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The reversible magnetization of oxygen deficient YBa2Cu3O7−δ
PHYSlCA
Physica C 183 (1991) 293-302 North-Holland
i
The reversible magnetization of oxygen deficient
YBaECU307_a
Manfred D~iumling IBM T.J. Watson Research Center, Yorktown Heights, NY 10598, USA Received 3 September 1991
The reversible magnetization M,~vof polycrystalline YBa2Cu307_a (0 < tJ< 0.5 ) was measured. Due to a small grain size and low critical current densities in oxygen deficient specimens M,~vcould be measured over most of the superconducting regime from l 0 K to T¢up to a magnetic field of 5.5 T. The magnetization data is in excellent agreement with calculated values obtained from Ginzburg-Landau (GL) theory. Values for the thermodynamic critical field Hc and the G L parameter r are obtained. High values of r ~ 170-300 (for H~c) are necessary to fit the magnetization data. He( T= 0 ) decreases strongly for increasing oxygen deficiencies up to ~ 0 . 1 5 , and then remains nearly constant. Specific heat jumps Ac at T¢ were calculated from the data and the fit. Quantitative agreement with data in the literature is obtained. Just like He, the specific heat jump is strongly dependent on the oxygen deficiency in the near stoichiometric regime.
1. Introduction In a superconductor c o m p l e t e knowledge o f the reversible magnetization as a function o f field a n d t e m p e r a t u r e enables the d e t e r m i n a t i o n o f all superconducting p a r a m e t e r s [ 1 ]. I f only parts o f the magnetization in the H - T space are known then theoretical expressions [ 2 - 4 ] allow a fit o f the magnetization using a set o f p a r a m e t e r s like the critical field He ( T ) a n d the G i n z b u r g - L a n d a u p a r a m eter x. F r o m these p a r a m e t e r s o t h e r quantities like the u p p e r critical field Hc2(T) can be d e t e r m i n e d even if magnetization d a t a is not available up to H¢2. T h e r m o d y n a m i c a l l y the m a g n e t i z a t i o n is linked to the j u m p in the specific heat at T¢ via the temperature d e p e n d e n c e o f the critical field He. Knowledge o f these p a r a m e t e r s as a function o f oxygen concentration in YBa2Cu307_a allows better u n d e r s t a n d i n g o f the flux pinning properties. C o n t r a r y to the countless n u m b e r s o f publications on other superconducting properties m e a s u r e m e n t s o f the reversible magnetization are sparse. This is mostly due to the high critical current densities J¢ typically found in YBa2Cu307_, which cause large irreversibilities in the magnetization. A l m o s t all m e a s u r e m e n t s were carried out on n o m i n a l l y fully oxygenated "90 K " specimens. Welp et al. [ 5 ] have m e a s u r e d the mag-
netization in single crystals for both the HIIc and H Z c orientations, m a i n l y for the purpose o f obtaining a value for the u p p e r critical field He2. H a o et al. [ 3 ] d e v e l o p e d a simplified theoretical solution o f the G L equations a n d a p p l i e d it to m e a s u r e m e n t s on a single crystal, deriving values for He, x a n d H¢2 for the HIIc orientation. Others [6,7] m e a s u r e d the reversible magnetization in oriented powders close to T¢ in ord e r to investigate the role o f fluctuations. Only one m e a s u r e m e n t exists on an oxygen deficient crystal [ 8 ]. The investigation o f oxygen deficient specimens is c o m p l i c a t e d by the a p p a r e n t existence o f multiple T¢ values for a given 8 [9-11 ], indicating the possibility o f a phase separation [ 12 ] for certain oxygen stoichiometries. It was a t t e m p t e d to avoid this problem by quenching the samples from a high t e m p e r a t u r e single phase regime.
2. Experimental details 2.1. Specimen preparation Polycrystalline ceramics were p r o d u c e d by a solid state m e t h o d [ 13 ]. Second phase content was small (barely detectable by X - r a y s ) . Two batches o f ceramics were produced: one that h a d a relative den-
0921-4534/91/$03.50 © 1991 Elsevier Science Publishers B.V. All fights reserved.
294
M. Diiumfing/ The reversiblemagnetization of YBaeCu~Oz_6
sity of about 90%, and a second one that only was about 67% dense. In the second batch the pores are interconnected, thus making the diffusion length for oxygen very small (the grain radius). Grain sizes were slightly different in the two batches: about 3 ~tm for the dense specimens, and about 2 ~m for the second batch. These measurements were carried out on polycrystalline specimens for two reasons: firstly, due to the small dimension of the grains the irreversible components of the magnetization are much smaller than in single crystals, thus drastically enlarging the reversible regime. Secondly, in open porosity specimens equilibration times with respect to oxygen diffusion are orders of magnitude lower relative to single crystals, also due to the small grain size. Different oxygen contents were produced by annealing the specimens in 1 at of oxygen at a various temperatures [ 14 ], and subsequently quenching the specimen either into liquid nitrogen or onto a fiat piece of aluminum. Specimens were thinned to less than 1 m m in order to facilitate heat transfer during the quenching process. Typical annealing times were about 20 h. The specimens with ~=0.43 and 0.5 were produced by an anneal in air, and then annealed at 300°C for two weeks. The equilibrations were carried out with the specimens sealed into evacuated quartz tubes. After the heat treatment the tubes were quenched into water. The fully oxygenated specimen was produced by a slow cool ( 1 K / m i n ) from 940°C to 400°C, held at 400°C for 8 h, followed by a slow cool to room temperature (furnace cool, about 4 h). For comparison purposes a commercially obtained specimen (GFS Chemicals) was also measured, it was oxygenated as a powder using the schedule described above. Chemical analysis of the oxygen content [ 15 ] of selected specimen confirmed the oxygen deficiency ~ to within + / - 0.02.
2.2. Magnetic measurements Magnetic measurements were carried out in a commercial Quantum Design SQUID magnetometer. A 5 cm scan length was used. The measurements were carried out in the following manner: first the specimen was cooled to the lowest measuring temperature (depending on stoichiometry between 20 K and 50 K) in the trapped field of the superconducting magnet (about 1.5 roT). Then the field was raised
to the measuring field ( 1 T or greater), leaving the magnet in persistent mode. After a waiting period of 5 min the first measurement was taken. Then the temperature was raised (leaving the magnetic field constant) and periodic measurements taken until the maximum temperature was reached (typically 200 K). This procedure was repeated for different magnetic fields noting whether the field had to be increased from the previous value. It should be noted that the field in which the specimen is cooled is irrelevant as long as care is taken to create a fully penetrated critical state in the specimen at the lowest measuring temperature. Magnetization data was considered reversible once the difference between the magnetization measured in an increasing or decreasing magnetic field was less than 2%. In the instances where increasing and decreasing field data was not available the irreversibility temperature was estimated based on the specimens where this data was available.
