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Magnetization curves and the scaled Jc characteristics in various superconductors
Physica C 426–431 (2005) 726–730 www.elsevier.com/locate/physc
Magnetization curves and the scaled Jc characteristics in various superconductors N. Sakamoto a
a,*
, T. Akune a, Y. Matsumoto b, H.R. Khan c, K. Lu¨ders
d
Department of Electrical Engineering, Kyushu Sangyo University, 2-3-1 Matsukadai, 813-8503 Fukuoka, Japan b Department of Electrical Engineering, Fukuoka University, 8-19-1 Nanakuma, 814-0180 Fukuoka, Japan c Forschungsinstitut fu¨r Edelmetalle und Metallchemie, D-73525 Schwaebisch Gmu¨nd, Germany d Freie Universita¨t Berlin, Institut fu¨r Experimentalphysik, 14 Arnimallee, D-14195 Berlin, Germany Received 23 November 2004; accepted 25 January 2005 Available online 15 July 2005
Abstract From the shape of magnetization curves, the important superconducting characteristics can be evaluated. The critical current densities, the irreversibility fields and the losses of the superconductors can be estimated from hysteretic curves. Magnetic field and temperature dependence of the pinning strength Fp in type-II superconductors is known to be well described by the scaling law of the pinning force as F p ¼ AH mc2 ðB=Bc2 Þc ð1 B=Bc2 Þd , where Hc2 is the upper critical field, c, d and m are the pinning parameters. In high temperature superconductors, the scaling law fails to describe the pinning properties since the irreversibility field Birr is much smaller than the upper critical field Bc2. Conversion of field dependence term in the scaling law is accomplished by replacing Bc2 by Birr. The magnetization curves differentially computed using the scaled Jc with the pinning parameters of c, d and m show various shapes and can be fitted well to the observed curves of MgB2 and Ag–Hg1223 superconductors in a wide range of temperature and magnetic field. Ó 2005 Elsevier B.V. All rights reserved. Keywords: Magnetization; MgB2; Ag–Hg1223; Scaling law
1. Introduction High temperature superconductors attract high interest for practical application due to their the *
Corresponding author. Fax: +81 092 673 5091. E-mail address: [email protected] (N. Sakamoto).
highest critical temperature Tc up to 135 K of Hg-based cuprate compounds [1]. Hysteretic magnetization curves of these superconductors give many useful quantities; critical current densities Jc, irreversibility fields Birr and ac losses. The electromagnetic behavior of type-II superconductors is well described by the critical state model,
0921-4534/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2005.01.047
N. Sakamoto et al. / Physica C 426–431 (2005) 726–730
where the field or current density distribution is determined by the force balance equation between the pinning force densities Fp and the Lorentz force densities. Temperature and magnetic field dependence of Fp is well described by the scaling law [2]. Magnetization and ac susceptibility are computed from this force balance based on the scaling law and satisfactorily compared with the observation in type-II superconductors. In oxide superconductors the pinning properties disappear at the irreversibility field Birr much lower than Bc2. In this report replacement of Bc2 by Birr in the scaling formula is accomplished and magnetization M are evaluated. Magnetization of Agx(HgBa1.9Bi0.1Ca2Cu3O8+d)1x composites (x = 0.2) and MgB2 superconductors is measured. Scaling parameters available in the wide range of temperature and field can be obtained. Magnetization curves are numerically computed using the scaling law and agree well with the observed data.
