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Magnetic flux pinning and flux jumps in polycrystalline MgB2
Cryogenics 45 (2005) 415–420 www.elsevier.com/locate/cryogenics
Magnetic flux pinning and flux jumps in polycrystalline MgB2 Kunitoshi Murai a, JunÕya Hori a, Yoshiko Fujii a
a,*
, Jonah Shaver b, Gregory Kozlowski
b
Department of Applied Physics, Okayama University of Science, Ridaicho 1-1, Okayama 700-0005, Japan b Wright State University, Dayton, OH 45435, USA Received 1 October 2004; received in revised form 3 March 2005; accepted 11 March 2005
Abstract MgB2 polycrystalline samples were fabricated under varying conditions of isostatic pressing in argon gas. The critical current densities (JC) were determined through measurements of hysteresis loops, and the highest value of JC at 10 K was 1.9 · 104 A/ cm2 at 4.8 T. The depinning temperatures were measured at various magnetic fields using the vibrating reed technique. Flux jumps appeared below 7.4 K. The hysteresis loops were carefully examined to determine the temperature and magnetic field range where flux jumps appeared. 2005 Elsevier Ltd. All rights reserved. Keywords: MgB2 polycrystal; Hysteresis loop; Critical current density; Flux jump
1. Introduction Since the discovery of the new superconductor MgB2, many studies have been conducted on its basic properties and practical applications. From a practical point of view, the value of the critical current density, JC, is important. JC for polycrystalline MgB2 is high at zero field, but falls rapidly with increasing magnetic field compared with conventional metallic superconductors [1–3]. The grain boundaries of MgB2 powder do not show weak coupling. Thus, high-density bulk samples have been fabricated by high-pressure synthesis to obtain samples having a high JC [1,4]. We have also prepared samples by high-pressure sintering under varying conditions. The magnetic hysteresis loops were measured and the JC values were obtained. Using the vibrating reed technique, the flux depinning was measured. The appearance of flux jumps reported at low temperature and low field is detrimental in practical applications
*
Corresponding author. Tel./fax: +81 86 256 9470. E-mail address: [email protected] (Y. Fujii).
0011-2275/$ - see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.cryogenics.2005.03.001
[5–7]. We have carefully studied the behavior of flux jumps by hysteresis loop measurements below 8 K.
2. Experimental 2.1. Sample preparation Samples were prepared from MgB2 powder (325 mesh size, 98% purity, Alfa Aesar Inc.). Each pellet (5 g) was uniaxially pre-pressed at 140 MPa for 1 h in a 0.5-in. die, then encased in an evacuated stainless steel (SUS 304) can, and hot isostatically pressed under 207 MPa at elevated temperature for 2 h. This procedure was performed in a furnace under argon gas atmosphere. The evacuation was performed at room temperature (sample Nos. 1 and 2) or at 500 C (sample Nos. 3, 4, and 5) for outgassing. The sintering temperature was 900 C (sample No. 3), 950 C (sample Nos. 1 and 4) or 1000 C (sample Nos. 2 and 5). The temperature and pressure were increased at a rate of 15 C/min and 3.45 MPa/min, respectively. After the 2-h sintering run, the temperature was ramped
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K. Murai et al. / Cryogenics 45 (2005) 415–420
Table 1 Summary of sample preparation Sample
Tc (K)
DT (K)
Sintering temp. (C)
Sintering pressure (MPa)
Pressure during cool down (MPa)
Evacuation temp. before sintering (C)
No. No. No. No. No.
