- Email: [email protected]
La-doping effects on pinning properties of MgB2
Physica C 412–414 (2004) 402–406 www.elsevier.com/locate/physc
La-doping effects on pinning properties of MgB2 Yoshihide Kimishima *, Masatomo Uehara, Tetsuji Kuramoto, Sachiko Takano, Satoshi Takami Department of Physics, Faculty of Engineering, Graduate School of Yokohama National University, Tokiwadai 79-5, Hodogaya, Yokohama 240-8501, Japan Received 29 October 2003; accepted 19 January 2004 Available online 7 May 2004
Abstract The La-doped MgB2 samples were sintered from the mixture of Mg, B and La powder with the mole ratio of Mg:B:La ¼ 1.2:2(1+3x):x, where x was 0, 0.01 and 0.02. The solid reaction of the powder mixture was performed in the microreactor at 1023 K under Ar-atmosphere of 40 MPa. For the prepared samples, the X-ray diffraction results showed the production of impurity phase of LaB6 nano-particles within the bulk MgB2 except for small amount of MgO. The slight reduction of Tc ’s and the decreasing of decay rates of Jc against the magnetic field could be characterized for x ¼ 0:01 sample. 2004 Elsevier B.V. All rights reserved. PACS: 74.60.Ge; 74.60.Jg; 74.72.)h Keywords: Critical current density; Critical state model; Magnetization; MgB2 ; La-doping
1. Introduction Since the superconductivity of MgB2 with the Tc of about 40 K was discovered, the enhancement of the pinning properties was studied by many authors. Especially, the critical current density Jc and the irreversible field Hirr at 20 K have been important topics for the application of MgB2 as the liquid hydrogen superconductor [1–10]. At 20 K, pure MgB2 generally has the Jc of about 104 A/ cm2 under 1 T and the Hirr is about 4 T [11]. As for the Ti-doping, a few or 10% Ti-doped MgB2
*
Corresponding author. Tel./fax: +81-45-339-4182. E-mail address: [email protected] (Y. Kimishima).
showed the Jc values larger than 105 A/cm2 under 1 T and the Hirr near 5 T at 20 K with small Tc reductions [1–3]. The reason of pinning enhancement was considered as that the small (10 nm) MgB2 grains were surrounded by thin (1 nm) TiB2 layers which was good pinning centers by crystallographic matching with MgB2 . On the other hand, the recent remarkable success was nanoSiC-doping [4]. The 10% nano-SiC-doped MgB2 had large Jc of 5 · 105 A/cm2 under 1 T and the Hirr of 7 T at 20 K with scarce Tc -reduction. In this system, about 10 nm inclusions of Mg2 Si, SiC and intra-grain defects were confirmed as the effective pinning centers. The nano-Si or nano-C-doping also induced the effective pinning. In the nano-Sidoped MgB2 [5], the Mg2 Si or Si inclusions with
0921-4534/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2004.01.061
Y. Kimishima et al. / Physica C 412–414 (2004) 402–406
x=0
1500
0.01 0.03 1000
MgO (200) MgB2 (100)
LaB6 (110)
500
0 29
30
31
32
33
34
41
42
43
2 θ (deg) Fig. 1. XRD patterns of (LaB6 )x (MgB2 )1x for x ¼ 0, 0.01, 0.02 and 0.03.
half widths of diffraction peaks in Fig. 1 showed the production of 8–10 nm LaB6 nano-particles in the MgB2 phase with the small amount of MgO. So we investigated the pinning properties for the x ¼ 0:01 and 0.02 mainly. Another technique of rapid formation method [10] was also tried for Ladoping in the vacuum quartz cell at 1123 K for 30 min. However the LaB6 phase became more dominant in the samples by this method.