2. Magnetization curves computed from the scaling law The pinning force density Fp at a temperature T and a magnetic field B is well known to follow the scaling law [2] F p ¼ AH mc2 ðT Þbc ð1 bÞd c d B B m ¼ AH c2 ðT Þ 1 ; Birr Birr
ð1Þ
where the upper critical field Bc2 is replaced by the irreversibility field Birr since the Birr is much smaller than Bc2 in the high Tc superconductors [3]. Then the critical current density Jc is given by 2 m1
J c ¼ J c ð1 t Þ
B Birr
c1
B 1 Birr
d ;
ð2Þ
where Jc is defined as the Jc at T = 0, B = 0 and m1 c = 1 and given by J c ¼ lm A. By explic0 Bc2 ð0Þ itly expressing the temperature variation of the irreversibility field Birr(T) = Birr(0)(1 t2)n, where t = T/Tc [4],
727
c1 B Birr ð0Þ d B 1 1 . n Birr ð0Þ ð1 t2 Þ
J c ¼ J c ð1 t2 Þm1þnð1cÞ
ð3Þ
Flux distribution in the superconducting slab with a half thickness d is given by using the Maxwell equation and the critical state model, DBðxÞ ¼ l0 J c ðT ; B; xÞ. Dx
ð4Þ
By a differential computation of the above equations, the field distribution of B(x) is obtained and the pinning characteristic field Bp at which the field front reaches the center of the superconductor is determined. The magnetization M at an applied field B0 is given using the averaged flux density hBi as [5] M ¼ hBi B0 .
ð5Þ
The symmetric and well observed magnetization curves at several temperatures of T/Tc = 0.2, 0.4, 0.6, 0.8 are drawn in Fig. 1(a) in the case of c = 0.5, n = 3, Birr(0)/Bc = 100, m = 4 and d = 2, where Bc is defined as Bc = ldJc. The magnetization curves for c = 0, 0.2, 0.4, 0.6, 0.8, 1 and d = 1, 2, 3 are plotted in Fig. 1(b) and (c). Various curve shapes are produced by adjusting the pinning parameters c, n, m and d.
3. Experimental Commercial MgB2 powder (Alfa Aesar Co., 98% purity) was ground in an agate mortor and were divided into three samples with different particle size 45 < d < 50 lm (MgB2-45) 50 < d < 75 lm (MgB2-50) and 75 < d < 100 lm (MgB275) by sieves with several mesh sizes [6]. These powders were fixed in epoxy resin. The critical temperatures observed from the temperature dependence of magnetic moment are 38.5 K. Ag-mixed Hg1223 superconductors Agx(HgBa1.9Bi0.1Ca2Cu3O8+d)1x(x = 0.2 named as Ag-02) were synthesized by direct route without preparation of precursor as described in the preceding paper [7]. The critical temperature is 131 K.
728
N. Sakamoto et al. / Physica C 426–431 (2005) 726–730 5 0.2
M / Bγ
0
a
0 B / Bγ
0
M / Bγ
n=3 γ = 0.5 m=4 δ =2
0.6
–5 –100
10
T / Tc = 0.2~0.8 Birr(0) / Bγ = 100
–10 –100
100
0 B / Bγ
b
100
δ = 1~3 T / Tc = 0.2 Birr(0) / B = 100 n=3 m=4 γ = 0.5
5
1 M / Bγ
0.6 0
γ = 0~1 T / Tc = 0.2 Birr(0) / Bγ = 100 n=3 m=4 δ =2
0 3
–5 –100
0
100
B / Bγ
c
Fig. 1. Magnetization curves differentially computed using the scaling law of the pinning force density, where the upper critical field Bc2 is replaced by the irreversibility field Birr. (a) Computed magnetization curves at temperatures T/Tc = 0.2–0.8 and the pinning parameters: c = 0.5, n = 3, Birr(0)/Bc = 100, m = 4 and d = 2, where Bc is defined as Bc = ldJc. (b) Computed magnetization curves for c = 0, 0.2, 0.4, 0.6, 0.8 and 1 at the temperatures T/Tc = 0.2. (c) Magnetization curves for d = 1, 2 and 3 at the temperatures T/Tc = 0.2.
The superconducting volumes were estimated from the temperature dependence of the Meissner magnetization slopes. DC magnetizations were measured using SQUID and PPMS magnetometers.
4. Results and discussion Hysteresis width DM of a slab with thickness d gives the critical current density as J c ¼ DM=l0 d.