38.54 38.23 38.85 38.78 38.79
0.16 0.09 0.10 0.13 0.10
950 1000 900 950 1000
207 207 207 207 207
0 0 207 207 207
Room temp. Room temp. 500 500 500
1 2 3 4 5
down at a rate of 25 C/min, while the pressure was ramped down as fast as possible (sample Nos. 1 and 2) or held constant at 207 MPa in order to preserve stoichiometry by preventing magnesium from escaping (sample Nos. 3, 4 and 5). X-ray-diffraction analyses showed that the samples evacuated at room temperature had a higher MgO content than those evacuated at 500 C. The superconducting transition temperature was determined by AC susceptibility measurements, and the transition width was obtained from the loss part of the susceptibility. The results are summarized in Table 1. 2.2. Magnetization measurements The samples were cut into rectangular parallelepipeds in order to diminish the demagnetizing field. The dimensions were 0.270 · 0.472 · 3.02 mm3 (No. 1), 0.275 · 0.475 · 3.10 mm3 (No. 2), 0.232 · 0.362 · 3.05 mm3 (No. 3), 0.335 · 0.548 · 3.00 mm3 (No. 4) and 0.308 · 0.569 · 3.00 mm3 (No. 5). Magnetization measurements were performed using a Quantum Design Magnetometer (MPMS-XL5). The magnetization hysteresis loops were obtained under a magnetic field of up to 5 T and in temperature range from 5 K to 30 K. The magnetic field axis was parallel to the longest axis of each sample. 2.3. Depinning temperature measurements The flux-line pinning was investigated using the vibrating reed technique developed by Esquinazi et al. [8]. The set-up and block diagram is schematized in Fig. 1. A MgB2 sample was glued with GE7031 varnish to a Si host reed sandwiched between two aluminum layers. The reed was clamped at one end between copper plates mounted on a rotatable holder. The applied magnetic field applied is shown in Fig. 1. Flexural vibration was induced by driving the free end of a Si reed electrostatically with one electrode. The temperature dependence of the resonance frequency f and the amplitude u of a reed were measured as parameters pertaining to the applied magnetic field. The damping, C, is calculated from the following formulas:
Schematic set-up of a Vibrating reed MgB2 Drive electrode
Detect electrode Si plate with Al coat
Magnetic field Holder
156 V
Pre-amplifier
Two phase lock-in amplifier
Ref. Voltage controlled oscillator
Oscilloscope Frequency counter
Fig. 1. Schematic of the vibrating reed set-up and block diagram of the measurements.
uð0Þxð0Þ 1 C ¼ C0 uðBÞxðBÞ C0 ¼ Q1 ð0Þ
xð0Þ 2
Qð0Þ ¼
Dx xð0Þ
1
ð1Þ
where u(0) and u(B) are the resonance amplitude at zero field and the applied field, respectively, x(0) and x(B) are the corresponding resonance angular frequencies, and Dx is the half-width obtained by the resonance curve at zero field. The depinning temperature, TD, was decided at the peak of C. 3. Results and discussion 3.1. Magnetic hysteresis loop and critical current density The magnetic hysteresis loops of sample Nos. 1–5 were measured at 10, 20, and 30 K. No flux jump was observed at these temperatures. Fig. 2 shows the hysteresis loops of sample No. 3. Using the critical-state model, JC was estimated from the magnetization hysteresis, DM, via the following formula: 1 2 b J C ¼ DM 1 ð2Þ b 3a
K. Murai et al. / Cryogenics 45 (2005) 415–420
plained by the reaction between MgB2 and Ni in SUS 304 [9]. On the other hand, the JC of sample No. 2, sintered at 1000 C, is higher at low magnetic fields than that of sample No. 1, sintered at 950 C. This indicates that the contact between grain boundaries is stronger at higher sintering temperatures [4], and that this strong contact works effectively at low fields even if the sample is contaminated with reacted Ni and MgO. Sample No. 3 showed the highest JC values (1.4 · 106 A/cm2 at zero field and 1.9 · 104 A/cm2 at 4.8 T) at 10 K. These JC values are higher than those of other samples prepared by high-pressure synthesis [1,3].
1000 800
10 K 20 K 30 K
No.3
Magnetization (emu/cm3)
600 400 200 0 -200 -400 -600 -800 -1000 -5
-4
-3
-2
-1 0 1 Magnetic field (T)
2
3
4
5
Fig. 2. Magnetization hysteresis loops of sample No. 3 at 10, 20 and 30 K.
3.2. Depinning temperature The resonance frequency change caused by flux-line depinning is normalized by the frequency difference between 5 K and 40 K. Fig. 4(a) shows the temperature dependence of the normalized resonance frequency change at various magnetic fields. Damping, C, exhibited a sharp peak at a temperature (depinning temperature, TD) where the absolute value of df/dT was maximum, as shown in Fig. 4(b). Fig. 5 shows the magnetic field dependence of TD for sample Nos. 1–5. A sample that shows a higher TD at a given magnetic field is thought to have a stronger flux pinning. This qualitatively agrees with the JC values obtained for the five samples at 30 K. The TD of sample No. 3 at 7 T is 22.5 K, which means that the BC2 (upper critical field) at 22.5 K is higher than 7 T.