1.2
x=0 0.01 0.02
2. Experimental 1.0
300
0.8 ρ/ ρ
The La-doped MgB2 samples were sintered from the mixture of Mg, B and La powders with the mole ratio of Mg:B:La ¼ 1.2:2+6x:x for the purpose of forming (LaB6 )x (MgB2 )1x system, where x was 0, 0.01, 0.02 and 0.03. The solid phase reactions of these powder mixture were performed in the microreactor cell at 1023 K under 40 MPa Ar-atmosphere for 30 h. In Fig. 1, the CuKa X-ray powder diffraction (XRD) patterns are shown for the prepared samples. The intensities of ð1 0 0Þ and ð1 0 1Þ peaks of MgB2 monotonously decreased with increasing x, and these peaks disappeared at x ¼ 0:03. On the other hand, the ð1 1 0Þ peak intensity of LaB6 increased with increasing of Lacontent. For the x ¼ 0:01 and 0.02 samples, the
MgB 2 (101)
0.02
Intensity
10–30 nm size enhanced the Jc as large as that in the nano-SiC-doped system at 1 T and 20 K, but it decayed rapidly in higher field. In the nano-carbon system [6,7], 5% nano-C-doped MgB2 had the Jc of 105 A/cm2 under 1 T at 20 K, but the Jc disappeared at Hirr of 5 T being lower than the Hirr of about 7 T in the SiC-doped system. The effective pinning centers were formed by the uniformly distributed 5–10 nm C, Mg2 C3 and MgB2 C2 precipitates in 100 nm MgB2 grains [6]. Meanwhile the formation of MgAlB4 superstructure in MgB2 by Al-doping [8] gave no improvement of pinning property probably due to the reduction of density of state near the Fermi level which resulted in decreasing of superconducting transition temperature. The Pb-doped MgB2 with the impurity phases of Pb, MgO and MgB4 also reduced Tc of MgB2 , but the jdHc2 =dT j increased with increasing the Pb content [9]. In the recent report [10], the doping of Y2 O3 nano-particles enhanced the Jc to 2 · 105 A/cm2 under 1 T and the Hirr to 5.5 T at 20 K, producing regular distribution of nano-metric (3–5 nm) YB4 particles in bulk MgB2 by rapid formation technique. If the improvements of Jc and Hirr were due to the nano-YB4 pinning centers, the same effects can be also expected for the formation of the other nano-rare earth boride such as LaB6 by the Ladoping to the MgB2 .
403
0.6 0.4 0.2 0.0 0
50
100
150
200
250
300
T (K) Fig. 2. Temperature dependence of normalized resistivities of x ¼ 0, 0.01 and 0.02 samples.
404
Y. Kimishima et al. / Physica C 412–414 (2004) 402–406
Electrical resistivities q were measured by DC four terminals method for x ¼ 0, 0.01 and 0.02 samples produced in the microreactor cell. The temperature dependence of normalized resistivities [qðT Þ=q (300 K)] was shown in Fig. 2. The superconducting transition temperatures Tc were 38.4, 37.8 and 37.2 K for x ¼ 0, 0.01 and 0.02 samples, respectively. The small amount of jdTc =dxj was preferable to improve the pinning property in this system.
3. Magnetization analysis The magnetization measurements were performed by the MPMS SQUID (Quantum Design) magnetometer at 5, 15, 25 and 35 K up to the field of 5 T. The experimental results were given in Figs. 3 and 4 for x ¼ 0, 0.01 and 0.02 samples, respectively. The theoretical curves in these figures were obtained from the following expressions for magnetization [12,13]. The initial magnetization after zero field cooling (ZFC) are given as l0 Mvir ¼ l0 H
for 0 6 H 6 Hc1 ;
ð1Þ
Fig. 4. Field dependence of (Jc =Jc0 ) of x ¼ 0, 0.01 and 0.02 samples at 5 K.
1 2 ðB0 KÞ ðB0 þ 2KÞ 3A for Hc1 6 H 6 Hp ;
l0 Mvir ¼ l0 H þ
ð2Þ
and
2 3=2 fK 3 ðK 2 AÞ g l0 Mvir ¼ l0 H B0 3A for Hp 6 H 6 Hm :
ð3Þ
The following Eqs. (4)–(8) represent the upper hysteresis curve Mu ðH Þ on the field decreasing process from Hm to Hm 2 fK 3 þ ðKm2 AÞ3=2 l0 Mu ¼ l0 H B0 þ 3A 1 3=2 pffiffiffi ðKm2 þ K 2 Þ g 2 for Hm P H P Hd ; ð4Þ where Hd was defined by Beq ðHd Þ ¼ fðKm2 1=2 2AÞ B0 g. 2 3=2 fK 3 ðK 2 þ AÞ g l0 Mu ¼ l0 H B0 þ 3A for Hd P H P Hc1 ;
Fig. 3. ZFC magnetization curves of x ¼ 0, 0.01 and 0.02 samples at 5 K. Bold solid lines are theoretical curves calculated using parameters in Table 1.