ð6Þ
At first the availability of the scaling law is examined in the metallic superconductor MgB2. Fig. 2 depicts the observed hysteresis width DM for the sample MgB2-45 at temperatures of 5, 10, 15, 20, 25 and 30 K. Solid lines using Eq. (3) give a satisfactory agreement with the observed data, where the pinning parameters are c 0.4, n = 2, m = 2, d = 2, Birr(0) = 10.4 T and Tc = 38.5 K. The field distributions B(x) are numerically determined using Eqs. (3) and (4). Magnetizations are computed by Eq. (5) using the numerically averaged field hBi. The final results of M are shown as solid lines in Fig. 3. They agree well with the
N. Sakamoto et al. / Physica C 426–431 (2005) 726–730 10
729
0
MgB2–45
T= 20 K 0.2
5 10
15
10
M (T)
∆M (T)
20 25 -2
30
n=2
T (K)
γ ~ 0.4 10
Birr (0) = 10.4 T
–0.2
0
1
B (T)
Fig. 2. Field dependence of the hysteresis width DM for the sample MgB2-45 at temperatures of 5, 10, 20, 25 and 30 K. Solid lines computed differentially using Eq. (3) agree with the observed data, where the pinning parameters are c 0.4, n = 2, m = 2, d = 2, Birr(0) = 10.4 T and Tc = 38.5 K.
MgB2 – 45
T (K) = 5, 10, 15, 20, 25, 30
0.2
5K
M (T)
Bγ (mT)
n=2
MgB2 – 45
32
γ ~ 0.4
MgB2 – 50 MgB2 – 75
39
m=2
63
δ=2
T c= 38.5 K
m=2 δ=2 Bγ = 32 mT
-4
0
0
–1
0
Fig. 4. Hysteretic magnetization curves of the sample MgB2-45, MgB2-50 and MgB2-75 at T = 20 K.
ing law represents quite well the temperature and field dependence in the metallic superconductor MgB2. Magnetization curves of Ag–Hg1223 superconductor at temperatures of 20, 30, 40, 50, 60, 70 and 77 K are shown in Fig. 5. An asymmetric diamag-
0.1
Ag 02
10
Tc = 38.5 K Birr (0) = 10.4 T –1
0
1
B (T)
10 10
30 K
–2
–3
T (K)
–4
0
0.5 B (T)
1
0
Fig. 3. Hysteretic magnetization curves of the sample MgB2-45. Solid lines are computed differentially using Eqs. (4) and (5).
measured data except the low field region, where the magnetic field scarcely penetrate into the superconductor. The observed and numerically computed magnetizations of MgB2-45, MgB2-50 and MgB2-75 are compared in Fig. 4. Here the calculated curves fit well the measured data in the whole range of temperature. It indicates the scal-
10
Ag 02
–1
20 K
M (T)
–0.2
∆M (T)
T (K) = 20, 30, 40, 50, 60, 70, 77
n=2 γ ~ 0.4 m=2 δ=2 Bγ = 32 mT
1
B (T)
–0.1
n = 3.4 γ ~ 0.4 m=6 δ =2 Bγ = 18 mT –1
Tc = 131 K Birr (0) = 8.15 T 0
1
B (T) Fig. 5. Asymmetric magnetization curves of Hg1223 sample Ag-02 at T = 20, 30, 40, 50, 60, 70 and 77 K. Solid lines are numerically calculated taking into consideration of the field step DBs induced by Meissner shielding current at the surface.
730
N. Sakamoto et al. / Physica C 426–431 (2005) 726–730
netic nature is observed. It is well known that the magnetic field just inside the superconductor Bs differs from the applied magnetic field B0 due to a Meissner shielding current flowing along the surface [6]. Then the field is expressed as Bs = B0 DBs, where DBs is the magnetic field step at the surface. The field Bs is used for numerical computation of Eqs. (4) and (5). The irreversibility field and critical temperature are Birr(0) = 8.15 T and Tc = 131 K. The pinning parameters are estimated to be c 0.4, n = 2, m = 2, d = 2 from measured DM data shown in the inset of Fig. 5. Introduction of the field step at the surface results in a better agreement of M. For example the magnetization M curve at T = 20 K is fitted well when DBs = 15 mT. This is closely related to the effectiveness of the surface property in Hg1223 superconductors. MÕs at different temperatures are summarized in Fig. 5. Good agreement of the computed curves indicates the validity of the scaling law of the pinning force density for the MgB2 and Ag–Hg1223 superconductors. 5. Conclusions Pinning parameters in the scaling law are evaluated from the measured magnetization width. Field distributions are differentially calculated using the parameters and the hysteric magnetization characteristics are obtained from the averaged field. In several particle sizes of MgB2, the scaling law corresponds well to the field and temperature dependence of the critical current density Jc.