106
106
10
5
105
10
4
10
3
10
2
10
1
No. 3
No. 1
No. 4
No. 2 0
(a)
1
JC (A/cm2)
JC (A/cm2)
where a and b (a > b) are the sample sizes perpendicular to the applied magnetic field. Fig. 3(a)–(c) show the dependence of critical current density on the applied magnetic field at 10, 20, and 30 K for five samples. The JC values for the samples evacuated at 500 C (Nos. 3, 4, and 5) were higher than those evacuated at room temperature (Nos. 1 and 2). The samples evacuated at room temperature had a higher MgO content than those evacuated at 500 C. These results indicate that the presence of MgO reduces JC [1]. A comparison of sample Nos. 3, 4 and 5 indicates that sintering at higher temperature reduces JC, especially at 1000 C, which degrades the flux pinning at high field and high temperature. Degradation of flux pinning can be ex-
10 K
No. 5 2
3
104
20 K
103 10
No.1
No. 4
10
1
No.2
No. 5
0
1
(b)
Magnetic field (T)
No. 3
2
5
4
417
2
3
4
5
Magnetic field (T)
106
JC (A/cm2)
105 104
30 K
103
No. 1
No. 4
101
No. 2
No. 5
10
0
(c)
No. 3
2
1
2
3
4
5
Magnetic field (T)
Fig. 3. Magnetic field dependence of the critical current density JC for samples Nos. 1–5 at (a) 10 K, (b) 20 K and (c) 30 K.
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K. Murai et al. / Cryogenics 45 (2005) 415–420 8 No. 1
0.8 0.6
1T
No. 3
3T
0.4
5T 0.2
No. 3 No. 4
4
No. 5 2
7T
0
0
0
10
20
(a)
30
10
40
15
20
25
30
35
40
Depinning temperature (K)
Temperature (K)
Fig. 5. Magnetic field dependence of depinning temperature, TD, for sample Nos. 1–5.
250 200 Damping (s-1)
No. 2
6 Magnetic field (T)
Normalized resonance frequency change
1
3.3. Flux jumps
150
1T
No. 3
The hysteresis curves of sample No. 3 were measured between 8 K and 5 K at increments of 0.2 K. Below 7.4 K, flux jumps were observed. Fig. 6(a)–(f) show the typical flux jump patterns, which are classified into three stages with decreasing temperature. In the first stage, flux jumps occurred at 1.1 T and +1.1 T and the absolute value of the field at which the flux jumped slightly decreased as the temperature decreased. In these jumps, the magnetization did not decrease to zero, but a value of about ±80 emu/cm3 was maintained (Fig. 6(a)). In
3T
100
5T 50
7T
0 0
10
20
(b)
30
40
Temperature (K)
Fig. 4. The normalized resonance frequency change and the damping of sample No. 3 as a function of temperature at 1, 3, 5 and 7 T.
Magnetization (emu/cm3)
800
400 0 -400 -800 -2
0
2
0 -400
(b)
6.4 K Magnetization (emu/cm3)
400 0 -400 -800
-2
0
2
-2
0
2
Magnetic field (T)
4
-400
-4
5.2 K
0 -400
-2
0
2
4
Magnetic field (T)
800
400
5.0 K
400 0 -400 -800
-4
(e)
0
(c)
-800 -4
400
4
Magnetic field (T)
800
6.6 K
-800 -4
4
Magnetic field (T)
3
Magnetization (emu/cm )
400
Magnetization (emu/cm3)
-4
(d)
800
-800
(a)
800
6.8 K Magnetization (emu/cm3)
7.4 K
3
Magnetization (emu/cm )
800
-2
0
2
Magnetic field (T)
4
-4
(f)
-2
0
2
Magnetic field (T)
Fig. 6. Hysteresis loops of sample No. 3 between 7.4 and 5 K. Flux jumps were observed below 7.4 K.
4
K. Murai et al. / Cryogenics 45 (2005) 415–420 1.5
1.0
BFJ (T)
0.5
0
-0.5
-1.0
-1.5 4
5
6
7
8
Temperature (K)
400
No. 1
3
800
the second stage, flux jumps occurred more easily; this was at 0 T and +0 T. The magnetization decreased to almost zero (Fig. 6(d)). In the third stage, flux jumps occurred at +0 T, 1.3 T, 0 T and +1.3 T. The magnetization decreased down to zero at +0 T and 0 T, while the magnetization did not decrease down to zero, but a value of about ±80 emu/cm3 at 1.3 T and +1.3 T was maintained (Fig. 6(f)). Fig. 7 shows the relationship between the temperature and magnetic field at which the flux jumps occurred (BFJ). The direction of the top of the triangle shows the direction of the hysteresis measurement process. The hysteresis loops were typically taken at a magnetic sweep rate of approximately 0.2 T/min. When flux jumps appeared, we reduced the rate to approximately 0.02 T/min. Then, the flux jumps at about 1 T sometimes disappeared, while those at about 0 T did not. This indicates that the flux pinned
Magnetization (emu/cm )
3
Magnetization (emu/cm )
Fig. 7. The relationship between temperature and the magnetic field at which flux jumps occurred (BFJ). See the text for symbols.