ð5Þ
2 3 3
fB ðBeq þ B0 Þ g l0 Mu ¼ l0 H B0 þ 3A 0 for Hc1 P H P Hc1 ; ð6Þ
Y. Kimishima et al. / Physica C 412–414 (2004) 402–406
2 fK 3 3B0 ðK 2 B20 Þ l0 Mu ¼ l0 H B0 þ 3A 3=2 ðA K 2 þ 2B20 Þ g for Hc1 P H P Hp ;
ð7Þ
and
2 3=2 3 2 fK ðK AÞ g l0 Mu ¼ l0 H þ B0 3A for Hp P H P Hm :
at 5 K, where the magnetic quantities were multiplied by vacuum permeability of l0 ¼ 4p 107 (T m/A). The numerical results were also given in Table 1. The equilibrium critical current density jJceq ðH Þj at inner sample surface was estimated by the following equation jJceq ðH Þj ¼
ð8Þ
The lower hysteresis curve of M‘ ðH Þ on the field increasing process from Hm to Hm can be obtained from the transformation of Mu ðH Þ in Eqs. (4)–(8). In the above equations, the definitions of A ¼ B eq ðB eq þ 2B0 Þ, K ¼ jBeq ðH Þj þ B0 , Km ¼ Beq ðHm Þ þ B0 and B eq ¼ Beq ðHp ) were used, where Beq ðH Þ is the flux density at the sample surface, Hm is the maximum field in the MðH Þ-measurement. The Hp is the full penetration field above which the internal flux density, Bint , becomes non-zero at the center of the slab. The B0 can be called as the cross-over flux density [12,13] between the Bean [14] and the Anderson–Kim states [15]. Analysis of ZFC MðH Þ curves were performed using Eqs. (1)–(8). The parameters B eq , B0 and the normalization factor c were evaluated from the least square fitting of the experimental MðH Þ-data to these equations by the Gauss–Jordan method. In this fitting, the equilibrium magnetization, Meq ðH Þ, was approximated to be ðMu þ M‘ Þ=2, and Hp was determined as the field at which the initial magnetization Mvir and M‘ curves meet each other. In Fig. 3, the MðH Þ-data and theoretical curves were depicted for x ¼ 0, 0.01 and 0.02
405
B eq ðB eq þ 2B0 Þ A ¼ ; 2l0 afjBeq ðH Þj þ B0 g 2l0 aK
ð9Þ
using a of 104 m estimated by the SEM observation. The observed thickness of a means the agglomeration of MgB2 nano-particles with the diameter of a few tens nm. Hereafter we call the Jceq ðH Þ as the critical current density Jc as shown in Table 1. In the present nano-LaB6 -doped (LaB6 )x (MgB2 )1x system, Jc ¼ 2 104 A/cm2 under 1 T and Hirr ¼ 3:5 T at 20 K for x ¼ 0.01, and Jc ¼ 6:5 103 A/cm2 under 1 T and the Hirr ¼ 3:3 T at 20 K for x ¼ 0:02. Thus the strong pinning could not be proved for the 10 nm LaB6 -doped MgB2 . However, as shown in Table 1, the crossover parameter B0 of x ¼ 0:01 became larger than that of pure MgB2 . The large B0 allows the mixed state of 2nd kind superconductor to have a Bean like critical state [12] in which Jc is constant for H [14]. So this result means the decreasing of Jc reduction rate against H of jd½Jc ðH Þ=Jc0 =dH j in the x ¼ 0:01 sample, where Jc0 is the Jc at zerofield. Actually the Jc ðH Þ=Jc0 of x ¼ 0:01 sample was larger than that of x ¼ 0 sample at 5 K as shown in Fig. 4 and Table 1. Therefore it can be concluded that the nano-LaB6 inclusions suppress the decay of Jc by H with no Tc -reduction. One of the origin of Jc reduction by LaB6 -doping should be due to the insufficient growing of MgB2 grains
Table 1 Magnetic parameters and Jceq of Lax Mg1x B2 T (K)
5
x B eq (mT) l0 Hp (mT) B0 (mT) l0 Hirr (T) Jc0 (104 A/cm2 ) Jc1T (104 A/cm2 ) eq Jc1T =Jc0
0 365 420 271 >5 49 10 0.20
15 0.01 172 180 401 >5 17 4.8 0.29
0.02 100 100 176 5 11 1.5 0.14
0 273 300 201 5 37 6.0 0.16
25 0.01 153 164 218 4.5 16 3.0 0.18
0.02 74 80 146 4 7.3 0.9 0.13
0 172 210 133 2.5 23 2.7 0.12
35 0.01 82 88 138 2.5 8.5 1.0 0.12
0.02 40 50 101 2.5 3.9 0.35 0.09
0 36 36 30 0.5 5.0 – –
0.01 2 2 2 0.04 0.2 – –
0.02 8 10 22 0.5 0.8 – –
406
Y. Kimishima et al. / Physica C 412–414 (2004) 402–406
with the size of 20–30 nm. Successive studies are needed to enhance the pinning property of MgB2 , using the La2 O3 nano-particles as the start materials and now in progress.
