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Restricted reversible region and strongly enhanced pinning in MPMG YBa2Cu3O7 with Y2BaCuO5 inclusions
PhysicaC 172 (1991) North-Holland
495-500
Restricted reversible region and strongly enhanced pinning in MPMG YBa2Cu307 with Y,BaCu05 inclusions L.T. Sagdahl, T. hgreid
and K. Fossheim
Division of Physics. The Norwegian Institute of Technology and SINTEF Applied Physics, 7034 Trondheim, Norway
M. Murakami, and S. Tanaka
H. Fujimoto,
S. Gotoh, K. Yamaguchi, H. Yamauchi, N. Koshizuka
Superconductivity Research Laboratory, InternationalSuperconductivity Koto-ku. Tokyo 135, Japan Received
9 October
Technology Center, l-10-13. Shinonome,
1990
Recent work has shown that the melt-powder-melt-grown (MPMG) high temperature superconductor YBa+&O, with Y,BaCuO, inclusions sustains unusually high critical current in the bulk. In the present paper the magnetic irreversibility line of this material is studied by AC permeability measurements. The irreversibility line is much steeper and is moved to higher temperatures compared to single crystal YBa#&O, and the reversible region between the irreversibility line and the Hc2 line is drastically shrunk. From standard flux creep analysis the pinning energy is found to be increased by one order of magnitude as compared to YBaZCu30,. The measurements further show that the irreversibility temperature increases in a simple logarithmic fashion with increasing frequency. The magnetic AC field response is found to be highly nonlinear even when &,I&,lo-‘.
1. Introduction Since the discovery [ I] of high temperature oxide superconductors extensive research has been conducted worldwide to produce materials with high critical current for applications. Most applications require a high critical current density, J,(B=O) of the order 104-lo6 A cm-’ at 77 K, preferably not strongly dependent on magnetic field, with. The observed dissipative flux motion [ 2-41 believed to be caused by weak pinning and high critical temperature results in low J, values in many high-T, materials especially when prepared in bulk. High quality single crystals have a rather low pinning energy, possibly related to low defect density. To meet the requirement of high J,, extensive research is needed to increase systematically the pinning strength in highT, oxide superconductors and to avoid depression of J, by the weak links which are present in sintered samples. Recently it has been found that it is possible to increase J, strongly by introduction of fine YzBaCuOs 092 l-4534/9
l/$03.50
0 199 1 - Elsevier Science Publishers
(2 11) particles into the YBa2Cu30, matrix through a melt-powder-melt-growth (MPMG) process [ 5 1. J, could be further increased by increasing the volume fraction of 2 11 particles [ 5 1. It has been suggested that the non-superconducting 2 11 particles act as strong pinning centers [ 6-8 1. Still, the details of the pinning mechanism are not well understood. In any case MPMG samples of YBa2Cu30, with YzBaCuO, inclusions exhibit much stronger flux pinning behaviour than single crystals. In addition, the weak link problem seems to be much reduced in the MPMG material. A way of characterizing pinning behaviour is to measure the so-called irreversibility line, which according to the standard interpretation marks the boundary between reversible and irreversible regions in the field-temperature plane [ 9 1. From AC permeability measurements a point on the irreversibility line is determined from the maximum of the imaginary part of the permeability as a function of temperature at a given applied DC magnetic field, measuring frequency and AC excitation field amplitude. The interpretation of
B.V. (North-Holland)
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L. T. Sagdahl et al. /MPMG YBa2Cu30, with Y,BaCuO, inclusions
this line has been the subject of intense study [ 41, with theoretical proposals ranging from a granular glass superconducting model [ 10 1, to thermally activated depinning of vortices [ 2,4,11], vortex lattice melting [ 12- 14 ] and vortex lattice freezing [ 15 1. In the ongoing effort to understand the flux dynamics in high-T, superconductors it is essential to establish the basic experimental features of the irreversibility line for different samples with different defect densities, anisotropies and types of pinning centers. It was recently reported that the irreversibility line is largely independent of the defect density in YBazCuSO, single crystals even when the density is changed so much as to enhance the critical current by more than an order of magnitude [ 16 1. The present paper represents the beginning of extensive and systematic study of flux dynamics in the important MPMG modification of YBazCu307. We report measurements of the complex magnetic permeability, p= p’ + ip”, on MPMG YBa2Cu30, with YzBaCuO, inclusions. The measurements were made with excitation fields in the range from 0.2x 1O-4 to 30x 10e4 T in the temperature range 82 to 92 K, employing frequencies from 10 to 1O5Hz and external fields up to 8 T. A central result of this paper is that the irreversibility line of MPMG YBa2Cu307 with Y2BaCuOS inclusions is steeper and is moved to higher temperatures compared to single crystal YBazCu30, samples. As will be discussed below, this result is consistent with the picture that the reversible region is narrower in samples with stronger pinning. Analysis of the data show that the effective pinning energy is increased by an order of magnitude. It is further documented that the irreversibility line is very sensitive to the excitation field used in dynamic permeability measurements, even at AC fields less than 1O-4 T in an 8T static field, i.e. when BAc/ BDc< 10-5. The irreversibility line further depends logarithmically on probing time, i.e. on the frequency of the excitation field. Previous work by the Trondheim group [ 17 ] has shown that the field penetration in the AC case is frequency limited through an effective skin depth, B_o-‘12.