5K
0 -400
-4
No. 2 5K
400 0 -400
4
-4
3
Magnetization (emu/cm )
5K
0 -400 -800 -2 0 2 Magnetic field (T)
3
800
800
4
No. 4 5K
400 0 -400 -800
4
-4
(d)
-2 0 2 Magnetic field (T)
No. 5 5K
400 0 -400 -800 -4
(e)
-2 0 2 Magnetic field (T)
(b)
No. 3
-4
(c)
-2 0 2 Magnetic field (T)
Magnetization (emu/cm )
3
Magnetization (emu/cm )
(a)
400
800
-800
-800
800
419
-2 0 2 Magnetic field (T)
4
Fig. 8. Hysteresis loops of sample Nos. 1–5 at 5.0 K.
4
420
K. Murai et al. / Cryogenics 45 (2005) 415–420
at higher fields is less stable at zero field than at the applied field. The above phenomena may be explained as follows. It is thought that the stability of flux jumps in MgB2 may be analyzed within the framework of the adiabatic approximation [5]. The heat capacity becomes small below about 10 K at low magnetic field [10,11]. Then, the temperature rises abruptly to TC as a result of the avalanche process if the superconductor becomes unstable, triggered by a small fluctuation of temperature or magnetic field. In the case of flux jumps occurring under the applied magnetic field, magnetization did not decrease to zero, which could be explained by the rapid increase in specific heat with increasing magnetic field [10,11]. Fig. 8(a)–(e) show the hysteresis loops of five samples at 5.0 K. The shape for Nos. 2 and 5 correspond to the first and second stages, respectively, while those for No. 3 and No. 4 correspond to the third stage; that for No. 1 roughly corresponds to that of the third stage. This indicates that flux jumps occur more frequently in samples with higher JC.
4. Conclusion The bulk MgB2 samples were fabricated by changing the hot isostatic pressing conditions (207 MPa). The critical current densities, JC, were derived by the measurements of hysteresis loop. Sample No. 3, evacuated at 500 C before being sintered at 900 C for 2 h, had the highest JC values: 1.4 · 106 A/cm2 at zero field and 1.9 · 104 A/cm2 at 4.8 T at 10 K. Our results show that MgB2 reacts with the SUS surface above 1000 C, and the contaminated material serves to hinder the flux pinning. Moreover, the evacuation at 500 C for outgassing before sintering reduces the MgO contamination, which also hinders the flux pinning. The depinning temperature, TD, obtained by the vibrating reed technique, showed qualitatively the same trends with the strength of flux pinning as JC. TD decreased rapidly with increasing magnetic field.
The flux jumps appeared below about 8 K under fields lower than about 1.5 T. Flux jumps occurred more frequently in samples with higher JC.
Acknowledgement The authors gratefully acknowledge Dr. Iman Maartense for carrying out the ac susceptibility measurements.