Acknowledgements The present work has been supported by the Takahashi Industrial and Economical Research Foundation.
References [1] Y. Zhao, Y. Feng, D.X. Huang, T. Machi, C.H. Cheng, K. Nakao, N. Chikumoto, Y. Fudamoto, N. Koshizuka, M. Murakami, Physica C 378–381 (2002) 122. [2] Y. Zhao, C.H. Cheng, Y. Feng, T. Machi, D.X. Huang, L. Zhou, N. Koshizuka, M. Murakami, Physica C 386 (2003) 581. [3] N.E. Anderson Jr., W.E. Straszheim, S.L. Bud’ko, P.C. Canfield, D.K. Finnemore, R.J. Suplinskas, Physica C 390 (2003) 11.
[4] S.X. Dou, S. Soltanian, J. Horvat, X.L. Wang, P. Munroe, S.H. Zhou, M. Ionescu, H.K. Liu, M. Tomsic, Appl. Phys. Lett. 81 (2002) 3419. [5] X.L. Wang, S.H. Zhou, M.J. Qin, P.R. Munroe, S. Soltanian, H.K. Liu, S.X. Dou, Physica C 385 (2003) 461. [6] S. Soltanian, J. Horvat, X.L. Wang, P. Munroe, S.X. Dou, Physica C 390 (2003) 185. [7] R.A. Ribeiro, S.L. Bud’ko, C. Petrovic, P.C. Canfield, Physica C 384 (2003) 227. [8] J.Y. Xiang, D.N. Zheng, J.Q. Li, H.H. Wen, Z.X. Zhao, Physica C 386 (2003) 611. [9] D.W. Gu, Y.M. Cai, J.K.F. Yau, Y.G. Cui, T. Wu, G.Q. Yuan, L.J. Shen, X. Jin, Physica C 386 (2003) 643. [10] J. Wang, Y. Bugoslavsky, A. Berenov, L. Cowey, A.D. Caplin, L.F. Cohen, J.L. MacManus Driscoll, L.D. Cooley, X. Song, D.C. Larbalestier, Appl. Phys. Lett. 81 (2002) 2026. [11] P.C. Canfield, S.L. Bud’ko, D.K. Finemore, Physica C 385 (2003) 1. [12] Y. Kimishima, M. Uehara, T. Kuramoto, Y. Ichiyanagi, Y. Iriyama, K. Yorimasa, Physica C 377 (2002) 196. [13] K. Yorimasa, M. Uehara, T. Kuramoto, H. Inoue, Y. Kimishima, Physica C 392–396 (2003) 306. [14] C.P. Bean, Rev. Mod. Phys. 36 (1964) 31. [15] P.W. Anderson, Y.B. Kim, Rev. Mod. Phys. 36 (1964) 39.