2. Experimental procedure 2.1. Sample preparation The material used in the present study was prepared by the MPMG process. Y203, BaC03, and CuO were mixed in the ratio powders Y:Ba:Cu= 1.2:2.1:3.1 and calcined at 900°C for 8 h. The samples were melted at 1350°C for 20 min and quenched using copper plates. The quenched samples were crushed into powder and then pressed into pellets 3 cm in diameter and 2 cm in thickness. The pellets were heated to 1100°C for 20 min and cooled down to 1000°C at a rate of lOO”C/h followed by slow-cooling at a rate of 1 “C/h down to 900’ C and then furnace cooled. These processes were conducted in air. Finally the samples were annealed in flowing oxygen. The samples for AC measurements were cut from the pellet and their crystal orientation was determined by microstructural observation. Figure 1 shows a transmission electron micrograph of the MPMG processed sample with nominal composition Y,,,Ba2.,Cu,.,0,. The sample from this pellet is called MPMG-Y1.2. It is notable that small 2 11 particles with diameter less than 1 pm are dispersed in the 123 matrix. The sample exhibits J, values of 4 x 1O4 A/cm2 in zero field and 1 x 1O4 A/cm2 in 1 T(Hllc axis) at 77 K.
Fig. 1. Transmission electron micrograph for microstructure of MPMG processed Y,.2Ba2.,Cu3.,0,.
491
L. T. Sagdahl et al. /MPMG YBa2CuJ07 with Y2BaCu05 inclusions 2.2, Measurement
technique
In our permeability measurements an adjustable AC magnetic excitation field generates a response in the sample placed inside the coil. This response in its turn induces a voltage in a pick-up coil wound tight around the sample. The pick-up voltage is proportional to the complex permeability, p, of the sample. Real and imaginary components of ,LIare recorded separately. The demagnetization factor for the sample was not determined and therefore p is not calibrated. The temperature was stabilized within 10 mK. When measuring in an applied DC field, the resistance in the thermometer was carefully corrected for magnetoresistance.
3. Results and discussion The irreversibility line is determined from the maximum in the imaginary part of the permeability in different applied fields (O-8 T). Figure 2 shows the irreversibility lines measured at BAC= 1 X 10p4 T on the sample MPMG-Y 1.2. For comparison we have shown measurements of the irreversibility line in a 9
a
Fig. 2. The irreversibility line B*( T*) (square symbols) in the field range 0 to 8 T ( L H, c) = 24” ) determined from AC permeability measurements on the sample MPMG-Y 1.2 with f= 12 1 Hz and BAc= 1 x 10m4T. The solid line is drawn as a guide to the eye. Circles indicate the irreversibility line Bo( T*) of a single crystal YBaQ,O, measured withf= 121 Hz and BA,=3x 10m4 T and Hllc. The straight solid line is J&(T) (Hllc) taken from ref. [20].
single crystal YBa2Cu307, at the same frequency but slightly higher excitation field (&= 3 X lop4 T) [ 171. It is evident from fig. 2 that the reversible region in MPMG is much narrower than in the single crystal. In order to compare the pinning strength in these samples we use flux creep model [ 18,191 to characterize the effective pinning potential from our measurements. The predicted equation for the irreversibility line in this model [ 19 ] is: U/kT*=
-ln(o/oe)
,
(1)
where w is the measuring frequency, w. is attempt frequency for flux lines to escape from a pinning site with a pinning potential U, usually taken to go as U=Aj( 1 -T/T,)“/B. Aj depends on the current in the sample. The exponent n is expected to be 3/2 in the simplest mean field picture [ 17 1. The irreversibility line can be described in the flux creep model by introducing in eq. ( 1) the temperature and field dependence of U given above. After rearranging the terms in eq. ( 1) we obtained in the mean field limit [ 191: B*=C(o)(
where
l-T*/T
c )3’2P,
C(o)=-Aj/k’ln(c~~/oo)
(2)
with
T,=
T*(&=O).