Numerically computed magnetization curves agree well with the observation. Ag-mixed composites of Agx(HgBa1.9Bi0.1Ca2Cu3O8+d)1x (x = 0.2) superconductor showed high critical temperatures Tc = 131 K. Scaling law of the pinning force density describes well the temperature and field dependence of Jc when Bc2 is replaced by the irreversibility field Birr. Introduction of the field steps at the surface leads to a good agreement with the measured data with an asymmetric nature. The scaling law of the pinning force density Fp using the irreversibility field Birr is confirmed to describe successfully the field and temperature dependence in the metallic MgB2 and high-Tc Hg1223 superconductors.
References [1] S. Noguchi, T. Akune, N. Sakamoto, H.R. Khan, K. Lu¨ders, Physica C 378–381 (2002) 381. [2] A.M. Campbell, J.E. Evetts, Adv. Phys. 21 (1972) 372. [3] K. Noda, M. Nozue, E.S. Otabe, T. Matsushita, T. Umemura, S. Miyashita, H. Higuma, F. Uchikawa, Adv. Supercond. 7 (1995) 501. [4] T. Matsushita, T. Nakatani, E.S. Otabe, K. Yamafuji, K. Takamuku, N. Kosizuka, Jpn. J. Appl. Phys. 32 (1993) L720. [5] N. Sakamoto, T. Ohashi, T. Akune, Y. Matsumoto, in: A. Andreone et al. (Eds.), Applied Superconductivity 2003, Inst. Phys. Conf. Series, 181, Inst Phys. Pub., Bristol and Philadelphia, 2004, p. 2202. [6] T. Akune, H. Abe, A. Koga, N. Sakamoto, Y. Matsumoto, Physica C 378–381 (2002) 234. [7] T. Ohashi, T. Akune, N. Sakamoto, H.R. Khan, K. Lu¨ders, Physica C 392–396 (2003) 373.
Magnetization curves and the scaled Jc characteristics in various superconductors N. Sakamoto a
a,*
, T. Akune a, Y. Matsumoto b, H.R. Khan c, K. Lu¨ders
d
Department of Electrical Engineering, Kyushu Sangyo University, 2-3-1 Matsukadai, 813-8503 Fukuoka, Japan b Department of Electrical Engineering, Fukuoka University, 8-19-1 Nanakuma, 814-0180 Fukuoka, Japan c Forschungsinstitut fu¨r Edelmetalle und Metallchemie, D-73525 Schwaebisch Gmu¨nd, Germany d Freie Universita¨t Berlin, Institut fu¨r Experimentalphysik, 14 Arnimallee, D-14195 Berlin, Germany Received 23 November 2004; accepted 25 January 2005 Available online 15 July 2005
Abstract From the shape of magnetization curves, the important superconducting characteristics can be evaluated. The critical current densities, the irreversibility fields and the losses of the superconductors can be estimated from hysteretic curves. Magnetic field and temperature dependence of the pinning strength Fp in type-II superconductors is known to be well described by the scaling law of the pinning force as F p ¼ AH mc2 ðB=Bc2 Þc ð1 B=Bc2 Þd , where Hc2 is the upper critical field, c, d and m are the pinning parameters. In high temperature superconductors, the scaling law fails to describe the pinning properties since the irreversibility field Birr is much smaller than the upper critical field Bc2. Conversion of field dependence term in the scaling law is accomplished by replacing Bc2 by Birr. The magnetization curves differentially computed using the scaled Jc with the pinning parameters of c, d and m show various shapes and can be fitted well to the observed curves of MgB2 and Ag–Hg1223 superconductors in a wide range of temperature and magnetic field. Ó 2005 Elsevier B.V. All rights reserved. Keywords: Magnetization; MgB2; Ag–Hg1223; Scaling law
1. Introduction High temperature superconductors attract high interest for practical application due to their the *
Corresponding author. Fax: +81 092 673 5091. E-mail address: [email protected] (N. Sakamoto).