La-doping effects on pinning properties of MgB2 Yoshihide Kimishima *, Masatomo Uehara, Tetsuji Kuramoto, Sachiko Takano, Satoshi Takami Department of Physics, Faculty of Engineering, Graduate School of Yokohama National University, Tokiwadai 79-5, Hodogaya, Yokohama 240-8501, Japan Received 29 October 2003; accepted 19 January 2004 Available online 7 May 2004
Abstract The La-doped MgB2 samples were sintered from the mixture of Mg, B and La powder with the mole ratio of Mg:B:La ¼ 1.2:2(1+3x):x, where x was 0, 0.01 and 0.02. The solid reaction of the powder mixture was performed in the microreactor at 1023 K under Ar-atmosphere of 40 MPa. For the prepared samples, the X-ray diffraction results showed the production of impurity phase of LaB6 nano-particles within the bulk MgB2 except for small amount of MgO. The slight reduction of Tc ’s and the decreasing of decay rates of Jc against the magnetic field could be characterized for x ¼ 0:01 sample. 2004 Elsevier B.V. All rights reserved. PACS: 74.60.Ge; 74.60.Jg; 74.72.)h Keywords: Critical current density; Critical state model; Magnetization; MgB2 ; La-doping
1. Introduction Since the superconductivity of MgB2 with the Tc of about 40 K was discovered, the enhancement of the pinning properties was studied by many authors. Especially, the critical current density Jc and the irreversible field Hirr at 20 K have been important topics for the application of MgB2 as the liquid hydrogen superconductor [1–10]. At 20 K, pure MgB2 generally has the Jc of about 104 A/ cm2 under 1 T and the Hirr is about 4 T [11]. As for the Ti-doping, a few or 10% Ti-doped MgB2
*
Corresponding author. Tel./fax: +81-45-339-4182. E-mail address: [email protected] (Y. Kimishima).
showed the Jc values larger than 105 A/cm2 under 1 T and the Hirr near 5 T at 20 K with small Tc reductions [1–3]. The reason of pinning enhancement was considered as that the small (10 nm) MgB2 grains were surrounded by thin (1 nm) TiB2 layers which was good pinning centers by crystallographic matching with MgB2 . On the other hand, the recent remarkable success was nanoSiC-doping [4]. The 10% nano-SiC-doped MgB2 had large Jc of 5 · 105 A/cm2 under 1 T and the Hirr of 7 T at 20 K with scarce Tc -reduction. In this system, about 10 nm inclusions of Mg2 Si, SiC and intra-grain defects were confirmed as the effective pinning centers. The nano-Si or nano-C-doping also induced the effective pinning. In the nano-Sidoped MgB2 [5], the Mg2 Si or Si inclusions with
0921-4534/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2004.01.061
Y. Kimishima et al. / Physica C 412–414 (2004) 402–406
x=0
1500
0.01 0.03 1000
MgO (200) MgB2 (100)
LaB6 (110)
500
0 29
30
31
32
33
34
41
42
43
2 θ (deg) Fig. 1. XRD patterns of (LaB6 )x (MgB2 )1x for x ¼ 0, 0.01, 0.02 and 0.03.
half widths of diffraction peaks in Fig. 1 showed the production of 8–10 nm LaB6 nano-particles in the MgB2 phase with the small amount of MgO. So we investigated the pinning properties for the x ¼ 0:01 and 0.02 mainly. Another technique of rapid formation method [10] was also tried for Ladoping in the vacuum quartz cell at 1123 K for 30 min. However the LaB6 phase became more dominant in the samples by this method.
1.2
x=0 0.01 0.02
2. Experimental 1.0
300
0.8 ρ/ ρ
The La-doped MgB2 samples were sintered from the mixture of Mg, B and La powders with the mole ratio of Mg:B:La ¼ 1.2:2+6x:x for the purpose of forming (LaB6 )x (MgB2 )1x system, where x was 0, 0.01, 0.02 and 0.03. The solid phase reactions of these powder mixture were performed in the microreactor cell at 1023 K under 40 MPa Ar-atmosphere for 30 h. In Fig. 1, the CuKa X-ray powder diffraction (XRD) patterns are shown for the prepared samples. The intensities of ð1 0 0Þ and ð1 0 1Þ peaks of MgB2 monotonously decreased with increasing x, and these peaks disappeared at x ¼ 0:03. On the other hand, the ð1 1 0Þ peak intensity of LaB6 increased with increasing of Lacontent. For the x ¼ 0:01 and 0.02 samples, the
MgB 2 (101)
0.02
Intensity
10–30 nm size enhanced the Jc as large as that in the nano-SiC-doped system at 1 T and 20 K, but it decayed rapidly in higher field. In the nano-carbon system [6,7], 5% nano-C-doped MgB2 had the Jc of 105 A/cm2 under 1 T at 20 K, but the Jc disappeared at Hirr of 5 T being lower than the Hirr of about 7 T in the SiC-doped system. The effective pinning centers were formed by the uniformly distributed 5–10 nm C, Mg2 C3 and MgB2 C2 precipitates in 100 nm MgB2 grains [6]. Meanwhile the formation of MgAlB4 superstructure in MgB2 by Al-doping [8] gave no improvement of pinning property probably due to the reduction of density of state near the Fermi level which resulted in decreasing of superconducting transition temperature. The Pb-doped MgB2 with the impurity phases of Pb, MgO and MgB4 also reduced Tc of MgB2 , but the jdHc2 =dT j increased with increasing the Pb content [9]. In the recent report [10], the doping of Y2 O3 nano-particles enhanced the Jc to 2 · 105 A/cm2 under 1 T and the Hirr to 5.5 T at 20 K, producing regular distribution of nano-metric (3–5 nm) YB4 particles in bulk MgB2 by rapid formation technique. If the improvements of Jc and Hirr were due to the nano-YB4 pinning centers, the same effects can be also expected for the formation of the other nano-rare earth boride such as LaB6 by the Ladoping to the MgB2 .