3. Theory
3.1. Magnetization of a polycrystal In order to calculate the magnetization of a polycrystalline specimen composed of anisotropic grains the magnetizations of the grains have to be averaged. At a given temperature T ( < To) the upper critical field (and thus x) of each grain depends on the misorientation angle ~ of its c-axis with the applied magnetic field according to [ 16 ] H~2 (~) = ~
• Hc2 (0) ~ ,
(l)
where e is the ratio of the effective masses of the charge carriers in the planes and along the c-axis. This ratio is about 1/30 for YBa2Cu307_a [ 17]. The upper critical field can be written as H~2=x/~xH~. where x is the angle-dependent Ginzburg-Landau p a r a m e t e r [18] (assuming x = x z = x 3 = x ~ ) , and H~ is the thermodynamical critical field, which is independent of misorientation angle. The magnetization of each grain is given by an expression that contains Hc and x, and the applied field H. Close to H~2 there is a linear relationship between the magnetization and the applied field for a single grain. The
M. Diiumling / The reversiblemagnetization of YBa2Cu~Oz_n averaging of the magnetizations for a polycrystalline aggregate in this linear regime has been carried out analytically [ 19 ]. For intermediate fields the magnetization is not a linear function of the magnetic field. However, this function is dependent on the Ginzburg-Landau parameter x only. Analytical general solutions are not available for this curve, but numeric solutions have been obtained [2-4]. The problem is now to calculate the magnetization of each grain according to its x(q~), average it numerically using a random distribution of misorientation angles, and fit it to measured data. Due to the the computational effort necessary for the solution it was attempted to simplify the problem by reducing the number of parameters that have to be fitted. The trade-off is an increase in error in the fitted parameters. 3.2. Fitting procedure For the analysis it was assumed that the grains in the specimen are randomly oriented. Furthermore, it was assumed that the magnetization of each grain points parallel to the c-axis. Each grain contributes to the measured magnetization only with the projection of its magnetization onto the magnetic field axis. Making these assumptions results in a model that is similar (but not identical) to a material with infinite anisotropy. The total measured magnetization is the average of these projected grain magnetizations. This leads to a reduction of the total magnetization of a randomly oriented ensemble of grains by a factor of 2, compared to an ensemble of aligned grains. The data was multiplied by 2 before fitting in order to compensate for the randomness of the orientation. The difference between this type of analysis and the real behavior outlined in the previous paragraph is that for a real material the H~2 increases as the misorientation angle increases, leading to slightly smaller magnetization than in the simpler model. The advantage of the simplified model is that the numerical integration over the angle 0 does not have to be performed. The fitting parameters used are the GinzburgLandau parameter x (for Hll c ), the bulk critical temperature T GL and the critical field H ¢ ( T = 0 ) . The numerical solution of the G~nzburg-Landau ( G L ) equations derived by Koppe and Willebrand [2 ] was
295
used to compute the field dependence of Mrev. This expression agrees well with other approximations [4,18 ], and smoothly spans the range from lower to upper critical field. A temperature dependence for the critical field of the type He ( T ) ~He (0) = 1 - ( T / To) 2 was used. If, for simplicity, the small temperature dependence [ 18 ] of x is neglected, then all of the temperature dependence of the magnetization is contained in a term containing He(T). A mastercurve can then be generated (in which the field and magnetization axes are normalized by x / ~ H ~ ( T ) ) which only depends on x. In practice the magnetization for HJ_c is much smaller than for nllc, but not zero [ 5,8 ]. Therefore the data analysis will result in errors in the parameters extracted from the data. In order to estimate this error the magnetization for a polycrystalline specimen was computed using the full expressions for the magnetization as described above, including the correct angular dependence of x, for values of x(0) =50, ~=1/25, T¢=90 K, and x//-2nc(0) = 1.0X 106 A/m. The result is shown in fig. 1. For comparison the magnetization for a single crystal oriented so that 0 = 0 is shown as well. The influence of the higher H¢2 of the misoriented grains is very clear close to To, where the grains with low Hc2 become nonsuperconducting. The single crystal therefore shows zero magnetizations where the polycrystal does not. The resulting "data" (for the polycrystalline specimen) was fitted just like real data. The results are also shown in fig. 1. The fit overestimates both H ¢ ( + 4 0 % ) and x ( + 3 0 % ) . T¢GL is quite sensitive to the error sum and can be determined .to better than 0.5 K. Changes in the grain anisotropy have only little influence on the magnetization of the polycrystal. If the anisotropy is increased to e= 1/ 100 (keeping other parameters constant) the resulting fitting parameters differ little from the one that was obtained with E= 1/25. The errors of the analysis for other values of x(0) are similar. Because of the overestimate for He and x values the upper critical field H¢2 is overestimated by about a factor of two. This can be seen directly in fig. 1 from the dependence of T~ on the magnetic field. Another quantity easily obtained is the jump of the specific heat at the critical temperature. It is given by [20] A c / T c = l t o ( d H ¢ / dT[r¢) 2. Since the j u m p in the specific heat at T¢
M. Diiumling I The reversiblemagnetization of YBa2Cu~Oz_j
296
xlO ~
are found using this analysis are valid whether the results are corrected or not.
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Temperature (K)
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. . . . . . . . .
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Temperature (K)
The magnetization for a specimen with 6 = 0.04 in magnetic fields of 1, 3 and 5 T is shown in fig. 2. Data for increasing and decreasing magnetic fields is shown for fields of l and 5 T. The normal state susceptibility g, for this particular specimen is 3.5 × l 0 - s at T = 100 K. The temperature dependence of Z• is very small, and below the noise level for some specimens. There is more variation (of order 20%) in Z, for different specimens with identical oxygen stoichiometry than there is for specimens of different 6. To obtain the magnetization due to superconductivity alone the background was subtracted assuming it had the same temperature dependence above and below To. In order to minimize the influence of fluctuations only susceptibilities at temperatures higher than l 0 K above the critical temperature were used to determine the temperature dependence Of Zn. This procedure led to curves with zero susceptibility far above To. Figures 3 to 6 show the reversible magnetizations for specimens with varying oxygen deficiencies as a
Fig. 1. Solid squares: calculated magnetization vs. temperature for polycrystalline specimen using the full angular averaging. The parameters used are T¢=90 K, x = 5 0 and v / 2 H ¢ ( 0 ) = 1.0× 106
A/m. Dashed curves: magnetization for a single crystal with identical superconducting parameters. Solid curves: fit obtained using the simplified fitting model using the parameters To=90 K, x=66 and x/~H¢(0)= 1.40x 106 A/m. The magnetic fields are 5.5, 4, 2.5 and 1 T, top to bottom (respectively).
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sample 62 = 0.04
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-1 scales with the square of the critical field slope, this quantity will be overestimated by about a factor of two. In order to be able to compare the absolute values of for example the upper critical field slope or the specific heat jump to measurements performed on single crystals the values obtained from fitting the data (given in the following sections) have been corrected using the error estimates given above. This correction is done for comparison purposes only, since the specimens all have identical morphology and the only change is oxygenation. The trends that
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. . . . . . . . i* . . . . . . . . , . . . . . . . . . j . . . . . . . . . , . . . . . . . 0 50 1O0 150 200 250 Temperature (K)
Fig. 2. Raw magnetizationvs. temperature in magnetic fields of 1, 3 and 5 T. Increasing and decreasing fields arc shown for fields of 1 and 5 T. The specimen has an oxygen deficiency of 6=0.04. Open (closed) symbols represent data taken when the field was increased (decreased) to reach the measuring field.