highest critical temperature Tc up to 135 K of Hg-based cuprate compounds [1]. Hysteretic magnetization curves of these superconductors give many useful quantities; critical current densities Jc, irreversibility fields Birr and ac losses. The electromagnetic behavior of type-II superconductors is well described by the critical state model,
0921-4534/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2005.01.047
N. Sakamoto et al. / Physica C 426–431 (2005) 726–730
where the field or current density distribution is determined by the force balance equation between the pinning force densities Fp and the Lorentz force densities. Temperature and magnetic field dependence of Fp is well described by the scaling law [2]. Magnetization and ac susceptibility are computed from this force balance based on the scaling law and satisfactorily compared with the observation in type-II superconductors. In oxide superconductors the pinning properties disappear at the irreversibility field Birr much lower than Bc2. In this report replacement of Bc2 by Birr in the scaling formula is accomplished and magnetization M are evaluated. Magnetization of Agx(HgBa1.9Bi0.1Ca2Cu3O8+d)1x composites (x = 0.2) and MgB2 superconductors is measured. Scaling parameters available in the wide range of temperature and field can be obtained. Magnetization curves are numerically computed using the scaling law and agree well with the observed data.
2. Magnetization curves computed from the scaling law The pinning force density Fp at a temperature T and a magnetic field B is well known to follow the scaling law [2] F p ¼ AH mc2 ðT Þbc ð1 bÞd c d B B m ¼ AH c2 ðT Þ 1 ; Birr Birr
ð1Þ
where the upper critical field Bc2 is replaced by the irreversibility field Birr since the Birr is much smaller than Bc2 in the high Tc superconductors [3]. Then the critical current density Jc is given by 2 m1
J c ¼ J c ð1 t Þ
B Birr
c1
B 1 Birr
d ;
ð2Þ
where Jc is defined as the Jc at T = 0, B = 0 and m1 c = 1 and given by J c ¼ lm A. By explic0 Bc2 ð0Þ itly expressing the temperature variation of the irreversibility field Birr(T) = Birr(0)(1 t2)n, where t = T/Tc [4],
727
c1 B Birr ð0Þ d B 1 1 . n Birr ð0Þ ð1 t2 Þ
J c ¼ J c ð1 t2 Þm1þnð1cÞ
ð3Þ
Flux distribution in the superconducting slab with a half thickness d is given by using the Maxwell equation and the critical state model, DBðxÞ ¼ l0 J c ðT ; B; xÞ. Dx
ð4Þ
By a differential computation of the above equations, the field distribution of B(x) is obtained and the pinning characteristic field Bp at which the field front reaches the center of the superconductor is determined. The magnetization M at an applied field B0 is given using the averaged flux density hBi as [5] M ¼ hBi B0 .
ð5Þ
The symmetric and well observed magnetization curves at several temperatures of T/Tc = 0.2, 0.4, 0.6, 0.8 are drawn in Fig. 1(a) in the case of c = 0.5, n = 3, Birr(0)/Bc = 100, m = 4 and d = 2, where Bc is defined as Bc = ldJc. The magnetization curves for c = 0, 0.2, 0.4, 0.6, 0.8, 1 and d = 1, 2, 3 are plotted in Fig. 1(b) and (c). Various curve shapes are produced by adjusting the pinning parameters c, n, m and d.
3. Experimental Commercial MgB2 powder (Alfa Aesar Co., 98% purity) was ground in an agate mortor and were divided into three samples with different particle size 45 < d < 50 lm (MgB2-45) 50 < d < 75 lm (MgB2-50) and 75 < d < 100 lm (MgB275) by sieves with several mesh sizes [6]. These powders were fixed in epoxy resin. The critical temperatures observed from the temperature dependence of magnetic moment are 38.5 K. Ag-mixed Hg1223 superconductors Agx(HgBa1.9Bi0.1Ca2Cu3O8+d)1x(x = 0.2 named as Ag-02) were synthesized by direct route without preparation of precursor as described in the preceding paper [7]. The critical temperature is 131 K.