403
0.6 0.4 0.2 0.0 0
50
100
150
200
250
300
T (K) Fig. 2. Temperature dependence of normalized resistivities of x ¼ 0, 0.01 and 0.02 samples.
404
Y. Kimishima et al. / Physica C 412–414 (2004) 402–406
Electrical resistivities q were measured by DC four terminals method for x ¼ 0, 0.01 and 0.02 samples produced in the microreactor cell. The temperature dependence of normalized resistivities [qðT Þ=q (300 K)] was shown in Fig. 2. The superconducting transition temperatures Tc were 38.4, 37.8 and 37.2 K for x ¼ 0, 0.01 and 0.02 samples, respectively. The small amount of jdTc =dxj was preferable to improve the pinning property in this system.
3. Magnetization analysis The magnetization measurements were performed by the MPMS SQUID (Quantum Design) magnetometer at 5, 15, 25 and 35 K up to the field of 5 T. The experimental results were given in Figs. 3 and 4 for x ¼ 0, 0.01 and 0.02 samples, respectively. The theoretical curves in these figures were obtained from the following expressions for magnetization [12,13]. The initial magnetization after zero field cooling (ZFC) are given as l0 Mvir ¼ l0 H
for 0 6 H 6 Hc1 ;
ð1Þ
Fig. 4. Field dependence of (Jc =Jc0 ) of x ¼ 0, 0.01 and 0.02 samples at 5 K.
1 2 ðB0 KÞ ðB0 þ 2KÞ 3A for Hc1 6 H 6 Hp ;
l0 Mvir ¼ l0 H þ
ð2Þ
and
2 3=2 fK 3 ðK 2 AÞ g l0 Mvir ¼ l0 H B0 3A for Hp 6 H 6 Hm :
ð3Þ
The following Eqs. (4)–(8) represent the upper hysteresis curve Mu ðH Þ on the field decreasing process from Hm to Hm 2 fK 3 þ ðKm2 AÞ3=2 l0 Mu ¼ l0 H B0 þ 3A 1 3=2 pffiffiffi ðKm2 þ K 2 Þ g 2 for Hm P H P Hd ; ð4Þ where Hd was defined by Beq ðHd Þ ¼ fðKm2 1=2 2AÞ B0 g. 2 3=2 fK 3 ðK 2 þ AÞ g l0 Mu ¼ l0 H B0 þ 3A for Hd P H P Hc1 ;
Fig. 3. ZFC magnetization curves of x ¼ 0, 0.01 and 0.02 samples at 5 K. Bold solid lines are theoretical curves calculated using parameters in Table 1.
