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Observation of enhanced diamagnetism above Tc in bulk superconductors due to thermodynamic fluctuations
OBSERVATION OF ENHANCED DIAMAGNETISM ABOVE T, IN BULK SUPERCONDUCTORS DUE TO THERMODYNAMIC FLUCTUATIONS? J. P. GOLLUB,S Deparlment
M. R. BEASLEY, of Physics
karvard
R. S. NEWBOWER$
and Division
University,
of Engineering
Cambridge,
and M. TINKHAM
andApplied
Massachusetts,
Physics,
USA
Synopsis
Measurements of a temperature-dependent enhanced diamagnetism above T, in pure bulk tin are presented whose behavior is in general agreement with that expected from the effects of thermal fluctuations.
We have previously reported’) measurements of an enhanced diamagnetism2) above T, in bulk indium which we attributed to the effects of thermal fluctuations. In this paper we present. measurements on tin, in which similar behavior is observed. These new results support our identification of the enhanced diamagnetism as a fluctuation effect and also show the same quantitative discrepancies from the recent theoretical calculation of Prange3). The tin sample for which results are reported here was a cylindrical single crystal (4 mm in diameter and 23 mm long) grown from 99.999% purity tin. As before, .we used a superconducting quantum interference magnetometer to measure the change in sample magnetization M as the temperature was decreased toward T, in constant applied fields of a few oersteds. It was suggested in ref. 1 and later shown more rigorously by Prange3) that near T, the data for all fields should lie on a single curve if M/H112 is plotted U~YSUS(T - T,)/H. In fig. 1 we present our results in this form and compare them with the predicted curve4) of Prange. Since we have measured only changes in magnetization with temperature and not the absolute value of the magnetization, the true zero is not known. For purposes of comparison, the data at each field have accordingly been adjusted to agree with the theoretical curve in the region of large (T - TJIH. The data do superimpose except for deviations at low (T - T,)/H which progressively disappear as the field is increased. These deviations were not seen in the earlier work on indium, and are a consequence of the significantly broadened first-order transition5) of t Work supported in part by the National Science Foundation, and the Advanced Research Projects Agency. $ Danforth Foundation Graduate Fellow. g National Science Foundation Graduate Fellow. 303
the Office of Naval Research,
304
J. P. GOLLUB,
M. R. BEASLEY,
R. S. NEWBOWER
AND M. TINKHAM
01 0.3 Oe q 0.6 Oe x 1.0Oe + 2.0 Oe . 3.3 Oe
I
0
0.10
I
I
0.20
0.30
I
0.40
0.50
wk,
Fig. I. Sample magnetization versus temperature, with ordinate and abscissa chosen to exhibit the expected scaling with magnetic field. The baselines for the experimental curves have been adjusted to give the best agreement with Prange’s theoretical result in the region of large (T - T,)/H.
the tin sample as compared to the indium sample of ref. 1. Some minute portions of the sample become superconducting starting about 50 millidegrees earlier than the bulk of the sample, causing the magnetization to rise more steeply than would be the case for the fluctuation effect alone. The effect of the broadening is less important at higher fields, where the fluctuation enhancement is observable over a larger range of temperatures, so that the broadened first-order transition becomes a smaller part of the relevant temperature range. Since temperature is plotted as (T- T,)/H, the broadened region should be progressively compressed in size as the field is increased, as is observed. In fact, a limiting behavioris reached in which the data from different fields do superimpose as expected. This limiting behavior is in qualitative agreement with the predicted curve. We feel that our ability to distinguish in this way between the broadened first-order transition and the fluctuation-enhanced diamagnetism lends additional support to the identification of the fluctuation effect. Figure 2 shows the tin data from fig. 1 and the indium data of ref. 1 plotted together. Those points from the tin data which were in the broadened transition region have been eliminated. The axes are normalized in such a way that the data from all superconductors are predicted? to lie on a universal curve, independent of material parameters. Our tin and indium results do coincide well. The small discrepancies probably do not exceed the experimental
ENHANCED
0
I
DIAMAGNETISM
2
ABOVE
3
4
305
T, IN BULK TIN
5
6
7
Fig. 2. The tin data of fig. 1 and the indium data of ref. 1 plotted together using normalized scales which are expected to bring the points onto a universal curve. The solid line represents Prange’s result.
uncertainty. However, there remains some quantitative discrepancy between I Prange’s calculation and our results. In conclusion, we have observed an enhanced diamagnetism of the expected magnitude in two very pure bulk superconductors which follows a single universal curve for a wide range of magnetic fields. This behavior supports our previous conclusion that the enhancement is due to thermal fluctuations, although some small discrepancies from the theory still remain. We plan to extend the measurements to higher temperatures and fields, and to measure the absolute magnetization in addition to its changes with temperature.
REFERENCES 1) Gollub, J. P., Beasley, M. R., Newbower, R. S. and Tinkham, M., Phys. Rev. Letters 22 (1969) 1288. 2) The earliest theoretical treatments are by Schmidt, H., Z. Phys. 216 (1968) 336 and Schmid, A., Phys. Rev. 180 (1969) 527. 3) Prange, R., Phys. Rev. Bl(1970) 2349. 4) This theroetical curve depends on a parameter IWH,e/dTI = d/2 . KlcW,/dTJ whose relevance to the fluctuation phenomenon is discussed in ref. 1 and 3. This parameter is 19.0 Oe/K for tin and 13.4 Oe/K for indium. 5) The transition to the superconducting state is first order in the presence of a field and occurs at the field-dependent thermodynamic critical temperature.