References [1] Kumakura H, Takano Y, Fujii H, Togano K, Kito H, Ihara H. Critical current densities and irreversibility fields of MgB2 bulks. Physica C 2001;363:179–83. [2] Canfield PC, BudÕko SL, Finnemore DK. An overview of the basic physical properties of MgB2. Physica C 2003;385:1–7. [3] Shi ZX, Pradhan AK, Tokunaga M, Yamazaki K, Tamegai T, Takano Y, et al. Flux-pinning properties of single crystalline and dense polycrystalline MgB2. Phys Rev B 2003;68:104514. [4] Takano Y, Takeya H, Fujii H, Kumakura H, Hatano T, Togano K. Superconducting properties of MgB2 bulk materials prepared by high-pressure sintering. Appl Phys Lett 2001;78:2914–6. [5] Chabanenko V, Puzniak P, Nabialek A, Vasiliev S, Rusakov V, Huanqian L, et al. Flux jumps and H–T diagram of instability for MgB2. J Low Temp Phys 2003;130:175–91. [6] Dou SX, Wang XL, Horvat J, Milliken D, Li AH, Konstantinov K, et al. Flux jumping and a bulk-to-granular transition in the magnetization of a compacted and sintered MgB2 superconductor. Physica C 2001;361:79–83. [7] Zhao ZW, Li SL, Ni YM, Yang HP, Liu ZY, Wen HH. Suppression of superconducting critical current density by small flux jumps in MgB2 thin films. Phys Rev B 2002;65:064512. [8] Esquinazi P, Neckel H, Weiss G, Brandt EH. A superconducting vibrating reed applied to flux-line pinning. II. Experiment. J Low Temp Phys 1986;64:1–20. [9] Kumakura H, Matsumoto A, Fujii H, Kitaguchi H, Ooi S, Togano K, et al. Fabrication and properties of powder-in-tube processed MgB2 tapes and wires. J Low Temp Phys 2003;131: 1085–93. [10] Bouquet F, Fisher RA, Phillips NE, Hinks DG, Jorgensen JD. Specific heat of Mg11B2: evidence for a second energy gap. Phys Rev Lett 2001;87:047001. [11] Yang HD, Lin J-Y, Li HH, Hsu FH, Liu CJ, Li S-C, et al. Order parameter of MgB2: a fully gapped superconductor. Phys Rev Lett 2001;87:167003.
Magnetic flux pinning and flux jumps in polycrystalline MgB2 Kunitoshi Murai a, JunÕya Hori a, Yoshiko Fujii a
a,*
, Jonah Shaver b, Gregory Kozlowski
b
Department of Applied Physics, Okayama University of Science, Ridaicho 1-1, Okayama 700-0005, Japan b Wright State University, Dayton, OH 45435, USA Received 1 October 2004; received in revised form 3 March 2005; accepted 11 March 2005
Abstract MgB2 polycrystalline samples were fabricated under varying conditions of isostatic pressing in argon gas. The critical current densities (JC) were determined through measurements of hysteresis loops, and the highest value of JC at 10 K was 1.9 · 104 A/ cm2 at 4.8 T. The depinning temperatures were measured at various magnetic fields using the vibrating reed technique. Flux jumps appeared below 7.4 K. The hysteresis loops were carefully examined to determine the temperature and magnetic field range where flux jumps appeared. 2005 Elsevier Ltd. All rights reserved. Keywords: MgB2 polycrystal; Hysteresis loop; Critical current density; Flux jump
1. Introduction Since the discovery of the new superconductor MgB2, many studies have been conducted on its basic properties and practical applications. From a practical point of view, the value of the critical current density, JC, is important. JC for polycrystalline MgB2 is high at zero field, but falls rapidly with increasing magnetic field compared with conventional metallic superconductors [1–3]. The grain boundaries of MgB2 powder do not show weak coupling. Thus, high-density bulk samples have been fabricated by high-pressure synthesis to obtain samples having a high JC [1,4]. We have also prepared samples by high-pressure sintering under varying conditions. The magnetic hysteresis loops were measured and the JC values were obtained. Using the vibrating reed technique, the flux depinning was measured. The appearance of flux jumps reported at low temperature and low field is detrimental in practical applications
*
Corresponding author. Tel./fax: +81 86 256 9470. E-mail address: [email protected] (Y. Fujii).
0011-2275/$ - see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.cryogenics.2005.03.001
[5–7]. We have carefully studied the behavior of flux jumps by hysteresis loop measurements below 8 K.
2. Experimental 2.1. Sample preparation Samples were prepared from MgB2 powder (325 mesh size, 98% purity, Alfa Aesar Inc.). Each pellet (5 g) was uniaxially pre-pressed at 140 MPa for 1 h in a 0.5-in. die, then encased in an evacuated stainless steel (SUS 304) can, and hot isostatically pressed under 207 MPa at elevated temperature for 2 h. This procedure was performed in a furnace under argon gas atmosphere. The evacuation was performed at room temperature (sample Nos. 1 and 2) or at 500 C (sample Nos. 3, 4, and 5) for outgassing. The sintering temperature was 900 C (sample No. 3), 950 C (sample Nos. 1 and 4) or 1000 C (sample Nos. 2 and 5). The temperature and pressure were increased at a rate of 15 C/min and 3.45 MPa/min, respectively. After the 2-h sintering run, the temperature was ramped
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K. Murai et al. / Cryogenics 45 (2005) 415–420
Table 1 Summary of sample preparation Sample
Tc (K)
DT (K)
Sintering temp. (C)
Sintering pressure (MPa)
Pressure during cool down (MPa)
Evacuation temp. before sintering (C)
No. No. No. No. No.
