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Investigation of high Tc superconductors by means of torque measurements
Physiea C 153-155 (1988) 1505-1506 North-Holland, Amsterdam
INVESTIGATION
W. A N D ~
OF HIGH T c SUPERCONDUCTORS
(a), H. DANAN
(b), R. HERGT
BY MEANS OF TORQUE MEASUREMENTS
(a), E. JAGER (c), T. KLUPSCH
(a), H. PFEIFFER
(a)
(a) Physikal.-Techn. Institut der Akad. der Wissenschaften der DDR, Helmholtzweg 4, 6900 Jena, GDR (b) Laboratoire P. Weiss, Institut de Physique, 3, rue de l'Universit~, F 67084 Strasbourg, France (c) Ingenieurschule fur Maschinenbau Fritz Heckert, Blechhammer 4-9, 6080 Schmalkalden, GDR
We have calculated and experimentally determined on two samples of YBa2Cu307_ 6 the torque due to the shape anisotropy in a magnetic field. Furthermore we observed in rotating fields losses which are obviously connected with the existence of superconductivity. This effect provides further informations as well as the possibility to detect small volumes of superconducting material.
i. INTRODUCTION Like a ferromagnetic sample an anisotropic superconducting body exposed to a magnetic field exhibits a torque G which can theoretically be derived for simple cases. A comparison with torque measurements supplies values of magnetic parameters. Moreover, in rotating fields losses can appear due to several mechanisms. If the losses can clearly be ascribed to superconductivity, loss measurements may yield further informations and may even be helpful to detect small volume portions of superconducting material. 2. SHAPE ANISOTROPY The torque exerted by an external field H e on a bulk ellipsoid of revolution is given by (i) (~o/2)H~×2(Nz-Nr)sin(2e) G/V = (I+XNz)(I+xN r) where V means the volume and X the susceptibility of the ellipsoid which is assumed to be isotropic. 0 is the angle between the field and the ellipsoid axis. The demagnetizing factors parallel and perpendicular to the axis are denoted by N z and N r, respectively. For the Meissner phase X = -i should be introduced. Samples of high T c superconductors (2,3,4) consist often of superconducting grains weakly coupled together and the formula is to be modified. Mean-field approximation for grains with one X value and diameter well above the penetration depth leads to the modified formula
can be calculated. The ratio ~ = G(exp)/G(calc) may be interpreted as the fraction of the solid phase behaving as Meissner phase. 3. ROTATIONAL LOSSES Losses in slowly rotating fields can be generated by different mechanisms, e.g. eddy currents, motion of magnetic domain walls or irreversible rotation of magnetization. In superconducting material, the pinning of fluxoids is one possible mechanism (5,6). Using a torquemeter, these losses can be measured by determining the area between the two torque curves G(@) for clockwise and counterclockwise rotation of H e where @ is the angle of H e with respect to the sample. 06 I
0.4
~
I I 0.2 ~
~ ~
0 ~....o____ i ~
~ ,
~
2
- 0.2 " ~ , ~
" ~ " ~" ,
,
3
4
H~. ~kAl~l 2
-0.4
-0.6
YB°zCu3Or-
-O.B
Somple U 2.2 Nz= 0"8~ Nr = 0"08
~=-14"
-10
G/V = {l+x(pNz+(l_p)/3)}{l+×(PNr+(l_p)/3)}
FIGURE i Torque density G/V as a function of the external field H e for constant angle 6 in increasing (o) and decreasing (e) field at T = 79 K.