M. Diiumling / The reversible magnetization of YBa2Cu3Oz_a
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Fig. 3. Reversible magnetization vs. temperature for specimen with J= 0.02 (batch 2). The solid lines are fits of the magnetization to the theoretical GL expression.
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Fig. 5. Reversible magnetization vs. temperature for specimens with J=0.18. (a) Closed porosity with larger grain size (batch l ). (b) Open porosity small grained sample (batch 2). The solid linesare fits of the magnetizationto the theoreticalGL expression.
5T
90
I . . . . . . . . .
40 Temperature (K)
100
500
........
I .........
, .........
, ........
6 = 0.31
Fig. 4. Reversible magnetization vs. temperature for specimen with J= 0.04 (batch 2). The solid lines are fits of the magnetization to the theoretical GL expression.
0
~.::_-oe*eee
E -500
function of field a n d temperature. The solid lines are fits of the magnetization to the theoretical G L expression (see below). Magnetizations from samples from both batches are shown. All curves have three regimes: 1 ) a high temperature regime close to the critical temperature Tc in which the curvature of M ( T ) is negative. 2) A n intermediate regime in which M ( T ) is almost linear. 3) A low temperature regime in which M ( T ) has a positive curvature. This third regime is not experimentally accessible in specimens with a high oxygen content due to large irrev-
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• 1T 2.5T 4T • 5.5T
:
-1500 -2000
. . . . . . . . .
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i ........
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80
Fig. 6. Reversible magnetization vs. temperature for specimen with t$--0.31 (batch 2). The solid lines are fits of the magnetization to the theoretical GL expression.
M. Diiumling / The reversiblemagnetization of YBa2Cu307_6
298
ersibilities in the magnetization, Critical current density measurements that were made on these specimens using this hysteretic regime are presented elsewhere [ 21 ].
500
. . . . . . . . i . . . . . . . . . i . . . . . . . . . ~. . . . . . . . . , . . . . . . . .
400 300
4.2. Derived results
\ •
• \
2OO In order to exclude the fluctuation regime from the fitting procedure data close to T¢( ( T ¢ - T) > 4 K) was excluded from the fits. The results of the fitting procedure are shown as solid lines in figs. 3 to 6. The fit can accommodate the shape of the M ( T ) curves in all three regimes. The field dependent slopes in regime 2 arise from high values of x. The curvature in regime 1 is a consequence o f a high X value as well (pointed out first by Hao et al. [ 3 ] ). This curvature is not due to fluctuations. Fluctuations might cause an additional lowering of the magnetization, thus possibly increasing the curvature. In fig. 7 the bulk critical temperature T ~ L versus oxygen deficiency 6 is shown. These quenched specimens show little o f the 90 K plateau. Some spread in T~ values for small oxygen deficiencies is found. The critical field H~ ( T = 0) and the G L parameter x versus oxygen deficiency J are shown in fig. 8. The critical field shows a strong stoichiometry dependence for small 6 values, but is almost insensitive to
100
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rum \n
80
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I'"''""I
~. . . . . . . .
l .....
" " l " "
.....
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20
........
0.0
I .........
0.1
I .........
0.2
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0.3
I .........
0.4
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0.5
0.6
Oxygen Deficiency 6
Fig. 7. Bulk critical temperature
•
100 0
E 1.0
~\
%
• open porosity • closed porosity • GFS powder
~*i
\ \ \
Q
\
" ~ 0.5
ii
. . . . .
0.0
I .........
0.1
I .........
I .........
0.2 0.3 Oxygen Deficiency6
lID
I ........
0.4
0.5
Fig. 8. Thermodynamic critical field Hc( T= 0) and GL parameter x vs. oxygendeficiency J. The dashed lines are a guide for the eye. J for J>_-0.12. The G L parameter has a different behavior. It seems to go through a m a x i m u m around = 0.O 7, and decreases up to J ~ 0.3. The rise o f r for higher oxygen deficiencies may be an artifact (see discussion). The calculated j u m p in the specific heat at Tc Ac/T¢ is plotted versus J in fig. 9. It also exhibits a pronounced dependence on the oxygen stoichiometry. Using standard expressions values for the upper critical field slope at T¢, the lower critical field Hcl, the penetration depth 2, and the coherence length are obtained and shown in table 1. All o f these values are for the HIIc orientation. The temperature dependence o f these quantities follows the temperature dependence o f He.
I .......
o\
40
*x---i---
T cGL VS. oxygen deficiency J.
M. D~iumling / The reversiblemagnetization of YBazCu307_6
0.10
..........
~ .........
' .........
' .........
I .........
[ .........
ie
0.08 o
E 0.06 q(
• open porosity • closed porosity • GFS powder
\ xx•
~_~ 0.04
x \
0.02
0.00 0.0
\
\#___._. . . . . .
0.1
=.....
,____
0.2 0.3 0.4 Oxygen Deficiency 6
0.5
0.6
Fig. 9. Calculated specific heat j u m p (at To) Ac/Tc vs. oxygen deficiency 8. The dashed line is a guide for the eye.
5. Discussion
5. I. General comments For specimens that have a nominal oxygen deficiency 8 close to zero there is a body of data in the literature. Therefore comparisons of the results found in this work with the work of others are possible. However, it should be noted that the results in the literature are not always consistent. For example, there are large spreads (up to a factor of three) in the values for the lower critical field Hc~. Hc~ is dif-
299
ficult to measure because the critical current densities are high. Due to the flux creep problem the upper critical field cannot be measured using resistive methods. Therefore a large number of early publications in which resistive "He2" measurements were performed have to be excluded from consideration. Properties that are not affected by flux creep are the equilibrium magnetization, and the specific heat. These quantities have to be measured as a function of magnetic field. However, for example the jump in the specific heat at Tc does not exhibit the classical shift to lower temperature with increased magnetic field [22], making a Hc2 determination very difficult. Even if the reversible magnetization is measured, it should be pointed out that in most cases a linear extrapolation of the magnetization to zero does not lead to a correct value for the upper critical field slope. Therefore values of the upper critical field slope (and its anisotropy) obtained this way should be discarded. Anisotropy values obtained from the shape of flux lines using flux decoration techniques [ 17 ] should be valid.
