- Email: [email protected]
Ac loss minimum in type II superconductors
Volume hA, number 4
PHYSICS LETTERS
26 May 1980
AC LOSS MINtMUM IN TYPE II SUPERCONDUCTORS M. CISZEK, G. KOZLOWSKI and P. TEKIEL Institute for Low Temperature and Structure Research, Polish Academy of Sciences, 53-529 Wroctaw, Poland
and E.A. GIJSBERTSE
L.J.M. van de KLUNDERT
and
Twente University of Technology, Department ofApplied Physics, Enschede, The Netherlands Received 27 February 1980
Theoretical predictions with respect to a minimum in the ac losses in type IL superconductors are compared with experimental results on Nb 50% Ti and Nb 10% Mo. Extensions of the theory are suggested to explain the deviations.
Recent experiments have shown that the ac losses in superconducting Nb3Ge exhibit a minimum when a dc magnetic induction B0 is superposed on an ac ripple field with amplitude b0 [1]. The occurrence of such a minimum can be explained qualitatively by the critical state model provided that a B-dependence of the critical current density ‘c and/or the critical entry and exit fields Ben(Ba) and Bex(Ba) are taken into account [2] (Ba is the applied magnetic induction). The critical current density/c describes the pinning of flux lines in the bulk of the sample while the surface screening currents are expressed in terms of Ben(Ba) and Bex(Ba). Clem’s calculations predict a minimum at an external field Bmin = Ben(O) when the Bdependence of the critical entry field is considered and a minimum at Bmin lb0 in the case of the Kim-like relation/c(B) =/c(O)(1 + IBIIA) 1 (A is a constant). In this paper we report results of ac loss measurements on Nb—50% Ti and Nb—1O% Mo samples. In both samples a minimum in the ac losses is observed when a dc field is superposed on the ac field. The position of this minimum, however, is not in agreement with the theory. The energy loss is measured with a method similar to the one described by Penczynski [3]. The lossesas in 3) are plotted a Nb—50% Ti slab (20 X 5 X 0.3 mm
a function of static field for various amplitudes in fig. 1. The results for Nb—1O% Mo were published elsewhere [4]. In fig. 2 the external fields at which the minima occur have been plotted against the amplitude of the ac field for both samples. Two deviations with b05aernT —502
1
10
—~
[ws/m2] 18 ~
102
—
—22:9
p
1O~~
I
0
10
I
I
20
40 0
I
50
60
I
70
80 [ml]
Fig. 1.foracvarious losses in a Nb 50% Ti slab as a function of static field amplitudes.
271
Volume 77A, number 4
PHYSICS LETTERS
26 May 1980
40
x
[mT]
0
Nb—50~foTI
30
15
~0
Bmin
I
0
30
40
50
~
60 [ml]
01
[~m] 45
I Q2
:~
I 03
60
I 04
75
05
~d~BQ~Sl
20
25 Fig. 2. The static field at which the mimmum m ac losses occurs as a function of amplitude for Nb—50% Ti and Nb 10% Mo.
30
-
-
2mT
\
\S\
\
B .155mT
\
30 B 0 ..77mT
respect to the theoretical predictions are observed. Even at amplitudes slightly exceeding the field of first penetration the minimum in the ac losses occurs at zero static field. Further increase of the amplitude is necessary to observe a shift of the position of the minimum. Also the point of intersection between the experimental curves and the line Bmin = 0 is larger than the observed field of first penetration which for Nb—50% Ti is about 18 mT. Secondly, the slopes of the curves in fig. 2 are not in agreement with the values 1 and l~ calculated by Clem. Only at large amplitudes the curves for Nb 50% Ti fit the theoretical results in the case of a B-dependent critical current density. For small amplitudes, however, the experimental value lies between the two calculated values, This suggests a combination of surface pinning and bulk pinning. For Nb—10% Mo, however, the slope of the curve is larger than 1, which is in contradiction with theory. In the description of ac losses three different mechanisms can be distinguished: bulk pinning, surface screening and flux flow. The contributions of these mechanisms can be separated experimentally with the help of trapezoidal ac fields [5]. In this way it is p05sible to determine the critical entry and exit fields Ben(Ba) and Bex(Ba) as well as the flux distribution inside the sample. In fig. 3 the flux distribution inside the Nb—50% Ti slab is shown for various external fields. From these curves it is concluded that both surface screening and bulk pinning play a role. At larger fields the surface screening disappears. Also it 272
35 40 [mT]
45
B0 6 ml
Fig. 3. Flux distribution in a Nb—50% Ti slab for various values of the external field (d is half the thickness of the slab: d = 150 i~m).