where p means the ratio of the actual density and the theoretical density. (i) Introducing experimental values of G/V and the known parameters of the right hand side two values are obtained as solutions of a quadratic equation. (ii) If X = -1 is introduced, a value of G
4. EXPERIMENTAL RESULTS AND DISCUSSION 4.1. Shape anisotropy The dependence of the torque G as a function of H e for a pellet of YBa2Cu307_ ~ is shown in Fig. i. The experimental points verify the theoretically expected proportionality up to about H e = 1.4 kA/m (17.60e). The deviation in higher
(~o/2)H~x2p2(Nz-Nr)sin(20)
0921 4534/88/$03.50 ©Elsevier Science Publishers B.V. (North-HoUand Physics Publishing Division)
W. Andrii et al. /Investigation of high-Tc superconductors
1506
fields may be caused by exceeding partially Hcl. This sample exhibits rotational losses which could be detected above H e = 2.4 kA/m. Using the measured value p = 0.58 the procedure (i) yields X = -0.95. Taking X = -i the procedure (ii) gives n = 0.83 indicating that 17% of the solid sample volume does not behave as Meissner phase caused either by impurities or by the finite penetration depths. 4.2. Rotational losses The volume density of rotational losses per angle unit Lrot/V is plotted as function of the temperature and of the field strength in Fig. 2 and 3. Eddy-current losses could be ruled out in additional investigations which showed an increase of Lro t by only 15% for an increase of the angular velocity ~ by a factor of 17. Lrot/V decreases rapidly and tends to zero near 85 K (Fig. 2) indicating a connection with the existence of superconductivity. The abrupt increase of Lrot/V beyond H o = 6.4 kA/m (Fig. 3) may be connected either with the lower critical field strength Hcl or with the minimum torque necessary to overcome flux pinning. Hcl measured by Isikawa e.a. (7) is of the same order of magnitude as H o.
"8 YBo~Cu307.,~
40 Somp[e
~
S3
I
30
~ 2o
10
,
~0y~_ ......~ --A~'I" I 4o
>
.~
2o
0 0
i
0
!
200
i
!
I
61
400 He , k A I m
10
i
i
O0
800
20 i
1000
=
FIGURE 3 Density of rotational losses Lrot/V as a function of the field amplitude H e for constant temperature T and constan t angular velocity ~. The different symbols denote : T = 80 K, m = O.i s-I (o) ; T = 80.5 K, ~ = 0.2 s -I (.) ; T = 79 K, = O.i s -I (n). conductivity. The dependence of Lro t on temperature and field strength may furnish some information with respect to different parameters (lower critical field, pinning forces, etc.). The existence of losses may be an indicator for the existence of superconducting material : our torquemeter seems to allow the detection of superconducting volumes V m = 10 -5 cm 3. However, there are possibilities to increase the sensitivity by more than one order of magnitude. ACKNOWLEDGEMENTS We would like to thank Dr. Villeminot from the Laboratory of Professor Bernier, ULP Strasbourg, for kindly providing the sample $3.
o
t
60
,~-T-
-=-- T ' - - , - - . - , -'°"
80
90
100
T,K
FIGURE 2 Density of rotational losses Lrot/V as a function of temperature in a rotating field of constant amplitude H e = 334 kA/m (4.2 kOe) with the angular velocity m = 0.2 s -I. 5. CONCLUSIONS A simple model for the torque exerted by an external field on a granular superconducting ellipsoid could experimentally be verified and gives the possibility to determine different material parameters. Rotational losses Lro t were found below the critical temperature of YBa2Cu307_ 6 which are obviously connected with the existence of super-
REFERENCES (i) L.D. Landau and E.M. Lifschitz, Elektrodynamik der Kontinua (Akademie-Verlag, Berlin 1967). (2) J.G. Bednorz and K.A. M~ller, Z. Phys. B64 (1986) 189. (3) M.K. Wu, J.R. Ashburn, C.J. Torng, P.H. Hor, R.L. Meng, L. Gao, Z.J. Huang, Y.Q. Wang and C.W. Chu, Phys. Rev. Letters 58 (1987) 908. (4) J.G. Bednorz, M. Takashige and K.A. M~ller, Europhys. Lett. 3 (1987) 379. (5) B.H. Heise, Rev. Mod. Phys. 36 (1964) 64. (6) C. Giovannella, G. Collin and I.A. Campbell, J. Physique 48 (1987) 1835. (7) Y. Isikawa, K. Mori, K. Kobayashi and K. Sato, Jap. J. Appl. Phys. 26 (1987) L1535.
