualitative difference between the results (2) and (5) suggests that even a moderate number of N-processes may lead to incorrect resuits being obtained by a straightforward application of eq. (2). If it were possible to arrange experimentally that N-processes should form the main source of phonon scatter, measurement of A W would yield data on the phonon-spin interaction through eq. (5).
References 1. R. Berman. J. C. F. Brock and D. J. Huntley. Phys. Letters 3 (1963) 310. 2. D. Walton. Phys. Rev. 151 (1966) 627. 3. J. H. Ziman. Electrons and phonons (Oxford 1960).
*****
SUPERHEATING
IN
PURE
SUPERCONDUCTING
NIOBIUM
*
J. C. RENARD and Y. A. ROCHER Bruyb-es le Chatel 91. France
Alcatel.
Received 28 March 1967
We present experimental evidences of superheating’ in pure niobium: our results are in agreement superheating
field larger
wiln a
than I&.
Superheating in the superconducting to mixed state transition of superconductors of second kind have been subjected to several theoretical approaches [l-9]. Some of the authors [l, 3-51, following a very physical picture of the nucleation process used the concept of a barrier field which prevents the entry of the first vortex line. Their calculations which hold in the limit K >> 1, lead to a field barrier, HSH, of the order of H,, the thermodynamical critical field. In other respects, from a study of the solutions of the one-dimensional Ginzburg-Landau equations, with special boundary conditions, De Gennes et al. [Z, 4] proved, that for K - 00 the superheating field is equal to Hc. More recently, Matricon and Saint James [8], by a numerical calculation based on the same assumption as the Orsay Group find HSH to be a decreasing function of K, which tends
towards H, when K ---) *, in agreement with the asymptotic solution given by De Gennes. We may also quote two other approaches. One has been proposed by Finck [7] and the other by Galaiko [6,9]. The former, starting from the GinzburgLandau expression for the difference of the magnetic Gibbs’ function of superconducting and normal states and making a debatable assumption, predicted that HSH = HC whatever the value of X. The second, in order to extend the Ginzburg-Lan, dau theory to arbitrary temperatures, expressed the Gibbs’ free energy function on the basis of the B. C; S. theory and found that the superconducting state is stable up co a certain critical field (Hh1 >Hcl and HL1 z 0.8 Hc for K >> 1). Earlier experimental [lo-121 determination of * This work is mainly supported by the D. R. M. E. 509
Volume 24A.
number
10
PHYSICS
Fig. 1. Magnetization curves near &I. calculated from induction measurements. at 4.2oK. * At the end of the sample. x At the center of the sample. The dotted line represents an average value of the magnetic moment in the sample. for an “Ends contribution” of 2046 in volum (i. e. on a length of the order of the radius of the sample): it is in good agreement with the shape of magnetization curves obtained directly.
HSH are consistent with most of these theoretical predictions. Available values of HSH are very close to H,, but up to now, we had no experimental evidences for HSH values greater than H,, as predicted by Matricon and Saint-James +. In fact, this situation is easy to understand if we take into account end effects and flaws in the surface of the specimen. Those are responsible for large local fields, resulting from demagnetising effects, and once the transition to the mixed state has started at a weak point (or at the ends of the sample), this phase propagates through the entire specimen as soon as this is energetically possible, i. e. when the applied field is equal to H,l. Then it is seldom possible to superheat the whole sample and only superheating for the ends or for a typical defect can be observed. The present work is devoted to studies of superheating in cylindrical Niobium samples by suppressing end effects. In earlier measurements of magnetization curves of pure niobium samples, by moving the sample in a uniform magnetic field between two counter-wound pick-up coils, we have observed some departures from perfect diagmagnetic behaviour for applied fields below Hcl : slight penetration of the field for applied fields even lower * However their results are in rough agreement with experiments on superconductors of the first kind [13].
510
LETTERS
6 May 1967
Fig. 2. Magnetic induction at the center of the sample versus H/He. H being the applied field (from direct magnetization measurements H, = 1565 I 5 G). Without end shieldings: . x Very slight penetration at the end of the sample (local (-4i’rM) value N 6% of the applied field).