38.54 38.23 38.85 38.78 38.79
0.16 0.09 0.10 0.13 0.10
950 1000 900 950 1000
207 207 207 207 207
0 0 207 207 207
Room temp. Room temp. 500 500 500
1 2 3 4 5
down at a rate of 25 C/min, while the pressure was ramped down as fast as possible (sample Nos. 1 and 2) or held constant at 207 MPa in order to preserve stoichiometry by preventing magnesium from escaping (sample Nos. 3, 4 and 5). X-ray-diffraction analyses showed that the samples evacuated at room temperature had a higher MgO content than those evacuated at 500 C. The superconducting transition temperature was determined by AC susceptibility measurements, and the transition width was obtained from the loss part of the susceptibility. The results are summarized in Table 1. 2.2. Magnetization measurements The samples were cut into rectangular parallelepipeds in order to diminish the demagnetizing field. The dimensions were 0.270 · 0.472 · 3.02 mm3 (No. 1), 0.275 · 0.475 · 3.10 mm3 (No. 2), 0.232 · 0.362 · 3.05 mm3 (No. 3), 0.335 · 0.548 · 3.00 mm3 (No. 4) and 0.308 · 0.569 · 3.00 mm3 (No. 5). Magnetization measurements were performed using a Quantum Design Magnetometer (MPMS-XL5). The magnetization hysteresis loops were obtained under a magnetic field of up to 5 T and in temperature range from 5 K to 30 K. The magnetic field axis was parallel to the longest axis of each sample. 2.3. Depinning temperature measurements The flux-line pinning was investigated using the vibrating reed technique developed by Esquinazi et al. [8]. The set-up and block diagram is schematized in Fig. 1. A MgB2 sample was glued with GE7031 varnish to a Si host reed sandwiched between two aluminum layers. The reed was clamped at one end between copper plates mounted on a rotatable holder. The applied magnetic field applied is shown in Fig. 1. Flexural vibration was induced by driving the free end of a Si reed electrostatically with one electrode. The temperature dependence of the resonance frequency f and the amplitude u of a reed were measured as parameters pertaining to the applied magnetic field. The damping, C, is calculated from the following formulas:
Schematic set-up of a Vibrating reed MgB2 Drive electrode
Detect electrode Si plate with Al coat
Magnetic field Holder
156 V
Pre-amplifier
Two phase lock-in amplifier
Ref. Voltage controlled oscillator
Oscilloscope Frequency counter
Fig. 1. Schematic of the vibrating reed set-up and block diagram of the measurements.
uð0Þxð0Þ 1 C ¼ C0 uðBÞxðBÞ C0 ¼ Q1 ð0Þ
xð0Þ 2
Qð0Þ ¼
Dx xð0Þ
1
ð1Þ
where u(0) and u(B) are the resonance amplitude at zero field and the applied field, respectively, x(0) and x(B) are the corresponding resonance angular frequencies, and Dx is the half-width obtained by the resonance curve at zero field. The depinning temperature, TD, was decided at the peak of C. 3. Results and discussion 3.1. Magnetic hysteresis loop and critical current density The magnetic hysteresis loops of sample Nos. 1–5 were measured at 10, 20, and 30 K. No flux jump was observed at these temperatures. Fig. 2 shows the hysteresis loops of sample No. 3. Using the critical-state model, JC was estimated from the magnetization hysteresis, DM, via the following formula: 1 2 b J C ¼ DM 1 ð2Þ b 3a
K. Murai et al. / Cryogenics 45 (2005) 415–420
plained by the reaction between MgB2 and Ni in SUS 304 [9]. On the other hand, the JC of sample No. 2, sintered at 1000 C, is higher at low magnetic fields than that of sample No. 1, sintered at 950 C. This indicates that the contact between grain boundaries is stronger at higher sintering temperatures [4], and that this strong contact works effectively at low fields even if the sample is contaminated with reacted Ni and MgO. Sample No. 3 showed the highest JC values (1.4 · 106 A/cm2 at zero field and 1.9 · 104 A/cm2 at 4.8 T) at 10 K. These JC values are higher than those of other samples prepared by high-pressure synthesis [1,3].