5.2. Data analysis There are a number of assumptions that enter the data analysis. Firstly, it is assumed that the vortices are parallel to the applied field. In the field regime used here this is a correct assumption. Buzdin and
Table 1 Derived superconducting parameters (for HIIc) from x and He. Samples with numbers below 10 are dense (batch 1 ), samples with numbers above 10 are from batch 2. The sample marked GFS is the commercial specimen that was oxygenated and measured as powder. Specimens marked with an asterik may not be single phase Sample GFS 11 62 3 25 57 1 28 2 45 26* 50*
8 0.02 0.02 0.04 0.07 0.07 0.12 0.18 0.18 0.31 0.31 0.43 0.5
/lod/-/c2/dTI rc (T/K)
~ (rim)
/~//cl ( 0 ) (T)
(llm)
12 11 12 10 13 4.1 3.5 4.1 3.5 5.4 6.2 12
0.75 0.79 0.78 0.88 0.77 1.5 1.7 1.6 1.8 1.5 1.4 1.1
0.017 0.023 0.015 0.012 0.011 0.011 0.010 0.0089 0.0092 0.0074 0.0060 0.0036
0.23 0.20 0.25 0.28 0.29 0.29 0.29 0.31 0.30 0.35 0.39 0.53
300
M. Dgiumling / The reversible magnetization of YBa2Cu307_a
Simonov [23] showed that for fields > 10Hal the vortices line up with the applied field for essentially all orientations of the crystal axis with respect to the field. Therefore only for very low fields is there a tendency of the vortices to align themselves with the a, b planes. Secondly, it is assumed that the magnetization of our fairly small-grained sample is identical to that of an infinite specimen. This is approximately the case since for example there is a 50% difference in grain size for the samples in fig. 5, but the extracted values for H~(0) and x are quite similar. Another aspect is the accuracy of the numerical solution used to compute the magnetization as a function of x and the applied field H. In order to obtain a comparison this fit program was used to fit the digitized data o f H a o et al. The parameters extracted are virtually identical to the ones given by Hao et al. themselves. Therefore there are only minor differences between these two different numerical solutions [ 2,3 ] of the Ginzburg-Landau equations. The numerical behavior of the fit program used is regular up to very high values of x. A more sophisticated theoretical approach should include a distinction of the different x parameters [ 18 ], also using their temperature dependence. This might also lead to a change in the temperature dependence of the thermodynamic critical field. Since the main goal of this work was to establish trends and since the approach currently used yielded very good results a more sophisticated fit was not used.
5.3. Fully oxygenated sample Tlieuss and Kronmiiller [24] also made measurements of M, ev on polycrystalline specimens. However, the magnetizations given here at a given temperature and field (for example 86.5 K and 1 T) are three times larger than theirs, and have a different field dependence. Unfortunately there is very little information on specimen preparation and oxygenation in their article, so that comparisons are rather difficult. Using a similar fitting method Hao et al. [ 3 ] obtain a x value of 55 for a nominally fully oxygenated single crystal with HIIc. Their value for He(0) is smaller than the value" obtained here. As the specimen was a single crystal, the irreversibilities were much larger than for our polycrystalline specimens,
thus making the reversible regime very small. In addition, the agreement between fit and data in their paper is significantly worse than in this work. Other measurements on single crystals produced in a similar fashion were made by Welp et al. [ 5 ] for both Hllc and H l c . They did not carry out a fitting procedure, but temperature and field dependence of their magnetizations were quite similar to the values obtained by Hao et al. In comparison to previous measurements values for the GL parameter x are found that are very high, even considering the possible errors due to the fact that the specimens are randomly oriented polycrystals. However, the magnetization of the polycrystalline specimens cannot be fitted using the single crystal parameters of Hao et al. This is due to the temperature dependence of the magnetization at lower temperatures (around 75 K). Unless a quite different temperature dependence for He is used, a fit with x = 55 creates a curvature, whereas the data is essentially straight in this regime. The high x values lead to very high values of the upper critical field slope, and thus to a very small coherence length, even for HIIc (see table 1 ). There should be no physical reason why the present results disagree with those of others. It therefore must be due to the material or specimen preparation. It is well-known that most single crystals contain fairly large amounts of gold in the structure (up to 10% substitution on the Cu chain sites). Gold increases the Tc value by up to 2 K [25 ], and may significantly influence x and the upper critical field. Palstra et al. [26] measured an upper critical field slope (using a thermomagnetic method) of about 8 T / K for H]lc on a crystal that did not contain gold. Unfortunately, no magnetizations were measured. Another issue is oxygenation. In the ceramic the is well-known because the times that are required to oxygenate them to equilibrium are small, and the oxygen content can be analyzed directly. That is not so in single crystals because of their small size. Due to long diffusion distances and the low mobility of O at the oxygenation temperature it must be expected that single crystals are somewhat oxygen deficient. Indeed, our oxygen deficient specimens show lower values of x and He, leading to a lower upper critical field slope. However, T¢ is below 90 K, which
M. Diiumling/ The reversiblemagnetization of YBa2CusO7_6 does not seem to be the case for the single crystals.
5.4. Oxygen deficient specimens As pointed out earlier [ 10 ], some variability in the magnetization was encountered with oxygen deficient specimens. According tO a recent phase diagram [ 12 ] specimens quenched from high temperature are most homogeneous, since a single phase field is predicted. At room temperature a two phase field is predicted for most stoichiometries, which makes the specimens metastable at room temperature. The increase of Tc after room (or slightly elevated) temperature annealing that has been observed by Veal et al. [27] may be a result of this metastability. Our specimens were measured days or weeks after the quench from the oxygenation temperature. No changes in the magnetization with time for times of the order of weeks were observed. For the specimens with ~=0.43 and 0.5 one more complication arises. The initial anneal takes place in a regime where the equilibrium structure is tetragonal [ 28 ] (nonsuperconducting). At room temperature the equilibrium structure is orthorhomic (superconducting). Thus the specimen has to transform its structure during the quench. In order to obtain an equilibrium state both of these specimens were postannealed. Therefore there is the possibility that the specimens are not single phase, which would make the results of the fitting procedure dubious.
5.5. Specific heat Specific heat measurements have been carried out on both single crystals [22 ] and polycrystalline ceramics [29,30]. Since Tc is high phononic contributions to the specific heat are high as well, leading to a small jump at T~ on top of a large background. Both thermal fluctuations and sample inhomogeneities tend to lower and broaden the specific heat jump. Typical values for the zero field jump Ac/Tc range from 50 to 60 m J / ( K 2 mol) for nominally fully oxygenated specimens. Good agreement between calculated and measured values if oxygen deficiencies J around 0.06 are assumed for most specimens in the literature. This is rather sensible since it is not difficult to achieve this oxygen content even in a fully dense specimen using typical oxygenation treat-
301
ments. Junod et al. [ 30 ] measured the specific heat j u m p as a function of oxygen deficiency. They find a strong dependence of the j u m p on t$. The highest value for Ac/T¢ that they measured was 67 m J / (K 2 mol). The same trend is certainly also found in this work. For fully oxygenated specimens even higher jumps in the specific heat are expected. However, these very small g values ( ~<0.02) are only expected in specimens that are oxygenated as a powder, or in ceramics where the pores are connected.
6. Conclusions The reversible magnetization in ceramic specimens of YBa2Cu3OT_a with 0.02 ~ ~< 0.5 was measured in magnetic fields up to 5.5 T. The magnetization fits very well to calculated values obtained using Ginzburg-Landau theory. However, for the fully oxygenated specimen values of x and He in the literature cannot fit the magnetization curves. Much higher values of x (between 170 and 300) have to be used to obtain a satisfactory fit. Resulting from the high x very high values of the upper critical field are obtained, leading to a very short coherence length even for the HIIc orientation. Both x and Hc values decrease with increasing ~. Specific heat jumps at Tc were computed from the temperature dependence of He, and quantitative agreement with measurements from the literature is obtained. It is predicted that fully oxygenated specimens with ~< 0.02 should exhibit a larger specific heat jump at T~ than what has been measured so far.