can be seen that the critical current density in a layer of about 3 pm from the surface is much larger than in the rest of the sample. The occurrence of deviations between theoretical predictions and experimental results may be avoided by removing some limitations in the model. Firstly, the theory is limited to small depths of penetration in comparison to the dimensions of the sample. Secondly, the theory should be extended to include an explicit dependence of the critical current density on the position. So far/c only depends on position through the magnetic induction B. Such an extension is clearly suggested by the experimental results (see fig. 3). Model calculations in which these two limitations are removed are in progress. In these calculations the influence of both surface and bulk currents will be considered. The results will be published in a subsequent paper together with a comparison with the experimental results.
Volume 77A, number 4
PHYSICS LETTERS
References [l] J.D. Thompson, M.P. Maley and J.R. Ciem, J. Appl. Phys. 50 (1979) 3531. [2] J.R. Cbm, J. Appl. Phys. 50 (1979) 3518.
26 May 1980
[ 31 P. Penczynski, Siemens Forsch. Entwickhmgsber.
2 (1973) 296. [4] M. Ciszek, G. Kozlowski and P. Tekiel, Phys. Stat. Sol., to be published. [S] L.J.M. van de Klundert, E.A. Gijsbertse and H.P. van de Braak, Physica 94B (1978) 41.
273
PHYSICS LETTERS
26 May 1980
AC LOSS MINtMUM IN TYPE II SUPERCONDUCTORS M. CISZEK, G. KOZLOWSKI and P. TEKIEL Institute for Low Temperature and Structure Research, Polish Academy of Sciences, 53-529 Wroctaw, Poland
and E.A. GIJSBERTSE
L.J.M. van de KLUNDERT
and
Twente University of Technology, Department ofApplied Physics, Enschede, The Netherlands Received 27 February 1980
Theoretical predictions with respect to a minimum in the ac losses in type IL superconductors are compared with experimental results on Nb 50% Ti and Nb 10% Mo. Extensions of the theory are suggested to explain the deviations.
Recent experiments have shown that the ac losses in superconducting Nb3Ge exhibit a minimum when a dc magnetic induction B0 is superposed on an ac ripple field with amplitude b0 [1]. The occurrence of such a minimum can be explained qualitatively by the critical state model provided that a B-dependence of the critical current density ‘c and/or the critical entry and exit fields Ben(Ba) and Bex(Ba) are taken into account [2] (Ba is the applied magnetic induction). The critical current density/c describes the pinning of flux lines in the bulk of the sample while the surface screening currents are expressed in terms of Ben(Ba) and Bex(Ba). Clem’s calculations predict a minimum at an external field Bmin = Ben(O) when the Bdependence of the critical entry field is considered and a minimum at Bmin lb0 in the case of the Kim-like relation/c(B) =/c(O)(1 + IBIIA) 1 (A is a constant). In this paper we report results of ac loss measurements on Nb—50% Ti and Nb—1O% Mo samples. In both samples a minimum in the ac losses is observed when a dc field is superposed on the ac field. The position of this minimum, however, is not in agreement with the theory. The energy loss is measured with a method similar to the one described by Penczynski [3]. The lossesas in 3) are plotted a Nb—50% Ti slab (20 X 5 X 0.3 mm
a function of static field for various amplitudes in fig. 1. The results for Nb—1O% Mo were published elsewhere [4]. In fig. 2 the external fields at which the minima occur have been plotted against the amplitude of the ac field for both samples. Two deviations with b05aernT —502
1
10
—~
[ws/m2] 18 ~
102
—
—22:9
p
1O~~
I
0
10
I
I
20
40 0
I
50
60
I
70
80 [ml]
Fig. 1.foracvarious losses in a Nb 50% Ti slab as a function of static field amplitudes.