From the irreversibility lines for Y 1.2 and the single crystal measured with an excitation field of 3~10~~ T and frequencyf=121 Hz using eq. (2) we find CZ 50 000 T K for MPMG-Y 1.2 and CZ 5000 T K for the single crystal. Since U is proportional to C, we conclude that the effective pinning potential as measured at this excitation field and frequency, is one order of magnitude larger for the MPMG-Y 1.2 sample than for the single crystal. The numerical value of U cannot be determined from eqs. ( 1) and (2) since o. is unknown. We note, however, that w. may be determined by fitting an appropriate ,u( w, T, B)-function to the p’ and p” data. When this was done in YBa2Cu30T the resulting w. was 2.2 x lo6 s- ’ [ 17 1. This corresponds to a value OfAj equal to (3.3 & 0.9) eV T. At 77 K and 1 T field this gives U= 0.14 eV. If we were to assume that w. is the same in the present case, the resulting pinning energy at 77 K and 1 T in MPMG-Y 1.2 is found to be U= 1.85 eV. Clearly this analysis is too simple, since we have used only one relaxation time. However, the relative sizes of U determined this way we
498
L. T. Sagdahl et al. /MPMG YBa2Cu30, with Y,BaCuO, inclusions
believe to be realistic. It should be noted that the details of this analysis is sensitive to the choice of exponent n in the temperature dependence of U, and also to the value of T,, as reported elsewhere [ 17 1. This will, however, not change the conclusion that the MPMG material shows substantially stronger pinning than single crystals. If w. is taken to be the same in both cases, the pinning potential is at least 10 times higher in MPMG than in YBazCu307 crystals. After performing all measurements it was discovered that the applied fields, both DC and AC, had been oriented at 24” from the c-axis. This means that the field along c was 90% of the total, instead of fully oriented along the c-axis. In our opinion this will only constitute a relatively small shift of the irreversibility line compared to the Hllc case. In no important way will it alter the central conclusions of the present work. Further studies on MPMG samples with different content of 2 11 particles and different values of J, in order to understand the influence of 211 concentration and dispersion on the irreversibility line, as well as the details of the pinning mechanism are in progress. The peaks in the imaginary part of the permeability in different applied fields (O-7 T) measured on the sample MPMG-Y 1.2 are shown in fig. 3. All measurements were done using BAC= 1 x 1Od4 T and 0.2
at a frequency f= 121 Hz. The amplitude of p” decreases and the width of the peaks increase with increasing DC field on MPMG-Y 1.2. Earlier measurements on a single crystal [ 17 ] showed an increase of the amplitude of p” with increasing applied field. The real part of the permeability in different applied fields is shown in fig. 4. We have studied the frequency dependence of the irreversibility temperature T*, in the frequency range from 10 to 1O5 Hz and in different applied DC-fields up to 6 T (fig. 5 ). We observe a logarithmic increase
Fig. 4. The real part of the AC permeability vs. temperature in different external fields from 0.6 to 7 T ( LIZ, c) =24” ) on MPMG-Y1.2 withf= 121 Hz and BAc= 1 x lo-“ T.
89.5
MPMG-Y1.2
89.0 88.5 -88.0 37.5
‘ZL
* 87.0 + 86.5 86.0 85.5 85.0
82 g2 Fig. 3. The imaginary part of the AC permeability vs. temperature in different external fields from 0.6 to 7 T ( L H, c) = 24” ) on MPMG-Y 1.2 withy= 12 1 Hz and BAc= 1 X 10m4 T. The solid lines are a guide to the eye.
Fig. 5. The irreversibility temperature determined from the maximum in the imaginary part of the permeability measured on MPMG-Y 1.2 as a function of frequency. The straight lines are logarithmic fits to the data.