INVESTIGATION
W. A N D ~
OF HIGH T c SUPERCONDUCTORS
(a), H. DANAN
(b), R. HERGT
BY MEANS OF TORQUE MEASUREMENTS
(a), E. JAGER (c), T. KLUPSCH
(a), H. PFEIFFER
(a)
(a) Physikal.-Techn. Institut der Akad. der Wissenschaften der DDR, Helmholtzweg 4, 6900 Jena, GDR (b) Laboratoire P. Weiss, Institut de Physique, 3, rue de l'Universit~, F 67084 Strasbourg, France (c) Ingenieurschule fur Maschinenbau Fritz Heckert, Blechhammer 4-9, 6080 Schmalkalden, GDR
We have calculated and experimentally determined on two samples of YBa2Cu307_ 6 the torque due to the shape anisotropy in a magnetic field. Furthermore we observed in rotating fields losses which are obviously connected with the existence of superconductivity. This effect provides further informations as well as the possibility to detect small volumes of superconducting material.
i. INTRODUCTION Like a ferromagnetic sample an anisotropic superconducting body exposed to a magnetic field exhibits a torque G which can theoretically be derived for simple cases. A comparison with torque measurements supplies values of magnetic parameters. Moreover, in rotating fields losses can appear due to several mechanisms. If the losses can clearly be ascribed to superconductivity, loss measurements may yield further informations and may even be helpful to detect small volume portions of superconducting material. 2. SHAPE ANISOTROPY The torque exerted by an external field H e on a bulk ellipsoid of revolution is given by (i) (~o/2)H~×2(Nz-Nr)sin(2e) G/V = (I+XNz)(I+xN r) where V means the volume and X the susceptibility of the ellipsoid which is assumed to be isotropic. 0 is the angle between the field and the ellipsoid axis. The demagnetizing factors parallel and perpendicular to the axis are denoted by N z and N r, respectively. For the Meissner phase X = -i should be introduced. Samples of high T c superconductors (2,3,4) consist often of superconducting grains weakly coupled together and the formula is to be modified. Mean-field approximation for grains with one X value and diameter well above the penetration depth leads to the modified formula
can be calculated. The ratio ~ = G(exp)/G(calc) may be interpreted as the fraction of the solid phase behaving as Meissner phase. 3. ROTATIONAL LOSSES Losses in slowly rotating fields can be generated by different mechanisms, e.g. eddy currents, motion of magnetic domain walls or irreversible rotation of magnetization. In superconducting material, the pinning of fluxoids is one possible mechanism (5,6). Using a torquemeter, these losses can be measured by determining the area between the two torque curves G(@) for clockwise and counterclockwise rotation of H e where @ is the angle of H e with respect to the sample. 06 I
0.4
~
I I 0.2 ~
~ ~
0 ~....o____ i ~
~ ,
~
2
- 0.2 " ~ , ~
" ~ " ~" ,
,
3
4
H~. ~kAl~l 2
-0.4
-0.6
YB°zCu3Or-
-O.B
Somple U 2.2 Nz= 0"8~ Nr = 0"08
~=-14"
-10
G/V = {l+x(pNz+(l_p)/3)}{l+×(PNr+(l_p)/3)}
FIGURE i Torque density G/V as a function of the external field H e for constant angle 6 in increasing (o) and decreasing (e) field at T = 79 K.