1000 800
10 K 20 K 30 K
No.3
Magnetization (emu/cm3)
600 400 200 0 -200 -400 -600 -800 -1000 -5
-4
-3
-2
-1 0 1 Magnetic field (T)
2
3
4
5
Fig. 2. Magnetization hysteresis loops of sample No. 3 at 10, 20 and 30 K.
3.2. Depinning temperature The resonance frequency change caused by flux-line depinning is normalized by the frequency difference between 5 K and 40 K. Fig. 4(a) shows the temperature dependence of the normalized resonance frequency change at various magnetic fields. Damping, C, exhibited a sharp peak at a temperature (depinning temperature, TD) where the absolute value of df/dT was maximum, as shown in Fig. 4(b). Fig. 5 shows the magnetic field dependence of TD for sample Nos. 1–5. A sample that shows a higher TD at a given magnetic field is thought to have a stronger flux pinning. This qualitatively agrees with the JC values obtained for the five samples at 30 K. The TD of sample No. 3 at 7 T is 22.5 K, which means that the BC2 (upper critical field) at 22.5 K is higher than 7 T.
106
106
10
5
105
10
4
10
3
10
2
10
1
No. 3
No. 1
No. 4
No. 2 0
(a)
1
JC (A/cm2)
JC (A/cm2)
where a and b (a > b) are the sample sizes perpendicular to the applied magnetic field. Fig. 3(a)–(c) show the dependence of critical current density on the applied magnetic field at 10, 20, and 30 K for five samples. The JC values for the samples evacuated at 500 C (Nos. 3, 4, and 5) were higher than those evacuated at room temperature (Nos. 1 and 2). The samples evacuated at room temperature had a higher MgO content than those evacuated at 500 C. These results indicate that the presence of MgO reduces JC [1]. A comparison of sample Nos. 3, 4 and 5 indicates that sintering at higher temperature reduces JC, especially at 1000 C, which degrades the flux pinning at high field and high temperature. Degradation of flux pinning can be ex-
10 K
No. 5 2
3
104
20 K
103 10
No.1
No. 4
10
1
No.2
No. 5
0
1
(b)
Magnetic field (T)
No. 3
2
5
4
417
2
3
4
5
Magnetic field (T)
106
JC (A/cm2)
105 104
30 K
103
No. 1
No. 4
101
No. 2
No. 5
10
0
(c)
No. 3
2
1
2
3
4
5
Magnetic field (T)
Fig. 3. Magnetic field dependence of the critical current density JC for samples Nos. 1–5 at (a) 10 K, (b) 20 K and (c) 30 K.
418
K. Murai et al. / Cryogenics 45 (2005) 415–420 8 No. 1
0.8 0.6
1T
No. 3
3T
0.4
5T 0.2
No. 3 No. 4
4
No. 5 2
7T
0
0
0
10
20
(a)
30
10
40
15
20
25
30
35
40
Depinning temperature (K)
Temperature (K)
Fig. 5. Magnetic field dependence of depinning temperature, TD, for sample Nos. 1–5.
250 200 Damping (s-1)
No. 2
6 Magnetic field (T)
Normalized resonance frequency change
1
3.3. Flux jumps
150
1T
No. 3
The hysteresis curves of sample No. 3 were measured between 8 K and 5 K at increments of 0.2 K. Below 7.4 K, flux jumps were observed. Fig. 6(a)–(f) show the typical flux jump patterns, which are classified into three stages with decreasing temperature. In the first stage, flux jumps occurred at 1.1 T and +1.1 T and the absolute value of the field at which the flux jumped slightly decreased as the temperature decreased. In these jumps, the magnetization did not decrease to zero, but a value of about ±80 emu/cm3 was maintained (Fig. 6(a)). In
3T
100
5T 50
7T
0 0
10
20
(b)
30
40
Temperature (K)
Fig. 4. The normalized resonance frequency change and the damping of sample No. 3 as a function of temperature at 1, 3, 5 and 7 T.
Magnetization (emu/cm3)
800
400 0 -400 -800 -2
0
2
0 -400
(b)
6.4 K Magnetization (emu/cm3)
400 0 -400 -800
-2
0
2
-2
0
2
Magnetic field (T)
4
-400
-4
5.2 K
0 -400
-2
0
2
4
Magnetic field (T)
800
400
5.0 K
400 0 -400 -800
-4
(e)
0
(c)
-800 -4
400
4
Magnetic field (T)
800
6.6 K
-800 -4
4
Magnetic field (T)
3
Magnetization (emu/cm )
400
Magnetization (emu/cm3)
-4
(d)
800
-800
(a)
800
6.8 K Magnetization (emu/cm3)
7.4 K
3
Magnetization (emu/cm )
800
-2
0
2
Magnetic field (T)
4
-4
(f)
-2
0
2
Magnetic field (T)
Fig. 6. Hysteresis loops of sample No. 3 between 7.4 and 5 K. Flux jumps were observed below 7.4 K.