ð5Þ
2 3 3
fB ðBeq þ B0 Þ g l0 Mu ¼ l0 H B0 þ 3A 0 for Hc1 P H P Hc1 ; ð6Þ
Y. Kimishima et al. / Physica C 412–414 (2004) 402–406
2 fK 3 3B0 ðK 2 B20 Þ l0 Mu ¼ l0 H B0 þ 3A 3=2 ðA K 2 þ 2B20 Þ g for Hc1 P H P Hp ;
ð7Þ
and
2 3=2 3 2 fK ðK AÞ g l0 Mu ¼ l0 H þ B0 3A for Hp P H P Hm :
at 5 K, where the magnetic quantities were multiplied by vacuum permeability of l0 ¼ 4p 107 (T m/A). The numerical results were also given in Table 1. The equilibrium critical current density jJceq ðH Þj at inner sample surface was estimated by the following equation jJceq ðH Þj ¼
ð8Þ
The lower hysteresis curve of M‘ ðH Þ on the field increasing process from Hm to Hm can be obtained from the transformation of Mu ðH Þ in Eqs. (4)–(8). In the above equations, the definitions of A ¼ B eq ðB eq þ 2B0 Þ, K ¼ jBeq ðH Þj þ B0 , Km ¼ Beq ðHm Þ þ B0 and B eq ¼ Beq ðHp ) were used, where Beq ðH Þ is the flux density at the sample surface, Hm is the maximum field in the MðH Þ-measurement. The Hp is the full penetration field above which the internal flux density, Bint , becomes non-zero at the center of the slab. The B0 can be called as the cross-over flux density [12,13] between the Bean [14] and the Anderson–Kim states [15]. Analysis of ZFC MðH Þ curves were performed using Eqs. (1)–(8). The parameters B eq , B0 and the normalization factor c were evaluated from the least square fitting of the experimental MðH Þ-data to these equations by the Gauss–Jordan method. In this fitting, the equilibrium magnetization, Meq ðH Þ, was approximated to be ðMu þ M‘ Þ=2, and Hp was determined as the field at which the initial magnetization Mvir and M‘ curves meet each other. In Fig. 3, the MðH Þ-data and theoretical curves were depicted for x ¼ 0, 0.01 and 0.02
405
B eq ðB eq þ 2B0 Þ A ¼ ; 2l0 afjBeq ðH Þj þ B0 g 2l0 aK
ð9Þ
using a of 104 m estimated by the SEM observation. The observed thickness of a means the agglomeration of MgB2 nano-particles with the diameter of a few tens nm. Hereafter we call the Jceq ðH Þ as the critical current density Jc as shown in Table 1. In the present nano-LaB6 -doped (LaB6 )x (MgB2 )1x system, Jc ¼ 2 104 A/cm2 under 1 T and Hirr ¼ 3:5 T at 20 K for x ¼ 0.01, and Jc ¼ 6:5 103 A/cm2 under 1 T and the Hirr ¼ 3:3 T at 20 K for x ¼ 0:02. Thus the strong pinning could not be proved for the 10 nm LaB6 -doped MgB2 . However, as shown in Table 1, the crossover parameter B0 of x ¼ 0:01 became larger than that of pure MgB2 . The large B0 allows the mixed state of 2nd kind superconductor to have a Bean like critical state [12] in which Jc is constant for H [14]. So this result means the decreasing of Jc reduction rate against H of jd½Jc ðH Þ=Jc0 =dH j in the x ¼ 0:01 sample, where Jc0 is the Jc at zerofield. Actually the Jc ðH Þ=Jc0 of x ¼ 0:01 sample was larger than that of x ¼ 0 sample at 5 K as shown in Fig. 4 and Table 1. Therefore it can be concluded that the nano-LaB6 inclusions suppress the decay of Jc by H with no Tc -reduction. One of the origin of Jc reduction by LaB6 -doping should be due to the insufficient growing of MgB2 grains
Table 1 Magnetic parameters and Jceq of Lax Mg1x B2 T (K)
5
x B eq (mT) l0 Hp (mT) B0 (mT) l0 Hirr (T) Jc0 (104 A/cm2 ) Jc1T (104 A/cm2 ) eq Jc1T =Jc0
0 365 420 271 >5 49 10 0.20
15 0.01 172 180 401 >5 17 4.8 0.29
0.02 100 100 176 5 11 1.5 0.14
0 273 300 201 5 37 6.0 0.16
25 0.01 153 164 218 4.5 16 3.0 0.18
0.02 74 80 146 4 7.3 0.9 0.13
0 172 210 133 2.5 23 2.7 0.12
35 0.01 82 88 138 2.5 8.5 1.0 0.12
0.02 40 50 101 2.5 3.9 0.35 0.09
0 36 36 30 0.5 5.0 – –
0.01 2 2 2 0.04 0.2 – –
0.02 8 10 22 0.5 0.8 – –
406
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with the size of 20–30 nm. Successive studies are needed to enhance the pinning property of MgB2 , using the La2 O3 nano-particles as the start materials and now in progress.
Acknowledgements The present work has been supported by the Takahashi Industrial and Economical Research Foundation.
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