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L. T. Sagdahl et al. / MPMG YBa2Cu307 with YzBaCuOs inclusions
in T* with increasing frequency. This is in agreement with flux creep theory. The frequency dependence of T * in the MPMG-Y 1.2 sample is very similar to that found in our earlier measurements [ 17 ] on a single crystal YBazCu30,, although the slope of the curves changes less with increasing applied field. The irreversibility lines measured on MPMG-Y 1.2 employing different frequencies are shown in fig. 6. The curvature, particularly at low applied fields, increases with increasing frequency. Measurements investigating the excitation field dependence (B,,=O.l x 1O-4-3O~ 10d4 T) of T* (fig. 7) were also performed. The irreversibility temperature is dependent of the AC field. The behaviour is strongly nonlinear in BAc even at very low AC fields (below 1Oe4 T) and the curvature changes when the applied B-field is changed. There is a tendency towards steeper BAC( T* )-curves at low DC fields. However, the curves measured at 4 and 8 T somewhat steeper and less curved than the 6 T curve. The AC field dependence implies that the curvature of the irreversibility line is independent on the value of the excitation field used in the experiment. The irreversibility lines measured on MPMG-Y 1.2 using five different excitation fields, are plotted in fig. 8. This feature makes it highly desirable to determine explicitly the AC field dependence of the irreversibility line. The strong AC field nonlinearity implies that the effectiveness of various pinning centers de-
MPMG-Yl.2 8
7
i
a
of=121
Hz
0f=1.2
klir
Of =12.1 kHz l
f =121 kHz
Fig. 6. The irreversibility lines B*( T*) on MPMG-Y 1.2 measured with BAc= 1 X lo-“ T and different frequencies. The solid lines are guides to the eye.
303.0-r -
25:
MPMG-Y1.2
00.4T o1.5 T
.
83
+4T
84
85
86
T"
Fig. 7. The AC field dependence of the irreversibility temperature on MPMG-Y 1.2 at different external fields ranging from 0 to 8 T determined from the maximum in the imaginary part of the permeability.
Y
O1.lOm’ T a
7
+2.10-’
T
+3.10s’
T
l540-’
T
Fig. 8. The irreversibility lines B*( T*) on MPMG-Y 1.2 measured withy= 121 Hz and different AC fields. The solid lines arc guides to the eye.
pends sensitively on the magnitude of current flowing in the sample. Examination of this behaviour could give valuable information about pinning mechanisms and the connection to J, in high T, materials. The nonlinear AC field dependence in these measurements also makes it difficult to use simple flux creep theories to extract the pinning strength unambiguously as long as we do not know the dependence on the excitation field BAc explicitly. From this one might draw the conclusion that only DC measurements should be used to determine the irrever-
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L. T. Sagdahl et al. /MPMG YBazCuJOr with Y2BaCu05 inclusions
sibility line. However, as was apparent in the original data of Miiller, Takashige and Bednorz [ lo], there is considerable uncertainty in determining the irreversibility point even in such measurements. Because of the promising possibilities for applications, it is important to study the MPMG material to gain an understanding of the physics in these materials.
4. Conclusions In this paper we have shown that the irreversibility line determine from AC permeability measurements on MPMG high temperature superconductor YBa2Cu30, with Y,BaCuO, inclusions is much steeper and is moved to considerably higher temperatures compared to single crystal YBa2Cu307 samples. The effective pinning energy is increased by an order of magnitude. This is consistent with the picture that the reversible region is smaller in samples with stronger pinning. It is further documented that the irreversibility line is very sensitive to the excitation field used in dynamic permeability measurements, even at AC fields less than 10m4 T in a 8 T static field, i.e. when B,,-/B,,< 10p5. T* further depends logarithmically on the frequency of the excitation field.
Acknowledgements This work was supported by The Norwegian Research Council for Science and the Humanities (NAVF) and Norsk Hydro A/S. One of us (L.T.S. ) especially acknowledges a stipend from NAVF. We would like to thank Svein Gjolmelsi, Pal Tuset, OlavMagnar Nes and Marcin Slaski for assistance and
helpful discussions. We are grateful to T. Oyama of SRL for sample preparation.