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K. Murai et al. / Cryogenics 45 (2005) 415–420 1.5
1.0
BFJ (T)
0.5
0
-0.5
-1.0
-1.5 4
5
6
7
8
Temperature (K)
400
No. 1
3
800
the second stage, flux jumps occurred more easily; this was at 0 T and +0 T. The magnetization decreased to almost zero (Fig. 6(d)). In the third stage, flux jumps occurred at +0 T, 1.3 T, 0 T and +1.3 T. The magnetization decreased down to zero at +0 T and 0 T, while the magnetization did not decrease down to zero, but a value of about ±80 emu/cm3 at 1.3 T and +1.3 T was maintained (Fig. 6(f)). Fig. 7 shows the relationship between the temperature and magnetic field at which the flux jumps occurred (BFJ). The direction of the top of the triangle shows the direction of the hysteresis measurement process. The hysteresis loops were typically taken at a magnetic sweep rate of approximately 0.2 T/min. When flux jumps appeared, we reduced the rate to approximately 0.02 T/min. Then, the flux jumps at about 1 T sometimes disappeared, while those at about 0 T did not. This indicates that the flux pinned
Magnetization (emu/cm )
3
Magnetization (emu/cm )
Fig. 7. The relationship between temperature and the magnetic field at which flux jumps occurred (BFJ). See the text for symbols.
5K
0 -400
-4
No. 2 5K
400 0 -400
4
-4
3
Magnetization (emu/cm )
5K
0 -400 -800 -2 0 2 Magnetic field (T)
3
800
800
4
No. 4 5K
400 0 -400 -800
4
-4
(d)
-2 0 2 Magnetic field (T)
No. 5 5K
400 0 -400 -800 -4
(e)
-2 0 2 Magnetic field (T)
(b)
No. 3
-4
(c)
-2 0 2 Magnetic field (T)
Magnetization (emu/cm )
3
Magnetization (emu/cm )
(a)
400
800
-800
-800
800
419
-2 0 2 Magnetic field (T)
4
Fig. 8. Hysteresis loops of sample Nos. 1–5 at 5.0 K.
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at higher fields is less stable at zero field than at the applied field. The above phenomena may be explained as follows. It is thought that the stability of flux jumps in MgB2 may be analyzed within the framework of the adiabatic approximation [5]. The heat capacity becomes small below about 10 K at low magnetic field [10,11]. Then, the temperature rises abruptly to TC as a result of the avalanche process if the superconductor becomes unstable, triggered by a small fluctuation of temperature or magnetic field. In the case of flux jumps occurring under the applied magnetic field, magnetization did not decrease to zero, which could be explained by the rapid increase in specific heat with increasing magnetic field [10,11]. Fig. 8(a)–(e) show the hysteresis loops of five samples at 5.0 K. The shape for Nos. 2 and 5 correspond to the first and second stages, respectively, while those for No. 3 and No. 4 correspond to the third stage; that for No. 1 roughly corresponds to that of the third stage. This indicates that flux jumps occur more frequently in samples with higher JC.
4. Conclusion The bulk MgB2 samples were fabricated by changing the hot isostatic pressing conditions (207 MPa). The critical current densities, JC, were derived by the measurements of hysteresis loop. Sample No. 3, evacuated at 500 C before being sintered at 900 C for 2 h, had the highest JC values: 1.4 · 106 A/cm2 at zero field and 1.9 · 104 A/cm2 at 4.8 T at 10 K. Our results show that MgB2 reacts with the SUS surface above 1000 C, and the contaminated material serves to hinder the flux pinning. Moreover, the evacuation at 500 C for outgassing before sintering reduces the MgO contamination, which also hinders the flux pinning. The depinning temperature, TD, obtained by the vibrating reed technique, showed qualitatively the same trends with the strength of flux pinning as JC. TD decreased rapidly with increasing magnetic field.
The flux jumps appeared below about 8 K under fields lower than about 1.5 T. Flux jumps occurred more frequently in samples with higher JC.
Acknowledgement The authors gratefully acknowledge Dr. Iman Maartense for carrying out the ac susceptibility measurements.
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