728
N. Sakamoto et al. / Physica C 426–431 (2005) 726–730 5 0.2
M / Bγ
0
a
0 B / Bγ
0
M / Bγ
n=3 γ = 0.5 m=4 δ =2
0.6
–5 –100
10
T / Tc = 0.2~0.8 Birr(0) / Bγ = 100
–10 –100
100
0 B / Bγ
b
100
δ = 1~3 T / Tc = 0.2 Birr(0) / B = 100 n=3 m=4 γ = 0.5
5
1 M / Bγ
0.6 0
γ = 0~1 T / Tc = 0.2 Birr(0) / Bγ = 100 n=3 m=4 δ =2
0 3
–5 –100
0
100
B / Bγ
c
Fig. 1. Magnetization curves differentially computed using the scaling law of the pinning force density, where the upper critical field Bc2 is replaced by the irreversibility field Birr. (a) Computed magnetization curves at temperatures T/Tc = 0.2–0.8 and the pinning parameters: c = 0.5, n = 3, Birr(0)/Bc = 100, m = 4 and d = 2, where Bc is defined as Bc = ldJc. (b) Computed magnetization curves for c = 0, 0.2, 0.4, 0.6, 0.8 and 1 at the temperatures T/Tc = 0.2. (c) Magnetization curves for d = 1, 2 and 3 at the temperatures T/Tc = 0.2.
The superconducting volumes were estimated from the temperature dependence of the Meissner magnetization slopes. DC magnetizations were measured using SQUID and PPMS magnetometers.
4. Results and discussion Hysteresis width DM of a slab with thickness d gives the critical current density as J c ¼ DM=l0 d.
ð6Þ
At first the availability of the scaling law is examined in the metallic superconductor MgB2. Fig. 2 depicts the observed hysteresis width DM for the sample MgB2-45 at temperatures of 5, 10, 15, 20, 25 and 30 K. Solid lines using Eq. (3) give a satisfactory agreement with the observed data, where the pinning parameters are c 0.4, n = 2, m = 2, d = 2, Birr(0) = 10.4 T and Tc = 38.5 K. The field distributions B(x) are numerically determined using Eqs. (3) and (4). Magnetizations are computed by Eq. (5) using the numerically averaged field hBi. The final results of M are shown as solid lines in Fig. 3. They agree well with the
N. Sakamoto et al. / Physica C 426–431 (2005) 726–730 10
729
0
MgB2–45
T= 20 K 0.2
5 10
15
10
M (T)
∆M (T)
20 25 -2
30
n=2
T (K)
γ ~ 0.4 10
Birr (0) = 10.4 T
–0.2
0
1
B (T)
Fig. 2. Field dependence of the hysteresis width DM for the sample MgB2-45 at temperatures of 5, 10, 20, 25 and 30 K. Solid lines computed differentially using Eq. (3) agree with the observed data, where the pinning parameters are c 0.4, n = 2, m = 2, d = 2, Birr(0) = 10.4 T and Tc = 38.5 K.
MgB2 – 45
T (K) = 5, 10, 15, 20, 25, 30
0.2
5K
M (T)
Bγ (mT)
n=2
MgB2 – 45
32
γ ~ 0.4
MgB2 – 50 MgB2 – 75
39
m=2
63
δ=2
T c= 38.5 K
m=2 δ=2 Bγ = 32 mT
-4
0
0
–1
0
Fig. 4. Hysteretic magnetization curves of the sample MgB2-45, MgB2-50 and MgB2-75 at T = 20 K.
ing law represents quite well the temperature and field dependence in the metallic superconductor MgB2. Magnetization curves of Ag–Hg1223 superconductor at temperatures of 20, 30, 40, 50, 60, 70 and 77 K are shown in Fig. 5. An asymmetric diamag-
0.1
Ag 02
10
Tc = 38.5 K Birr (0) = 10.4 T –1
0
1
B (T)
10 10
30 K
–2
–3
T (K)
–4
0
0.5 B (T)
1
0
Fig. 3. Hysteretic magnetization curves of the sample MgB2-45. Solid lines are computed differentially using Eqs. (4) and (5).