References [ 1] J.G. Bednorz and K.A. Miiller, Z. Phys. B64 ( 1986) 189. [2] Y. Yeshurun and A.P. Malozemoff, Phys. Rev. Lett. 60 (1988) 2202. [3]T.T.M. Palstra, B. Batlogg, R.B. van Dover, L.F. Schneemeyer and J.V. Waszczak, Appl. Phys. 54 (8) ( 1989). [4] A.P. Malozemoff, MRS Bull., Physica Properties of High Temperature Superconductors, ed. D. Ginsberg (World Scientific, Singapore, 1989) p. 7 1. [ 51M. Murakami, Mod. Phys. Lett. B4 (1990) 163. [6] R.I. Coote, J.E. Evetts andA.E. Campbell, Can. J. Phys. 50 (1972) 421. [7] M. Murakami, S. Gotoh, N. Koshizuka, S. Tanaka, T. Matsushita, S. Kambe and K. Kitazawa, Cryogenics 30 ( 1990) 390. [8] K. Matsumoto, H. Kikuchi, N. Uno and Y. Tanaka, Cryogenics 30 (1990) 5. [9] A.P. Malozemoff, T.K. Worthington, Y. Yeshurun, F. Holtzberg and P.H. Kes, Phys. Rev. B38 (1988) 7203. [lo] K.A. Miiller, M. Takashige and J.G. Bednorz, Phys. Rev. Lett. 58 (1987) 1143. [ 111 P.H. Kes and J. van den Berg, in: Studies of High Temperature Superconductors, ed. A. Narlikar (Nova Science Publ., New York), to be published. [ 121 P.L. Gammel, J. Appl. Phys. 67 (1990) 4676. [ 131 A. Houghton, R.A.Pelcovitz and A. Sudbe, Phys. Rev. B40 (1989) 6763. [ 141 E.H. Brandt, Phys. Rev. Lett. 63 (1989) 1106. [ 151 M.P.A. Fisher, Phys. Rev. Lett. 62 (1989) 1415; D.S. Fisher, M.P.A. Fisher and D.S. Huse (to be published). [ 16 ] L. Civale, A.D. Marwick, M. W. Elfresh, T.K. Worthington, A.P. Malozemoff and F.H. Holtzberg, Phys. Rev. Lett. 65 (1990) 1164. [ 17 ] L.T. Sagdahl, S. Gjelmelsi, T. Laegreid, K. Fossheim and W. Assmus, Phys. Rev. B (in press). [ 181 P.W. Anderson, Phys. Rev. Lett. 9 ( 1962) 309. [ 191 S. Gjolmelsi, L.T. Sagdahl, T. Liegreid and K. Fossheim, PhysicaC 162-164 (1989) 339. [20] U. Welp, W.K. Kwok, G. Crabtree, K.G. Vandervoort and J.Z. Liu, Phys. Rev. Lett. 62 (1989) 1908.
495-500
Restricted reversible region and strongly enhanced pinning in MPMG YBa2Cu307 with Y,BaCu05 inclusions L.T. Sagdahl, T. hgreid
and K. Fossheim
Division of Physics. The Norwegian Institute of Technology and SINTEF Applied Physics, 7034 Trondheim, Norway
M. Murakami, and S. Tanaka
H. Fujimoto,
S. Gotoh, K. Yamaguchi, H. Yamauchi, N. Koshizuka
Superconductivity Research Laboratory, InternationalSuperconductivity Koto-ku. Tokyo 135, Japan Received
9 October
Technology Center, l-10-13. Shinonome,
1990
Recent work has shown that the melt-powder-melt-grown (MPMG) high temperature superconductor YBa+&O, with Y,BaCuO, inclusions sustains unusually high critical current in the bulk. In the present paper the magnetic irreversibility line of this material is studied by AC permeability measurements. The irreversibility line is much steeper and is moved to higher temperatures compared to single crystal YBa#&O, and the reversible region between the irreversibility line and the Hc2 line is drastically shrunk. From standard flux creep analysis the pinning energy is found to be increased by one order of magnitude as compared to YBaZCu30,. The measurements further show that the irreversibility temperature increases in a simple logarithmic fashion with increasing frequency. The magnetic AC field response is found to be highly nonlinear even when &,I&,lo-‘.
1. Introduction Since the discovery [ I] of high temperature oxide superconductors extensive research has been conducted worldwide to produce materials with high critical current for applications. Most applications require a high critical current density, J,(B=O) of the order 104-lo6 A cm-’ at 77 K, preferably not strongly dependent on magnetic field, with. The observed dissipative flux motion [ 2-41 believed to be caused by weak pinning and high critical temperature results in low J, values in many high-T, materials especially when prepared in bulk. High quality single crystals have a rather low pinning energy, possibly related to low defect density. To meet the requirement of high J,, extensive research is needed to increase systematically the pinning strength in highT, oxide superconductors and to avoid depression of J, by the weak links which are present in sintered samples. Recently it has been found that it is possible to increase J, strongly by introduction of fine YzBaCuOs 092 l-4534/9
l/$03.50
0 199 1 - Elsevier Science Publishers
(2 11) particles into the YBa2Cu30, matrix through a melt-powder-melt-growth (MPMG) process [ 5 1. J, could be further increased by increasing the volume fraction of 2 11 particles [ 5 1. It has been suggested that the non-superconducting 2 11 particles act as strong pinning centers [ 6-8 1. Still, the details of the pinning mechanism are not well understood. In any case MPMG samples of YBa2Cu30, with YzBaCuO, inclusions exhibit much stronger flux pinning behaviour than single crystals. In addition, the weak link problem seems to be much reduced in the MPMG material. A way of characterizing pinning behaviour is to measure the so-called irreversibility line, which according to the standard interpretation marks the boundary between reversible and irreversible regions in the field-temperature plane [ 9 1. From AC permeability measurements a point on the irreversibility line is determined from the maximum of the imaginary part of the permeability as a function of temperature at a given applied DC magnetic field, measuring frequency and AC excitation field amplitude. The interpretation of