271
Volume 77A, number 4
PHYSICS LETTERS
26 May 1980
40
x
[mT]
0
Nb—50~foTI
30
15
~0
Bmin
I
0
30
40
50
~
60 [ml]
01
[~m] 45
I Q2
:~
I 03
60
I 04
75
05
~d~BQ~Sl
20
25 Fig. 2. The static field at which the mimmum m ac losses occurs as a function of amplitude for Nb—50% Ti and Nb 10% Mo.
30
-
-
2mT
\
\S\
\
B .155mT
\
30 B 0 ..77mT
respect to the theoretical predictions are observed. Even at amplitudes slightly exceeding the field of first penetration the minimum in the ac losses occurs at zero static field. Further increase of the amplitude is necessary to observe a shift of the position of the minimum. Also the point of intersection between the experimental curves and the line Bmin = 0 is larger than the observed field of first penetration which for Nb—50% Ti is about 18 mT. Secondly, the slopes of the curves in fig. 2 are not in agreement with the values 1 and l~ calculated by Clem. Only at large amplitudes the curves for Nb 50% Ti fit the theoretical results in the case of a B-dependent critical current density. For small amplitudes, however, the experimental value lies between the two calculated values, This suggests a combination of surface pinning and bulk pinning. For Nb—10% Mo, however, the slope of the curve is larger than 1, which is in contradiction with theory. In the description of ac losses three different mechanisms can be distinguished: bulk pinning, surface screening and flux flow. The contributions of these mechanisms can be separated experimentally with the help of trapezoidal ac fields [5]. In this way it is p05sible to determine the critical entry and exit fields Ben(Ba) and Bex(Ba) as well as the flux distribution inside the sample. In fig. 3 the flux distribution inside the Nb—50% Ti slab is shown for various external fields. From these curves it is concluded that both surface screening and bulk pinning play a role. At larger fields the surface screening disappears. Also it 272
35 40 [mT]
45
B0 6 ml
Fig. 3. Flux distribution in a Nb—50% Ti slab for various values of the external field (d is half the thickness of the slab: d = 150 i~m).
can be seen that the critical current density in a layer of about 3 pm from the surface is much larger than in the rest of the sample. The occurrence of deviations between theoretical predictions and experimental results may be avoided by removing some limitations in the model. Firstly, the theory is limited to small depths of penetration in comparison to the dimensions of the sample. Secondly, the theory should be extended to include an explicit dependence of the critical current density on the position. So far/c only depends on position through the magnetic induction B. Such an extension is clearly suggested by the experimental results (see fig. 3). Model calculations in which these two limitations are removed are in progress. In these calculations the influence of both surface and bulk currents will be considered. The results will be published in a subsequent paper together with a comparison with the experimental results.
Volume 77A, number 4
PHYSICS LETTERS
References [l] J.D. Thompson, M.P. Maley and J.R. Ciem, J. Appl. Phys. 50 (1979) 3531. [2] J.R. Cbm, J. Appl. Phys. 50 (1979) 3518.
26 May 1980
[ 31 P. Penczynski, Siemens Forsch. Entwickhmgsber.
2 (1973) 296. [4] M. Ciszek, G. Kozlowski and P. Tekiel, Phys. Stat. Sol., to be published. [S] L.J.M. van de Klundert, E.A. Gijsbertse and H.P. van de Braak, Physica 94B (1978) 41.
273