With end shieldings:
no penetration
0
i
A
I
at the
ends of the sample.
than 0.7 I&-l, this effect being more important in large samples than in small ones. In order to investigate this point and to ascertain whether it could be attributed to end effects, we carried out measurements of induction at the center and at the ends of the sample. The specimen, cylindrical 7.4 mm in diameter, 50 mm in length, was well out-gassed in vacuum better than 10-g Torr, and then electro-polished; it presented an almost reversible magnetization curve with a trapped flux less than 0.5% of the maximum (-4nm-value. It was placed in a static uniform magnetic field at 4.2OK, with two small pick-up coils wound around it -one at the center and the other at one end and connected to fluxmeters. The results of these measurements are shown in fig. 1 and explain the shape of magnetization curves near H,.l observed earlier by us and others [e.g. 141. In front of this relatively important end effect, we attempted to observe superheating on the same sample by suppressing them. For this we placed superconducting shieldings close to theends of the sample and observed, using a pick-coil, the first penetration of magnetic field at the center of the
PHYSICS
Volume 24A. number 10
sample, when this arrangement is placed in a static uniform magnetic field, parallel to its axis, at 4.2%. Some of our results are shown in fig. 2 and we can observe that all the values of HM, HM being the maximum field for which the sample remains in the Meissner state, are greater than Hc. Most of our results lie between 1.04 and 1.10 Hc (all our results are not presented on fig. 2); but we have observed superheating for fields up to 1.15 H,. As mentioned above, surface defects can control superheating, so we cannot assert that the observed HM-values are equal to the superheating field HSH, and we think that HM is a “minimum value” for HSH; these surface defects can account for the dispersion of our results, together with small changes in the field topography from one experiment to another, due to small modifications in the sample-screens-field geometry. The results are in contradiction with the predictions of Fink (HSH =Hc), but in qualitatively good agreement (HSH >H,), with the calculation of Matricon and Saint-James [8]. The measured values, HM, are a little smaller than the one predicted by this calculation. But this is easy to understand if HM is a “minimum value” for HSH. Besides, Matricon and Saint-James start from Ginzburg-Landau theory - which is only valid near equations. From Tc* - and use one-dimensional these restrictions, a quantitative comparison seems to be difficult. We would like to thank Dr. D. Saint-James Dr. G. Deutscher for fruitful discussions.
PARELEKTRISCHE G. HtjCHERL, 3. Physikalischen
and
RESONANZ
References Phvs. Rev. Letters 1. C. P. Bean and J. D. Livineston. ._ 12 (1964) 14.
2. P.G.DeGennes. Solid State Comm.3 (1965) 127. 3. G. B&e1 and C. F. Ratto. Solid State Comm. 3 (1965) 177. 4. Orsay Group on Superconductivity in Quantum fluids ed. D. F. Brewe (North-Holland Publ. Co.. Amsterdam. 1966). 5. J. Matricon. Th&se Orsay (1966). 6. V. P. Galaiko. Soviet Physics JETP 23 (1966) 475. 7. H. J. Fink. Phys. Letters 20 (1966) 356. 8. J. Matricon and D. Saint-James. Phys. Letters 24A (1967) 241.
9. V. P. Galaiko.
Soviet Physics JETP 23 (1966) 878. and W. J. Tomasch. Phys. Rev. Letters 12 (1964) 219. R. W. De Blois and W. De Sorbo. Phys. Rev. Letters 12 (1964) 499. G. Boato. G. Gallinaro and C. Rizzuto. Solid State Comm. 3 (1965) 173. J. P. Burger. J. Feder. S. R. Kiser, F. Rothwarf and C. Valette. Low Temperature Conf. Moscou (1966). D. P. Jones and J. G. Park. Phys. Letters 20 (1966) 111; D.K. Finnemore. T. F. Stromberg and C. A. Swenson. Phys. Rev. 149 (1966) 231. K. Maki and T. Tsuzuki. Phys. Rev. 139 (1965) A868: C.Carolli. M. Cyrot and P. G. De Gennes. Solid State Comm. 4 (1966) 17; E. Helfand and N. R. Werthamer. Phys. Rev. 147 (1966) 288.