Acknowledgements I thank T.M. Shaw, L.E. Levine and L. Civale for discussions, T.McGuire for the use of the magnetometer, and M.M. Plechaty for performing the oxygen analysis. The starting powders of YBa2Cu3OT_6 were provided by E. Olsson and P. Duncombe. The work was partially funded by DARPA under constract No. N00014-89-0112.
302
M. Dtiumling / The reversible magnetization of YBaeCu307_6
References [ 1 ] M. Tinkham, Introduction to Superconductivity (McGrawhill, New York ! 975 ). [ 2 ] H. Koppe and J. Willebrand, J. Low Temp. Phys. 2 (1970) 499. [3]Z. Hao, J.R. Clem, M.W. McElfresch, L. Civale, A.P. Malozemoffand F. Holtzberg, Phys. Rev. B 43 ( 1991 ) 2844. [4] E.H. Brandt, Phys. Status solidi B 51 (1972) 345. [5] U. Welp, W.K. Kwok, G.W. Crabtree, K.G. Vandervoort and J.Z. Liu, Phys. Rev. Lett. 62 (1989) 1908. [ 6 ] K.S. Athreya, O.B. Hyun, J.E. Ostenson, J.R. Clem and D.K. Finnemore, Phys. Rev. B 38 (1988) 11846. [7] Junho Gohng and D.K. Finnemore, Phys. Rev. B 42 (1990) 7946. [8] K.G. Vandervoort, U. Welp, J.E. Kessler, H. Claus, G.W. Crabtree, W.K. Kwok, A. Umezawa, B.W. Veal, J.D. Downey and A.P. Paulikas, (1990) preprint. [9] C. Namgung, J.T.S. Irvine and A.R. West, Physica C 168 (1990) 346. [ 10] M. Diiumling, L.E. Levine and T.M. Shaw, Adv. Cryogen. Eng. (Mater.), to be published, ( 1991 ). [11] L.E. Levine and M. Diiumling, Phys. Rev. Lett. (1991) submitted. [12]G. Ceder, M. Asta and D. de Fontaine, Physica C 177 (1991) 106. [ 13 ] D.R. Clarke, T.M. Shaw and D. Dimos, J. Am. Ceram. Soc. 72 (1989) 1103. [ 14] T.B. Lindemer, J.F. Hunley, J.E. Gates Jr., A.L. Sutton, J. Brynestad, C.R. Hubbard and P.K. Gallagher, J. Am. Ceram. Soc. 72 (1989) 1775.
[ 15 ] R.C. Taylor, M.M. Plechaty and D.B. Beach, Mat. Res. Bull. ( 1991 ) accepted; M.M. Plechaty, unpublished. [ 16] V.L. Kogan and J.R. Clem, Phys. Rev. B 24 ( 1981 ) 2497. [ 17 ] G.J. Dolan, F. Holtzberg, C. Feild and T~R. Dinger, Phys. Rev. Lett. 62 (1989) 2184. [18] R.G. Parks, ed., Superconductivity (Marcel Dekker, New York, 1969). [19] H. Zhou, J. Rammer, P. Schleger, W.N. Hardy and J.F. Carolan, Phys. Rev. B 43 ( 1991 ) 7968. [ 20 ] R. Becker, Theorie der W~irme. (Springer, Berlin, 1978 ). [ 2 i ] M. D~iumling, to be published ( 1991 ). [22 ] S.E. Inderhees, M.B. Salomon, J.P. Rice and D.M. Ginsberg, Phys. Rev. Lett. 66 ( 1991 ) 232. [23] A.I. Buzdin and A. Yu. Simonov, Physica C 175 ( 1991 ) 143. [24] H. Theuss and H. Kronmiiller, Physica C 168 (1990) 539. [25] M.Z. Cieplak, Gang Xiao, C.L. Chien, A. Bakhshai, D. Artymowicz, W. Bryden, J.K. Stalick and J.J. Rhyne, Phys. Rev. B 42 (1990) 6200. [26] T.T.M. Palstra, B. Batlogg, L.F. Schneemeyer and J.V. Waszczak, Phys. Rev. Lett. 64 (1990) 3090. [27] B.W. Veal, A.P. Paulikas, Hoydoo You, Hao Shi, Y. Fang and J.W. Downey, Phys. Rev. B 42 (1990) 6305. [28] E.D. Specht, C.J. Sparks, A.G. Dhere, J. Brynestad, O.B. Cavin, D.M. Kroeger, and H.A. Oye, Phys. Rev. B 37 (1988) 7426. [29] C. Meingast, R. Ahrens, B. Blank, H. Biirkle, B. Rudolf and H. Wtihl, Physica C 173 ( 1991 ) 309. [30] A. Junod, D. Eckert, T. Graf, G. T.riscione and J. Muller, Physica C 162-164 (1989) 482.
Physica C 183 (1991) 293-302 North-Holland
i
The reversible magnetization of oxygen deficient
YBaECU307_a
Manfred D~iumling IBM T.J. Watson Research Center, Yorktown Heights, NY 10598, USA Received 3 September 1991
The reversible magnetization M,~vof polycrystalline YBa2Cu307_a (0 < tJ< 0.5 ) was measured. Due to a small grain size and low critical current densities in oxygen deficient specimens M,~vcould be measured over most of the superconducting regime from l 0 K to T¢up to a magnetic field of 5.5 T. The magnetization data is in excellent agreement with calculated values obtained from Ginzburg-Landau (GL) theory. Values for the thermodynamic critical field Hc and the G L parameter r are obtained. High values of r ~ 170-300 (for H~c) are necessary to fit the magnetization data. He( T= 0 ) decreases strongly for increasing oxygen deficiencies up to ~ 0 . 1 5 , and then remains nearly constant. Specific heat jumps Ac at T¢ were calculated from the data and the fit. Quantitative agreement with data in the literature is obtained. Just like He, the specific heat jump is strongly dependent on the oxygen deficiency in the near stoichiometric regime.