where p means the ratio of the actual density and the theoretical density. (i) Introducing experimental values of G/V and the known parameters of the right hand side two values are obtained as solutions of a quadratic equation. (ii) If X = -1 is introduced, a value of G
4. EXPERIMENTAL RESULTS AND DISCUSSION 4.1. Shape anisotropy The dependence of the torque G as a function of H e for a pellet of YBa2Cu307_ ~ is shown in Fig. i. The experimental points verify the theoretically expected proportionality up to about H e = 1.4 kA/m (17.60e). The deviation in higher
(~o/2)H~x2p2(Nz-Nr)sin(20)
0921 4534/88/$03.50 ©Elsevier Science Publishers B.V. (North-HoUand Physics Publishing Division)
W. Andrii et al. /Investigation of high-Tc superconductors
1506
fields may be caused by exceeding partially Hcl. This sample exhibits rotational losses which could be detected above H e = 2.4 kA/m. Using the measured value p = 0.58 the procedure (i) yields X = -0.95. Taking X = -i the procedure (ii) gives n = 0.83 indicating that 17% of the solid sample volume does not behave as Meissner phase caused either by impurities or by the finite penetration depths. 4.2. Rotational losses The volume density of rotational losses per angle unit Lrot/V is plotted as function of the temperature and of the field strength in Fig. 2 and 3. Eddy-current losses could be ruled out in additional investigations which showed an increase of Lro t by only 15% for an increase of the angular velocity ~ by a factor of 17. Lrot/V decreases rapidly and tends to zero near 85 K (Fig. 2) indicating a connection with the existence of superconductivity. The abrupt increase of Lrot/V beyond H o = 6.4 kA/m (Fig. 3) may be connected either with the lower critical field strength Hcl or with the minimum torque necessary to overcome flux pinning. Hcl measured by Isikawa e.a. (7) is of the same order of magnitude as H o.
"8 YBo~Cu307.,~
40 Somp[e
~
S3
I
30
~ 2o
10
,
~0y~_ ......~ --A~'I" I 4o
>
.~
2o
0 0
i
0
!
200
i
!
I
61
400 He , k A I m
10
i
i
O0
800
20 i
1000
=
FIGURE 3 Density of rotational losses Lrot/V as a function of the field amplitude H e for constant temperature T and constan t angular velocity ~. The different symbols denote : T = 80 K, m = O.i s-I (o) ; T = 80.5 K, ~ = 0.2 s -I (.) ; T = 79 K, = O.i s -I (n). conductivity. The dependence of Lro t on temperature and field strength may furnish some information with respect to different parameters (lower critical field, pinning forces, etc.). The existence of losses may be an indicator for the existence of superconducting material : our torquemeter seems to allow the detection of superconducting volumes V m = 10 -5 cm 3. However, there are possibilities to increase the sensitivity by more than one order of magnitude. ACKNOWLEDGEMENTS We would like to thank Dr. Villeminot from the Laboratory of Professor Bernier, ULP Strasbourg, for kindly providing the sample $3.
o
t
60
,~-T-
-=-- T ' - - , - - . - , -'°"
80
90
100
T,K
FIGURE 2 Density of rotational losses Lrot/V as a function of temperature in a rotating field of constant amplitude H e = 334 kA/m (4.2 kOe) with the angular velocity m = 0.2 s -I. 5. CONCLUSIONS A simple model for the torque exerted by an external field on a granular superconducting ellipsoid could experimentally be verified and gives the possibility to determine different material parameters. Rotational losses Lro t were found below the critical temperature of YBa2Cu307_ 6 which are obviously connected with the existence of super-
REFERENCES (i) L.D. Landau and E.M. Lifschitz, Elektrodynamik der Kontinua (Akademie-Verlag, Berlin 1967). (2) J.G. Bednorz and K.A. M~ller, Z. Phys. B64 (1986) 189. (3) M.K. Wu, J.R. Ashburn, C.J. Torng, P.H. Hor, R.L. Meng, L. Gao, Z.J. Huang, Y.Q. Wang and C.W. Chu, Phys. Rev. Letters 58 (1987) 908. (4) J.G. Bednorz, M. Takashige and K.A. M~ller, Europhys. Lett. 3 (1987) 379. (5) B.H. Heise, Rev. Mod. Phys. 36 (1964) 64. (6) C. Giovannella, G. Collin and I.A. Campbell, J. Physique 48 (1987) 1835. (7) Y. Isikawa, K. Mori, K. Kobayashi and K. Sato, Jap. J. Appl. Phys. 26 (1987) L1535.