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L. T. Sagdahl et al. /MPMG YBa2Cu30, with Y,BaCuO, inclusions
this line has been the subject of intense study [ 41, with theoretical proposals ranging from a granular glass superconducting model [ 10 1, to thermally activated depinning of vortices [ 2,4,11], vortex lattice melting [ 12- 14 ] and vortex lattice freezing [ 15 1. In the ongoing effort to understand the flux dynamics in high-T, superconductors it is essential to establish the basic experimental features of the irreversibility line for different samples with different defect densities, anisotropies and types of pinning centers. It was recently reported that the irreversibility line is largely independent of the defect density in YBazCuSO, single crystals even when the density is changed so much as to enhance the critical current by more than an order of magnitude [ 16 1. The present paper represents the beginning of extensive and systematic study of flux dynamics in the important MPMG modification of YBazCu307. We report measurements of the complex magnetic permeability, p= p’ + ip”, on MPMG YBa2Cu30, with YzBaCuO, inclusions. The measurements were made with excitation fields in the range from 0.2x 1O-4 to 30x 10e4 T in the temperature range 82 to 92 K, employing frequencies from 10 to 1O5Hz and external fields up to 8 T. A central result of this paper is that the irreversibility line of MPMG YBa2Cu307 with Y2BaCuOS inclusions is steeper and is moved to higher temperatures compared to single crystal YBazCu30, samples. As will be discussed below, this result is consistent with the picture that the reversible region is narrower in samples with stronger pinning. Analysis of the data show that the effective pinning energy is increased by an order of magnitude. It is further documented that the irreversibility line is very sensitive to the excitation field used in dynamic permeability measurements, even at AC fields less than 1O-4 T in an 8T static field, i.e. when BAc/ BDc< 10-5. The irreversibility line further depends logarithmically on probing time, i.e. on the frequency of the excitation field. Previous work by the Trondheim group [ 17 ] has shown that the field penetration in the AC case is frequency limited through an effective skin depth, B_o-‘12.
2. Experimental procedure 2.1. Sample preparation The material used in the present study was prepared by the MPMG process. Y203, BaC03, and CuO were mixed in the ratio powders Y:Ba:Cu= 1.2:2.1:3.1 and calcined at 900°C for 8 h. The samples were melted at 1350°C for 20 min and quenched using copper plates. The quenched samples were crushed into powder and then pressed into pellets 3 cm in diameter and 2 cm in thickness. The pellets were heated to 1100°C for 20 min and cooled down to 1000°C at a rate of lOO”C/h followed by slow-cooling at a rate of 1 “C/h down to 900’ C and then furnace cooled. These processes were conducted in air. Finally the samples were annealed in flowing oxygen. The samples for AC measurements were cut from the pellet and their crystal orientation was determined by microstructural observation. Figure 1 shows a transmission electron micrograph of the MPMG processed sample with nominal composition Y,,,Ba2.,Cu,.,0,. The sample from this pellet is called MPMG-Y1.2. It is notable that small 2 11 particles with diameter less than 1 pm are dispersed in the 123 matrix. The sample exhibits J, values of 4 x 1O4 A/cm2 in zero field and 1 x 1O4 A/cm2 in 1 T(Hllc axis) at 77 K.
Fig. 1. Transmission electron micrograph for microstructure of MPMG processed Y,.2Ba2.,Cu3.,0,.
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L. T. Sagdahl et al. /MPMG YBa2CuJ07 with Y2BaCu05 inclusions 2.2, Measurement
technique
In our permeability measurements an adjustable AC magnetic excitation field generates a response in the sample placed inside the coil. This response in its turn induces a voltage in a pick-up coil wound tight around the sample. The pick-up voltage is proportional to the complex permeability, p, of the sample. Real and imaginary components of ,LIare recorded separately. The demagnetization factor for the sample was not determined and therefore p is not calibrated. The temperature was stabilized within 10 mK. When measuring in an applied DC field, the resistance in the thermometer was carefully corrected for magnetoresistance.