1. Introduction In a superconductor c o m p l e t e knowledge o f the reversible magnetization as a function o f field a n d t e m p e r a t u r e enables the d e t e r m i n a t i o n o f all superconducting p a r a m e t e r s [ 1 ]. I f only parts o f the magnetization in the H - T space are known then theoretical expressions [ 2 - 4 ] allow a fit o f the magnetization using a set o f p a r a m e t e r s like the critical field He ( T ) a n d the G i n z b u r g - L a n d a u p a r a m eter x. F r o m these p a r a m e t e r s o t h e r quantities like the u p p e r critical field Hc2(T) can be d e t e r m i n e d even if magnetization d a t a is not available up to H¢2. T h e r m o d y n a m i c a l l y the m a g n e t i z a t i o n is linked to the j u m p in the specific heat at T¢ via the temperature d e p e n d e n c e o f the critical field He. Knowledge o f these p a r a m e t e r s as a function o f oxygen concentration in YBa2Cu307_a allows better u n d e r s t a n d i n g o f the flux pinning properties. C o n t r a r y to the countless n u m b e r s o f publications on other superconducting properties m e a s u r e m e n t s o f the reversible magnetization are sparse. This is mostly due to the high critical current densities J¢ typically found in YBa2Cu307_, which cause large irreversibilities in the magnetization. A l m o s t all m e a s u r e m e n t s were carried out on n o m i n a l l y fully oxygenated "90 K " specimens. Welp et al. [ 5 ] have m e a s u r e d the mag-
netization in single crystals for both the HIIc and H Z c orientations, m a i n l y for the purpose o f obtaining a value for the u p p e r critical field He2. H a o et al. [ 3 ] d e v e l o p e d a simplified theoretical solution o f the G L equations a n d a p p l i e d it to m e a s u r e m e n t s on a single crystal, deriving values for He, x a n d H¢2 for the HIIc orientation. Others [6,7] m e a s u r e d the reversible magnetization in oriented powders close to T¢ in ord e r to investigate the role o f fluctuations. Only one m e a s u r e m e n t exists on an oxygen deficient crystal [ 8 ]. The investigation o f oxygen deficient specimens is c o m p l i c a t e d by the a p p a r e n t existence o f multiple T¢ values for a given 8 [9-11 ], indicating the possibility o f a phase separation [ 12 ] for certain oxygen stoichiometries. It was a t t e m p t e d to avoid this problem by quenching the samples from a high t e m p e r a t u r e single phase regime.
2. Experimental details 2.1. Specimen preparation Polycrystalline ceramics were p r o d u c e d by a solid state m e t h o d [ 13 ]. Second phase content was small (barely detectable by X - r a y s ) . Two batches o f ceramics were produced: one that h a d a relative den-
0921-4534/91/$03.50 © 1991 Elsevier Science Publishers B.V. All fights reserved.
294
M. Diiumfing/ The reversiblemagnetization of YBaeCu~Oz_6
sity of about 90%, and a second one that only was about 67% dense. In the second batch the pores are interconnected, thus making the diffusion length for oxygen very small (the grain radius). Grain sizes were slightly different in the two batches: about 3 ~tm for the dense specimens, and about 2 ~m for the second batch. These measurements were carried out on polycrystalline specimens for two reasons: firstly, due to the small dimension of the grains the irreversible components of the magnetization are much smaller than in single crystals, thus drastically enlarging the reversible regime. Secondly, in open porosity specimens equilibration times with respect to oxygen diffusion are orders of magnitude lower relative to single crystals, also due to the small grain size. Different oxygen contents were produced by annealing the specimens in 1 at of oxygen at a various temperatures [ 14 ], and subsequently quenching the specimen either into liquid nitrogen or onto a fiat piece of aluminum. Specimens were thinned to less than 1 m m in order to facilitate heat transfer during the quenching process. Typical annealing times were about 20 h. The specimens with ~=0.43 and 0.5 were produced by an anneal in air, and then annealed at 300°C for two weeks. The equilibrations were carried out with the specimens sealed into evacuated quartz tubes. After the heat treatment the tubes were quenched into water. The fully oxygenated specimen was produced by a slow cool ( 1 K / m i n ) from 940°C to 400°C, held at 400°C for 8 h, followed by a slow cool to room temperature (furnace cool, about 4 h). For comparison purposes a commercially obtained specimen (GFS Chemicals) was also measured, it was oxygenated as a powder using the schedule described above. Chemical analysis of the oxygen content [ 15 ] of selected specimen confirmed the oxygen deficiency ~ to within + / - 0.02.
2.2. Magnetic measurements Magnetic measurements were carried out in a commercial Quantum Design SQUID magnetometer. A 5 cm scan length was used. The measurements were carried out in the following manner: first the specimen was cooled to the lowest measuring temperature (depending on stoichiometry between 20 K and 50 K) in the trapped field of the superconducting magnet (about 1.5 roT). Then the field was raised
to the measuring field ( 1 T or greater), leaving the magnet in persistent mode. After a waiting period of 5 min the first measurement was taken. Then the temperature was raised (leaving the magnetic field constant) and periodic measurements taken until the maximum temperature was reached (typically 200 K). This procedure was repeated for different magnetic fields noting whether the field had to be increased from the previous value. It should be noted that the field in which the specimen is cooled is irrelevant as long as care is taken to create a fully penetrated critical state in the specimen at the lowest measuring temperature. Magnetization data was considered reversible once the difference between the magnetization measured in an increasing or decreasing magnetic field was less than 2%. In the instances where increasing and decreasing field data was not available the irreversibility temperature was estimated based on the specimens where this data was available.
3. Theory
3.1. Magnetization of a polycrystal In order to calculate the magnetization of a polycrystalline specimen composed of anisotropic grains the magnetizations of the grains have to be averaged. At a given temperature T ( < To) the upper critical field (and thus x) of each grain depends on the misorientation angle ~ of its c-axis with the applied magnetic field according to [ 16 ] H~2 (~) = ~
• Hc2 (0) ~ ,
(l)
where e is the ratio of the effective masses of the charge carriers in the planes and along the c-axis. This ratio is about 1/30 for YBa2Cu307_a [ 17]. The upper critical field can be written as H~2=x/~xH~. where x is the angle-dependent Ginzburg-Landau p a r a m e t e r [18] (assuming x = x z = x 3 = x ~ ) , and H~ is the thermodynamical critical field, which is independent of misorientation angle. The magnetization of each grain is given by an expression that contains Hc and x, and the applied field H. Close to H~2 there is a linear relationship between the magnetization and the applied field for a single grain. The