10. A. S. Joseph 11. 12. 13.
14.
15.
* At the present time there is no available theory for pure superconductors of the second kind, for temperature far from 7’~. In the case of our sample, from magnetization measurements at 4.2oK. we obtain K1 = 1.175 and K2 = 1.675.
IN
KC1
D. BLUMENSTOCK Institut der Technischen Eingegangen
8 May 1967
LETTERS
am 12 April
DOTIERT
MIT
=
HCl
und H. C. WOLF Hochschule Stuttgart 1967
The parelectric resonance spectrum of KCl-crystals doped with HCl is observed at 35 GHz. The resonance line at 7 kV/cm is due to H--ions or HCl-molecules which are able to reorient in the lattice. This line seems to be identical with a line which was attributed to OH--dipoles by Feher et al. in a recent paper.
In den letzten Jahren wurden verschiedene Stijrstellen mit permanentem elektrischem Dipolmoment in Alkalihalogenid-Kristallen bekannt, die noch bei tiefer Temperatur beweglich sind. Kuhn und Liity [l] haben darauf hingewiesen, dass
bei diesen StSrstellen die parelektrische Resonanz als Analogon zur paramagnetischen Resonanz beobachtbar sein sollte. In einer Reihe von Arbeiten [2-41 wurde iiber parelektrische Resonanz von OH-Dipolen in KC1 511
Volume 24A. number 10
and (4) that if W(=l/K) is the thermal resistance, the change in W produced by the magnetic field is given by AW=-
8% c2’!n
Sl-+hSZ dw I. s O-AD lw
(5)
Thus, under these circumstances, measurement of the change in conductivity yields information about the phonon-spin interaction, rather than about the phonon interactions in the absence of the magnetic field. The reason for this is that if there are a large number of N-processes, as we are at present postulating, energy flux is rapidly transferred from one phonon mode to another. Thus if energy is abstracted from a narrow band of modes due to the spin-phonon interaction, this is ‘felt’ by all the other modes, and thus leads to a net change in conductivity depending on the magnitude of this spin-phonon interaction.
LETTERS
8 May 1967
The above calculation is, of course, strictly valid only if the scatter due to N-processes is much larger than other scattering mechanisms. However, the qualitative difference between the results (2) and (5) suggests that even a moderate number of N-processes may lead to incorrect resuits being obtained by a straightforward application of eq. (2). If it were possible to arrange experimentally that N-processes should form the main source of phonon scatter, measurement of A W would yield data on the phonon-spin interaction through eq. (5).
References 1. R. Berman. J. C. F. Brock and D. J. Huntley. Phys. Letters 3 (1963) 310. 2. D. Walton. Phys. Rev. 151 (1966) 627. 3. J. H. Ziman. Electrons and phonons (Oxford 1960).
*****
SUPERHEATING
IN
PURE
SUPERCONDUCTING
NIOBIUM
*
J. C. RENARD and Y. A. ROCHER Bruyb-es le Chatel 91. France
Alcatel.
Received 28 March 1967
We present experimental evidences of superheating’ in pure niobium: our results are in agreement superheating
field larger
wiln a
than I&.