3. Results and discussion The irreversibility line is determined from the maximum in the imaginary part of the permeability in different applied fields (O-8 T). Figure 2 shows the irreversibility lines measured at BAC= 1 X 10p4 T on the sample MPMG-Y 1.2. For comparison we have shown measurements of the irreversibility line in a 9
a
Fig. 2. The irreversibility line B*( T*) (square symbols) in the field range 0 to 8 T ( L H, c) = 24” ) determined from AC permeability measurements on the sample MPMG-Y 1.2 with f= 12 1 Hz and BAc= 1 x 10m4T. The solid line is drawn as a guide to the eye. Circles indicate the irreversibility line Bo( T*) of a single crystal YBaQ,O, measured withf= 121 Hz and BA,=3x 10m4 T and Hllc. The straight solid line is J&(T) (Hllc) taken from ref. [20].
single crystal YBa2Cu307, at the same frequency but slightly higher excitation field (&= 3 X lop4 T) [ 171. It is evident from fig. 2 that the reversible region in MPMG is much narrower than in the single crystal. In order to compare the pinning strength in these samples we use flux creep model [ 18,191 to characterize the effective pinning potential from our measurements. The predicted equation for the irreversibility line in this model [ 19 ] is: U/kT*=
-ln(o/oe)
,
(1)
where w is the measuring frequency, w. is attempt frequency for flux lines to escape from a pinning site with a pinning potential U, usually taken to go as U=Aj( 1 -T/T,)“/B. Aj depends on the current in the sample. The exponent n is expected to be 3/2 in the simplest mean field picture [ 17 1. The irreversibility line can be described in the flux creep model by introducing in eq. ( 1) the temperature and field dependence of U given above. After rearranging the terms in eq. ( 1) we obtained in the mean field limit [ 191: B*=C(o)(
where
l-T*/T
c )3’2P,
C(o)=-Aj/k’ln(c~~/oo)
(2)
with
T,=
T*(&=O).
From the irreversibility lines for Y 1.2 and the single crystal measured with an excitation field of 3~10~~ T and frequencyf=121 Hz using eq. (2) we find CZ 50 000 T K for MPMG-Y 1.2 and CZ 5000 T K for the single crystal. Since U is proportional to C, we conclude that the effective pinning potential as measured at this excitation field and frequency, is one order of magnitude larger for the MPMG-Y 1.2 sample than for the single crystal. The numerical value of U cannot be determined from eqs. ( 1) and (2) since o. is unknown. We note, however, that w. may be determined by fitting an appropriate ,u( w, T, B)-function to the p’ and p” data. When this was done in YBa2Cu30T the resulting w. was 2.2 x lo6 s- ’ [ 17 1. This corresponds to a value OfAj equal to (3.3 & 0.9) eV T. At 77 K and 1 T field this gives U= 0.14 eV. If we were to assume that w. is the same in the present case, the resulting pinning energy at 77 K and 1 T in MPMG-Y 1.2 is found to be U= 1.85 eV. Clearly this analysis is too simple, since we have used only one relaxation time. However, the relative sizes of U determined this way we
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L. T. Sagdahl et al. /MPMG YBa2Cu30, with Y,BaCuO, inclusions
believe to be realistic. It should be noted that the details of this analysis is sensitive to the choice of exponent n in the temperature dependence of U, and also to the value of T,, as reported elsewhere [ 17 1. This will, however, not change the conclusion that the MPMG material shows substantially stronger pinning than single crystals. If w. is taken to be the same in both cases, the pinning potential is at least 10 times higher in MPMG than in YBazCu307 crystals. After performing all measurements it was discovered that the applied fields, both DC and AC, had been oriented at 24” from the c-axis. This means that the field along c was 90% of the total, instead of fully oriented along the c-axis. In our opinion this will only constitute a relatively small shift of the irreversibility line compared to the Hllc case. In no important way will it alter the central conclusions of the present work. Further studies on MPMG samples with different content of 2 11 particles and different values of J, in order to understand the influence of 211 concentration and dispersion on the irreversibility line, as well as the details of the pinning mechanism are in progress. The peaks in the imaginary part of the permeability in different applied fields (O-7 T) measured on the sample MPMG-Y 1.2 are shown in fig. 3. All measurements were done using BAC= 1 x 1Od4 T and 0.2
at a frequency f= 121 Hz. The amplitude of p” decreases and the width of the peaks increase with increasing DC field on MPMG-Y 1.2. Earlier measurements on a single crystal [ 17 ] showed an increase of the amplitude of p” with increasing applied field. The real part of the permeability in different applied fields is shown in fig. 4. We have studied the frequency dependence of the irreversibility temperature T*, in the frequency range from 10 to 1O5 Hz and in different applied DC-fields up to 6 T (fig. 5 ). We observe a logarithmic increase
Fig. 4. The real part of the AC permeability vs. temperature in different external fields from 0.6 to 7 T ( LIZ, c) =24” ) on MPMG-Y1.2 withf= 121 Hz and BAc= 1 x lo-“ T.