M. Diiumling / The reversiblemagnetization of YBa2Cu~Oz_n averaging of the magnetizations for a polycrystalline aggregate in this linear regime has been carried out analytically [ 19 ]. For intermediate fields the magnetization is not a linear function of the magnetic field. However, this function is dependent on the Ginzburg-Landau parameter x only. Analytical general solutions are not available for this curve, but numeric solutions have been obtained [2-4]. The problem is now to calculate the magnetization of each grain according to its x(q~), average it numerically using a random distribution of misorientation angles, and fit it to measured data. Due to the the computational effort necessary for the solution it was attempted to simplify the problem by reducing the number of parameters that have to be fitted. The trade-off is an increase in error in the fitted parameters. 3.2. Fitting procedure For the analysis it was assumed that the grains in the specimen are randomly oriented. Furthermore, it was assumed that the magnetization of each grain points parallel to the c-axis. Each grain contributes to the measured magnetization only with the projection of its magnetization onto the magnetic field axis. Making these assumptions results in a model that is similar (but not identical) to a material with infinite anisotropy. The total measured magnetization is the average of these projected grain magnetizations. This leads to a reduction of the total magnetization of a randomly oriented ensemble of grains by a factor of 2, compared to an ensemble of aligned grains. The data was multiplied by 2 before fitting in order to compensate for the randomness of the orientation. The difference between this type of analysis and the real behavior outlined in the previous paragraph is that for a real material the H~2 increases as the misorientation angle increases, leading to slightly smaller magnetization than in the simpler model. The advantage of the simplified model is that the numerical integration over the angle 0 does not have to be performed. The fitting parameters used are the GinzburgLandau parameter x (for Hll c ), the bulk critical temperature T GL and the critical field H ¢ ( T = 0 ) . The numerical solution of the G~nzburg-Landau ( G L ) equations derived by Koppe and Willebrand [2 ] was
295
used to compute the field dependence of Mrev. This expression agrees well with other approximations [4,18 ], and smoothly spans the range from lower to upper critical field. A temperature dependence for the critical field of the type He ( T ) ~He (0) = 1 - ( T / To) 2 was used. If, for simplicity, the small temperature dependence [ 18 ] of x is neglected, then all of the temperature dependence of the magnetization is contained in a term containing He(T). A mastercurve can then be generated (in which the field and magnetization axes are normalized by x / ~ H ~ ( T ) ) which only depends on x. In practice the magnetization for HJ_c is much smaller than for nllc, but not zero [ 5,8 ]. Therefore the data analysis will result in errors in the parameters extracted from the data. In order to estimate this error the magnetization for a polycrystalline specimen was computed using the full expressions for the magnetization as described above, including the correct angular dependence of x, for values of x(0) =50, ~=1/25, T¢=90 K, and x//-2nc(0) = 1.0X 106 A/m. The result is shown in fig. 1. For comparison the magnetization for a single crystal oriented so that 0 = 0 is shown as well. The influence of the higher H¢2 of the misoriented grains is very clear close to To, where the grains with low Hc2 become nonsuperconducting. The single crystal therefore shows zero magnetizations where the polycrystal does not. The resulting "data" (for the polycrystalline specimen) was fitted just like real data. The results are also shown in fig. 1. The fit overestimates both H ¢ ( + 4 0 % ) and x ( + 3 0 % ) . T¢GL is quite sensitive to the error sum and can be determined .to better than 0.5 K. Changes in the grain anisotropy have only little influence on the magnetization of the polycrystal. If the anisotropy is increased to e= 1/ 100 (keeping other parameters constant) the resulting fitting parameters differ little from the one that was obtained with E= 1/25. The errors of the analysis for other values of x(0) are similar. Because of the overestimate for He and x values the upper critical field H¢2 is overestimated by about a factor of two. This can be seen directly in fig. 1 from the dependence of T~ on the magnetic field. Another quantity easily obtained is the jump of the specific heat at the critical temperature. It is given by [20] A c / T c = l t o ( d H ¢ / dT[r¢) 2. Since the j u m p in the specific heat at T¢
M. Diiumling I The reversiblemagnetization of YBa2Cu~Oz_j
296
xlO ~
are found using this analysis are valid whether the results are corrected or not.
(a)
E
4. Results -2
~
-4!
d
"4~"
-6 / / .......
--8
/
/
/
4.1. Raw data am, exact
/
--fit
--
/
I .......
60
crystal
........
,,l,~,~,,,h,I
70
80
.
90
100
Temperature (K)
-~
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---
C
//
//
-500
//
/// ~ :z-1000
~
-1500
. . . . . . . . . .
80
, '
• random, exact -fit --
[ . . . . . . . . .
85
crystal
'
90
. . . . . . . . .
95
Temperature (K)
The magnetization for a specimen with 6 = 0.04 in magnetic fields of 1, 3 and 5 T is shown in fig. 2. Data for increasing and decreasing magnetic fields is shown for fields of l and 5 T. The normal state susceptibility g, for this particular specimen is 3.5 × l 0 - s at T = 100 K. The temperature dependence of Z• is very small, and below the noise level for some specimens. There is more variation (of order 20%) in Z, for different specimens with identical oxygen stoichiometry than there is for specimens of different 6. To obtain the magnetization due to superconductivity alone the background was subtracted assuming it had the same temperature dependence above and below To. In order to minimize the influence of fluctuations only susceptibilities at temperatures higher than l 0 K above the critical temperature were used to determine the temperature dependence Of Zn. This procedure led to curves with zero susceptibility far above To. Figures 3 to 6 show the reversible magnetizations for specimens with varying oxygen deficiencies as a
Fig. 1. Solid squares: calculated magnetization vs. temperature for polycrystalline specimen using the full angular averaging. The parameters used are T¢=90 K, x = 5 0 and v / 2 H ¢ ( 0 ) = 1.0× 106
A/m. Dashed curves: magnetization for a single crystal with identical superconducting parameters. Solid curves: fit obtained using the simplified fitting model using the parameters To=90 K, x=66 and x/~H¢(0)= 1.40x 106 A/m. The magnetic fields are 5.5, 4, 2.5 and 1 T, top to bottom (respectively).
1 xlO 3
E
0
sample 62 = 0.04
[o8o!
8 8 8
-1 scales with the square of the critical field slope, this quantity will be overestimated by about a factor of two. In order to be able to compare the absolute values of for example the upper critical field slope or the specific heat jump to measurements performed on single crystals the values obtained from fitting the data (given in the following sections) have been corrected using the error estimates given above. This correction is done for comparison purposes only, since the specimens all have identical morphology and the only change is oxygenation. The trends that
~E
-2
~;? t***t "~'~ =*" eo
1To 3T .
o
5TA
"
°.%
.v: -3
. . . . . . . . i* . . . . . . . . , . . . . . . . . . j . . . . . . . . . , . . . . . . . 0 50 1O0 150 200 250 Temperature (K)
Fig. 2. Raw magnetizationvs. temperature in magnetic fields of 1, 3 and 5 T. Increasing and decreasing fields arc shown for fields of 1 and 5 T. The specimen has an oxygen deficiency of 6=0.04. Open (closed) symbols represent data taken when the field was increased (decreased) to reach the measuring field.
M. Diiumling / The reversible magnetization of YBa2Cu3Oz_a
1
,,,
.....
I r',,
.....
297
I ' ' ' ' ' ' ' ' ' 1 ' ' ' ' ' ' ' '
6 = 0.19, closed xlO 3 ._.
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~=0.02
~ . ; 7 . :
(0)
0
v
._~ -1 *6
N
=,
/
L /'///
-2 f / / / /
i -$
60
70
80 Temperature (K)
90
* 2.5T = 4T = 5.5T
~-2
.25T • 4T
.
.
.
.
.
.
.
.
I .........
I .........
I''
......
= 0.19, open
1O0 E
Fig. 3. Reversible magnetization vs. temperature for specimen with J= 0.02 (batch 2). The solid lines are fits of the magnetization to the theoretical GL expression.
0
v
g-1
:.=
1
.' ........
I .........
xlO a
I .........
I ....
' ....
I ........
o
T
o°'-2
.5T T • 5.5T
~ = 0.04 --3
E
~
::e
. . . . . . . .
I . . . . . . . . .
20
0
-1
•
-3
50
60
70 80 Temperature (K)
I . . . . . . . .
60
80
Fig. 5. Reversible magnetization vs. temperature for specimens with J=0.18. (a) Closed porosity with larger grain size (batch l ). (b) Open porosity small grained sample (batch 2). The solid linesare fits of the magnetizationto the theoreticalGL expression.