M. R. BEASLEY, of Physics
karvard
R. S. NEWBOWER$
and Division
University,
of Engineering
Cambridge,
and M. TINKHAM
andApplied
Massachusetts,
Physics,
USA
Synopsis
Measurements of a temperature-dependent enhanced diamagnetism above T, in pure bulk tin are presented whose behavior is in general agreement with that expected from the effects of thermal fluctuations.
We have previously reported’) measurements of an enhanced diamagnetism2) above T, in bulk indium which we attributed to the effects of thermal fluctuations. In this paper we present. measurements on tin, in which similar behavior is observed. These new results support our identification of the enhanced diamagnetism as a fluctuation effect and also show the same quantitative discrepancies from the recent theoretical calculation of Prange3). The tin sample for which results are reported here was a cylindrical single crystal (4 mm in diameter and 23 mm long) grown from 99.999% purity tin. As before, .we used a superconducting quantum interference magnetometer to measure the change in sample magnetization M as the temperature was decreased toward T, in constant applied fields of a few oersteds. It was suggested in ref. 1 and later shown more rigorously by Prange3) that near T, the data for all fields should lie on a single curve if M/H112 is plotted U~YSUS(T - T,)/H. In fig. 1 we present our results in this form and compare them with the predicted curve4) of Prange. Since we have measured only changes in magnetization with temperature and not the absolute value of the magnetization, the true zero is not known. For purposes of comparison, the data at each field have accordingly been adjusted to agree with the theoretical curve in the region of large (T - TJIH. The data do superimpose except for deviations at low (T - T,)/H which progressively disappear as the field is increased. These deviations were not seen in the earlier work on indium, and are a consequence of the significantly broadened first-order transition5) of t Work supported in part by the National Science Foundation, and the Advanced Research Projects Agency. $ Danforth Foundation Graduate Fellow. g National Science Foundation Graduate Fellow. 303
the Office of Naval Research,
304
J. P. GOLLUB,
M. R. BEASLEY,
R. S. NEWBOWER
AND M. TINKHAM
01 0.3 Oe q 0.6 Oe x 1.0Oe + 2.0 Oe . 3.3 Oe
I
0
0.10
I
I
0.20
0.30
I
0.40
0.50
wk,
Fig. I. Sample magnetization versus temperature, with ordinate and abscissa chosen to exhibit the expected scaling with magnetic field. The baselines for the experimental curves have been adjusted to give the best agreement with Prange’s theoretical result in the region of large (T - T,)/H.
the tin sample as compared to the indium sample of ref. 1. Some minute portions of the sample become superconducting starting about 50 millidegrees earlier than the bulk of the sample, causing the magnetization to rise more steeply than would be the case for the fluctuation effect alone. The effect of the broadening is less important at higher fields, where the fluctuation enhancement is observable over a larger range of temperatures, so that the broadened first-order transition becomes a smaller part of the relevant temperature range. Since temperature is plotted as (T- T,)/H, the broadened region should be progressively compressed in size as the field is increased, as is observed. In fact, a limiting behavioris reached in which the data from different fields do superimpose as expected. This limiting behavior is in qualitative agreement with the predicted curve. We feel that our ability to distinguish in this way between the broadened first-order transition and the fluctuation-enhanced diamagnetism lends additional support to the identification of the fluctuation effect. Figure 2 shows the tin data from fig. 1 and the indium data of ref. 1 plotted together. Those points from the tin data which were in the broadened transition region have been eliminated. The axes are normalized in such a way that the data from all superconductors are predicted? to lie on a universal curve, independent of material parameters. Our tin and indium results do coincide well. The small discrepancies probably do not exceed the experimental
ENHANCED
0
I
DIAMAGNETISM
2
ABOVE
3
4
305
T, IN BULK TIN
5
6
7
Fig. 2. The tin data of fig. 1 and the indium data of ref. 1 plotted together using normalized scales which are expected to bring the points onto a universal curve. The solid line represents Prange’s result.
uncertainty. However, there remains some quantitative discrepancy between I Prange’s calculation and our results. In conclusion, we have observed an enhanced diamagnetism of the expected magnitude in two very pure bulk superconductors which follows a single universal curve for a wide range of magnetic fields. This behavior supports our previous conclusion that the enhancement is due to thermal fluctuations, although some small discrepancies from the theory still remain. We plan to extend the measurements to higher temperatures and fields, and to measure the absolute magnetization in addition to its changes with temperature.
REFERENCES 1) Gollub, J. P., Beasley, M. R., Newbower, R. S. and Tinkham, M., Phys. Rev. Letters 22 (1969) 1288. 2) The earliest theoretical treatments are by Schmidt, H., Z. Phys. 216 (1968) 336 and Schmid, A., Phys. Rev. 180 (1969) 527. 3) Prange, R., Phys. Rev. Bl(1970) 2349. 4) This theroetical curve depends on a parameter IWH,e/dTI = d/2 . KlcW,/dTJ whose relevance to the fluctuation phenomenon is discussed in ref. 1 and 3. This parameter is 19.0 Oe/K for tin and 13.4 Oe/K for indium. 5) The transition to the superconducting state is first order in the presence of a field and occurs at the field-dependent thermodynamic critical temperature.