89.5
MPMG-Y1.2
89.0 88.5 -88.0 37.5
‘ZL
* 87.0 + 86.5 86.0 85.5 85.0
82 g2 Fig. 3. The imaginary part of the AC permeability vs. temperature in different external fields from 0.6 to 7 T ( L H, c) = 24” ) on MPMG-Y 1.2 withy= 12 1 Hz and BAc= 1 X 10m4 T. The solid lines are a guide to the eye.
Fig. 5. The irreversibility temperature determined from the maximum in the imaginary part of the permeability measured on MPMG-Y 1.2 as a function of frequency. The straight lines are logarithmic fits to the data.
499
L. T. Sagdahl et al. / MPMG YBa2Cu307 with YzBaCuOs inclusions
in T* with increasing frequency. This is in agreement with flux creep theory. The frequency dependence of T * in the MPMG-Y 1.2 sample is very similar to that found in our earlier measurements [ 17 ] on a single crystal YBazCu30,, although the slope of the curves changes less with increasing applied field. The irreversibility lines measured on MPMG-Y 1.2 employing different frequencies are shown in fig. 6. The curvature, particularly at low applied fields, increases with increasing frequency. Measurements investigating the excitation field dependence (B,,=O.l x 1O-4-3O~ 10d4 T) of T* (fig. 7) were also performed. The irreversibility temperature is dependent of the AC field. The behaviour is strongly nonlinear in BAc even at very low AC fields (below 1Oe4 T) and the curvature changes when the applied B-field is changed. There is a tendency towards steeper BAC( T* )-curves at low DC fields. However, the curves measured at 4 and 8 T somewhat steeper and less curved than the 6 T curve. The AC field dependence implies that the curvature of the irreversibility line is independent on the value of the excitation field used in the experiment. The irreversibility lines measured on MPMG-Y 1.2 using five different excitation fields, are plotted in fig. 8. This feature makes it highly desirable to determine explicitly the AC field dependence of the irreversibility line. The strong AC field nonlinearity implies that the effectiveness of various pinning centers de-
MPMG-Yl.2 8
7
i
a
of=121
Hz
0f=1.2
klir
Of =12.1 kHz l
f =121 kHz
Fig. 6. The irreversibility lines B*( T*) on MPMG-Y 1.2 measured with BAc= 1 X lo-“ T and different frequencies. The solid lines are guides to the eye.
303.0-r -
25:
MPMG-Y1.2
00.4T o1.5 T
.
83
+4T
84
85
86
T"
Fig. 7. The AC field dependence of the irreversibility temperature on MPMG-Y 1.2 at different external fields ranging from 0 to 8 T determined from the maximum in the imaginary part of the permeability.
Y
O1.lOm’ T a
7
+2.10-’
T
+3.10s’
T
l540-’
T
Fig. 8. The irreversibility lines B*( T*) on MPMG-Y 1.2 measured withy= 121 Hz and different AC fields. The solid lines arc guides to the eye.
pends sensitively on the magnitude of current flowing in the sample. Examination of this behaviour could give valuable information about pinning mechanisms and the connection to J, in high T, materials. The nonlinear AC field dependence in these measurements also makes it difficult to use simple flux creep theories to extract the pinning strength unambiguously as long as we do not know the dependence on the excitation field BAc explicitly. From this one might draw the conclusion that only DC measurements should be used to determine the irrever-
500
L. T. Sagdahl et al. /MPMG YBazCuJOr with Y2BaCu05 inclusions
sibility line. However, as was apparent in the original data of Miiller, Takashige and Bednorz [ lo], there is considerable uncertainty in determining the irreversibility point even in such measurements. Because of the promising possibilities for applications, it is important to study the MPMG material to gain an understanding of the physics in these materials.
4. Conclusions In this paper we have shown that the irreversibility line determine from AC permeability measurements on MPMG high temperature superconductor YBa2Cu30, with Y,BaCuO, inclusions is much steeper and is moved to considerably higher temperatures compared to single crystal YBa2Cu307 samples. The effective pinning energy is increased by an order of magnitude. This is consistent with the picture that the reversible region is smaller in samples with stronger pinning. It is further documented that the irreversibility line is very sensitive to the excitation field used in dynamic permeability measurements, even at AC fields less than 10m4 T in a 8 T static field, i.e. when B,,-/B,,< 10p5. T* further depends logarithmically on the frequency of the excitation field.
Acknowledgements This work was supported by The Norwegian Research Council for Science and the Humanities (NAVF) and Norsk Hydro A/S. One of us (L.T.S. ) especially acknowledges a stipend from NAVF. We would like to thank Svein Gjolmelsi, Pal Tuset, OlavMagnar Nes and Marcin Slaski for assistance and
helpful discussions. We are grateful to T. Oyama of SRL for sample preparation.
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