Superheating in the superconducting to mixed state transition of superconductors of second kind have been subjected to several theoretical approaches [l-9]. Some of the authors [l, 3-51, following a very physical picture of the nucleation process used the concept of a barrier field which prevents the entry of the first vortex line. Their calculations which hold in the limit K >> 1, lead to a field barrier, HSH, of the order of H,, the thermodynamical critical field. In other respects, from a study of the solutions of the one-dimensional Ginzburg-Landau equations, with special boundary conditions, De Gennes et al. [Z, 4] proved, that for K - 00 the superheating field is equal to Hc. More recently, Matricon and Saint James [8], by a numerical calculation based on the same assumption as the Orsay Group find HSH to be a decreasing function of K, which tends
towards H, when K ---) *, in agreement with the asymptotic solution given by De Gennes. We may also quote two other approaches. One has been proposed by Finck [7] and the other by Galaiko [6,9]. The former, starting from the GinzburgLandau expression for the difference of the magnetic Gibbs’ function of superconducting and normal states and making a debatable assumption, predicted that HSH = HC whatever the value of X. The second, in order to extend the Ginzburg-Lan, dau theory to arbitrary temperatures, expressed the Gibbs’ free energy function on the basis of the B. C; S. theory and found that the superconducting state is stable up co a certain critical field (Hh1 >Hcl and HL1 z 0.8 Hc for K >> 1). Earlier experimental [lo-121 determination of * This work is mainly supported by the D. R. M. E. 509
Volume 24A.
number
10
PHYSICS
Fig. 1. Magnetization curves near &I. calculated from induction measurements. at 4.2oK. * At the end of the sample. x At the center of the sample. The dotted line represents an average value of the magnetic moment in the sample. for an “Ends contribution” of 2046 in volum (i. e. on a length of the order of the radius of the sample): it is in good agreement with the shape of magnetization curves obtained directly.
HSH are consistent with most of these theoretical predictions. Available values of HSH are very close to H,, but up to now, we had no experimental evidences for HSH values greater than H,, as predicted by Matricon and Saint-James +. In fact, this situation is easy to understand if we take into account end effects and flaws in the surface of the specimen. Those are responsible for large local fields, resulting from demagnetising effects, and once the transition to the mixed state has started at a weak point (or at the ends of the sample), this phase propagates through the entire specimen as soon as this is energetically possible, i. e. when the applied field is equal to H,l. Then it is seldom possible to superheat the whole sample and only superheating for the ends or for a typical defect can be observed. The present work is devoted to studies of superheating in cylindrical Niobium samples by suppressing end effects. In earlier measurements of magnetization curves of pure niobium samples, by moving the sample in a uniform magnetic field between two counter-wound pick-up coils, we have observed some departures from perfect diagmagnetic behaviour for applied fields below Hcl : slight penetration of the field for applied fields even lower * However their results are in rough agreement with experiments on superconductors of the first kind [13].
510
LETTERS
6 May 1967
Fig. 2. Magnetic induction at the center of the sample versus H/He. H being the applied field (from direct magnetization measurements H, = 1565 I 5 G). Without end shieldings: . x Very slight penetration at the end of the sample (local (-4i’rM) value N 6% of the applied field).
With end shieldings:
no penetration
0
i
A
I
at the
ends of the sample.
than 0.7 I&-l, this effect being more important in large samples than in small ones. In order to investigate this point and to ascertain whether it could be attributed to end effects, we carried out measurements of induction at the center and at the ends of the sample. The specimen, cylindrical 7.4 mm in diameter, 50 mm in length, was well out-gassed in vacuum better than 10-g Torr, and then electro-polished; it presented an almost reversible magnetization curve with a trapped flux less than 0.5% of the maximum (-4nm-value. It was placed in a static uniform magnetic field at 4.2OK, with two small pick-up coils wound around it -one at the center and the other at one end and connected to fluxmeters. The results of these measurements are shown in fig. 1 and explain the shape of magnetization curves near H,.l observed earlier by us and others [e.g. 141. In front of this relatively important end effect, we attempted to observe superheating on the same sample by suppressing them. For this we placed superconducting shieldings close to theends of the sample and observed, using a pick-coil, the first penetration of magnetic field at the center of the
PHYSICS
Volume 24A. number 10
sample, when this arrangement is placed in a static uniform magnetic field, parallel to its axis, at 4.2%. Some of our results are shown in fig. 2 and we can observe that all the values of HM, HM being the maximum field for which the sample remains in the Meissner state, are greater than Hc. Most of our results lie between 1.04 and 1.10 Hc (all our results are not presented on fig. 2); but we have observed superheating for fields up to 1.15 H,. As mentioned above, surface defects can control superheating, so we cannot assert that the observed HM-values are equal to the superheating field HSH, and we think that HM is a “minimum value” for HSH; these surface defects can account for the dispersion of our results, together with small changes in the field topography from one experiment to another, due to small modifications in the sample-screens-field geometry. The results are in contradiction with the predictions of Fink (HSH =Hc), but in qualitatively good agreement (HSH >H,), with the calculation of Matricon and Saint-James [8]. The measured values, HM, are a little smaller than the one predicted by this calculation. But this is easy to understand if HM is a “minimum value” for HSH. Besides, Matricon and Saint-James start from Ginzburg-Landau theory - which is only valid near equations. From Tc* - and use one-dimensional these restrictions, a quantitative comparison seems to be difficult. We would like to thank Dr. D. Saint-James Dr. G. Deutscher for fruitful discussions.