measured data except the low field region, where the magnetic field scarcely penetrate into the superconductor. The observed and numerically computed magnetizations of MgB2-45, MgB2-50 and MgB2-75 are compared in Fig. 4. Here the calculated curves fit well the measured data in the whole range of temperature. It indicates the scal-
10
Ag 02
–1
20 K
M (T)
–0.2
∆M (T)
T (K) = 20, 30, 40, 50, 60, 70, 77
n=2 γ ~ 0.4 m=2 δ=2 Bγ = 32 mT
1
B (T)
–0.1
n = 3.4 γ ~ 0.4 m=6 δ =2 Bγ = 18 mT –1
Tc = 131 K Birr (0) = 8.15 T 0
1
B (T) Fig. 5. Asymmetric magnetization curves of Hg1223 sample Ag-02 at T = 20, 30, 40, 50, 60, 70 and 77 K. Solid lines are numerically calculated taking into consideration of the field step DBs induced by Meissner shielding current at the surface.
730
N. Sakamoto et al. / Physica C 426–431 (2005) 726–730
netic nature is observed. It is well known that the magnetic field just inside the superconductor Bs differs from the applied magnetic field B0 due to a Meissner shielding current flowing along the surface [6]. Then the field is expressed as Bs = B0 DBs, where DBs is the magnetic field step at the surface. The field Bs is used for numerical computation of Eqs. (4) and (5). The irreversibility field and critical temperature are Birr(0) = 8.15 T and Tc = 131 K. The pinning parameters are estimated to be c 0.4, n = 2, m = 2, d = 2 from measured DM data shown in the inset of Fig. 5. Introduction of the field step at the surface results in a better agreement of M. For example the magnetization M curve at T = 20 K is fitted well when DBs = 15 mT. This is closely related to the effectiveness of the surface property in Hg1223 superconductors. MÕs at different temperatures are summarized in Fig. 5. Good agreement of the computed curves indicates the validity of the scaling law of the pinning force density for the MgB2 and Ag–Hg1223 superconductors. 5. Conclusions Pinning parameters in the scaling law are evaluated from the measured magnetization width. Field distributions are differentially calculated using the parameters and the hysteric magnetization characteristics are obtained from the averaged field. In several particle sizes of MgB2, the scaling law corresponds well to the field and temperature dependence of the critical current density Jc.
Numerically computed magnetization curves agree well with the observation. Ag-mixed composites of Agx(HgBa1.9Bi0.1Ca2Cu3O8+d)1x (x = 0.2) superconductor showed high critical temperatures Tc = 131 K. Scaling law of the pinning force density describes well the temperature and field dependence of Jc when Bc2 is replaced by the irreversibility field Birr. Introduction of the field steps at the surface leads to a good agreement with the measured data with an asymmetric nature. The scaling law of the pinning force density Fp using the irreversibility field Birr is confirmed to describe successfully the field and temperature dependence in the metallic MgB2 and high-Tc Hg1223 superconductors.
References [1] S. Noguchi, T. Akune, N. Sakamoto, H.R. Khan, K. Lu¨ders, Physica C 378–381 (2002) 381. [2] A.M. Campbell, J.E. Evetts, Adv. Phys. 21 (1972) 372. [3] K. Noda, M. Nozue, E.S. Otabe, T. Matsushita, T. Umemura, S. Miyashita, H. Higuma, F. Uchikawa, Adv. Supercond. 7 (1995) 501. [4] T. Matsushita, T. Nakatani, E.S. Otabe, K. Yamafuji, K. Takamuku, N. Kosizuka, Jpn. J. Appl. Phys. 32 (1993) L720. [5] N. Sakamoto, T. Ohashi, T. Akune, Y. Matsumoto, in: A. Andreone et al. (Eds.), Applied Superconductivity 2003, Inst. Phys. Conf. Series, 181, Inst Phys. Pub., Bristol and Philadelphia, 2004, p. 2202. [6] T. Akune, H. Abe, A. Koga, N. Sakamoto, Y. Matsumoto, Physica C 378–381 (2002) 234. [7] T. Ohashi, T. Akune, N. Sakamoto, H.R. Khan, K. Lu¨ders, Physica C 392–396 (2003) 373.