PARELEKTRISCHE G. HtjCHERL, 3. Physikalischen
and
RESONANZ
References Phvs. Rev. Letters 1. C. P. Bean and J. D. Livineston. ._ 12 (1964) 14.
2. P.G.DeGennes. Solid State Comm.3 (1965) 127. 3. G. B&e1 and C. F. Ratto. Solid State Comm. 3 (1965) 177. 4. Orsay Group on Superconductivity in Quantum fluids ed. D. F. Brewe (North-Holland Publ. Co.. Amsterdam. 1966). 5. J. Matricon. Th&se Orsay (1966). 6. V. P. Galaiko. Soviet Physics JETP 23 (1966) 475. 7. H. J. Fink. Phys. Letters 20 (1966) 356. 8. J. Matricon and D. Saint-James. Phys. Letters 24A (1967) 241.
9. V. P. Galaiko.
Soviet Physics JETP 23 (1966) 878. and W. J. Tomasch. Phys. Rev. Letters 12 (1964) 219. R. W. De Blois and W. De Sorbo. Phys. Rev. Letters 12 (1964) 499. G. Boato. G. Gallinaro and C. Rizzuto. Solid State Comm. 3 (1965) 173. J. P. Burger. J. Feder. S. R. Kiser, F. Rothwarf and C. Valette. Low Temperature Conf. Moscou (1966). D. P. Jones and J. G. Park. Phys. Letters 20 (1966) 111; D.K. Finnemore. T. F. Stromberg and C. A. Swenson. Phys. Rev. 149 (1966) 231. K. Maki and T. Tsuzuki. Phys. Rev. 139 (1965) A868: C.Carolli. M. Cyrot and P. G. De Gennes. Solid State Comm. 4 (1966) 17; E. Helfand and N. R. Werthamer. Phys. Rev. 147 (1966) 288.
10. A. S. Joseph 11. 12. 13.
14.
15.
* At the present time there is no available theory for pure superconductors of the second kind, for temperature far from 7’~. In the case of our sample, from magnetization measurements at 4.2oK. we obtain K1 = 1.175 and K2 = 1.675.
IN
KC1
D. BLUMENSTOCK Institut der Technischen Eingegangen
8 May 1967
LETTERS
am 12 April
DOTIERT
MIT
=
HCl
und H. C. WOLF Hochschule Stuttgart 1967
The parelectric resonance spectrum of KCl-crystals doped with HCl is observed at 35 GHz. The resonance line at 7 kV/cm is due to H--ions or HCl-molecules which are able to reorient in the lattice. This line seems to be identical with a line which was attributed to OH--dipoles by Feher et al. in a recent paper.
In den letzten Jahren wurden verschiedene Stijrstellen mit permanentem elektrischem Dipolmoment in Alkalihalogenid-Kristallen bekannt, die noch bei tiefer Temperatur beweglich sind. Kuhn und Liity [l] haben darauf hingewiesen, dass
bei diesen StSrstellen die parelektrische Resonanz als Analogon zur paramagnetischen Resonanz beobachtbar sein sollte. In einer Reihe von Arbeiten [2-41 wurde iiber parelektrische Resonanz von OH-Dipolen in KC1 511