5T
90
I . . . . . . . . .
40 Temperature (K)
100
500
........
I .........
, .........
, ........
6 = 0.31
Fig. 4. Reversible magnetization vs. temperature for specimen with J= 0.04 (batch 2). The solid lines are fits of the magnetization to the theoretical GL expression.
0
~.::_-oe*eee
E -500
function of field a n d temperature. The solid lines are fits of the magnetization to the theoretical G L expression (see below). Magnetizations from samples from both batches are shown. All curves have three regimes: 1 ) a high temperature regime close to the critical temperature Tc in which the curvature of M ( T ) is negative. 2) A n intermediate regime in which M ( T ) is almost linear. 3) A low temperature regime in which M ( T ) has a positive curvature. This third regime is not experimentally accessible in specimens with a high oxygen content due to large irrev-
"- -1000
• 1T 2.5T 4T • 5.5T
:
-1500 -2000
. . . . . . . . .
0
i . . . . . . . . .
20
i . . . . . . . . .
40 Temperature (K)
i ........
60
80
Fig. 6. Reversible magnetization vs. temperature for specimen with t$--0.31 (batch 2). The solid lines are fits of the magnetization to the theoretical GL expression.
M. Diiumling / The reversiblemagnetization of YBa2Cu307_6
298
ersibilities in the magnetization, Critical current density measurements that were made on these specimens using this hysteretic regime are presented elsewhere [ 21 ].
500
. . . . . . . . i . . . . . . . . . i . . . . . . . . . ~. . . . . . . . . , . . . . . . . .
400 300
4.2. Derived results
\ •
• \
2OO In order to exclude the fluctuation regime from the fitting procedure data close to T¢( ( T ¢ - T) > 4 K) was excluded from the fits. The results of the fitting procedure are shown as solid lines in figs. 3 to 6. The fit can accommodate the shape of the M ( T ) curves in all three regimes. The field dependent slopes in regime 2 arise from high values of x. The curvature in regime 1 is a consequence o f a high X value as well (pointed out first by Hao et al. [ 3 ] ). This curvature is not due to fluctuations. Fluctuations might cause an additional lowering of the magnetization, thus possibly increasing the curvature. In fig. 7 the bulk critical temperature T ~ L versus oxygen deficiency 6 is shown. These quenched specimens show little o f the 90 K plateau. Some spread in T~ values for small oxygen deficiencies is found. The critical field H~ ( T = 0) and the G L parameter x versus oxygen deficiency J are shown in fig. 8. The critical field shows a strong stoichiometry dependence for small 6 values, but is almost insensitive to
100
;"
......
rum \n
80
"-"
I'"''""I
~. . . . . . . .
l .....
" " l " "
.....
60
\ •
open
o closed
20
........
0.0
I .........
0.1
I .........
0.2
I .........
0.3
I .........
0.4
I ........
0.5
0.6
Oxygen Deficiency 6
Fig. 7. Bulk critical temperature
•
100 0
E 1.0
~\
%
• open porosity • closed porosity • GFS powder
~*i
\ \ \
Q
\
" ~ 0.5
ii
. . . . .
0.0
I .........
0.1
I .........
I .........
0.2 0.3 Oxygen Deficiency6
lID
I ........
0.4
0.5
Fig. 8. Thermodynamic critical field Hc( T= 0) and GL parameter x vs. oxygendeficiency J. The dashed lines are a guide for the eye. J for J>_-0.12. The G L parameter has a different behavior. It seems to go through a m a x i m u m around = 0.O 7, and decreases up to J ~ 0.3. The rise o f r for higher oxygen deficiencies may be an artifact (see discussion). The calculated j u m p in the specific heat at Tc Ac/T¢ is plotted versus J in fig. 9. It also exhibits a pronounced dependence on the oxygen stoichiometry. Using standard expressions values for the upper critical field slope at T¢, the lower critical field Hcl, the penetration depth 2, and the coherence length are obtained and shown in table 1. All o f these values are for the HIIc orientation. The temperature dependence o f these quantities follows the temperature dependence o f He.
I .......
o\
40
*x---i---
T cGL VS. oxygen deficiency J.
M. D~iumling / The reversiblemagnetization of YBazCu307_6
0.10
..........
~ .........
' .........
' .........
I .........
[ .........
ie
0.08 o
E 0.06 q(
• open porosity • closed porosity • GFS powder
\ xx•
~_~ 0.04
x \
0.02
0.00 0.0
\
\#___._. . . . . .
0.1
=.....
,____
0.2 0.3 0.4 Oxygen Deficiency 6
0.5
0.6
Fig. 9. Calculated specific heat j u m p (at To) Ac/Tc vs. oxygen deficiency 8. The dashed line is a guide for the eye.
5. Discussion
5. I. General comments For specimens that have a nominal oxygen deficiency 8 close to zero there is a body of data in the literature. Therefore comparisons of the results found in this work with the work of others are possible. However, it should be noted that the results in the literature are not always consistent. For example, there are large spreads (up to a factor of three) in the values for the lower critical field Hc~. Hc~ is dif-
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ficult to measure because the critical current densities are high. Due to the flux creep problem the upper critical field cannot be measured using resistive methods. Therefore a large number of early publications in which resistive "He2" measurements were performed have to be excluded from consideration. Properties that are not affected by flux creep are the equilibrium magnetization, and the specific heat. These quantities have to be measured as a function of magnetic field. However, for example the jump in the specific heat at Tc does not exhibit the classical shift to lower temperature with increased magnetic field [22], making a Hc2 determination very difficult. Even if the reversible magnetization is measured, it should be pointed out that in most cases a linear extrapolation of the magnetization to zero does not lead to a correct value for the upper critical field slope. Therefore values of the upper critical field slope (and its anisotropy) obtained this way should be discarded. Anisotropy values obtained from the shape of flux lines using flux decoration techniques [ 17 ] should be valid.
5.2. Data analysis There are a number of assumptions that enter the data analysis. Firstly, it is assumed that the vortices are parallel to the applied field. In the field regime used here this is a correct assumption. Buzdin and
Table 1 Derived superconducting parameters (for HIIc) from x and He. Samples with numbers below 10 are dense (batch 1 ), samples with numbers above 10 are from batch 2. The sample marked GFS is the commercial specimen that was oxygenated and measured as powder. Specimens marked with an asterik may not be single phase Sample GFS 11 62 3 25 57 1 28 2 45 26* 50*
8 0.02 0.02 0.04 0.07 0.07 0.12 0.18 0.18 0.31 0.31 0.43 0.5
/lod/-/c2/dTI rc (T/K)
~ (rim)
/~//cl ( 0 ) (T)
(llm)
12 11 12 10 13 4.1 3.5 4.1 3.5 5.4 6.2 12
0.75 0.79 0.78 0.88 0.77 1.5 1.7 1.6 1.8 1.5 1.4 1.1
0.017 0.023 0.015 0.012 0.011 0.011 0.010 0.0089 0.0092 0.0074 0.0060 0.0036
0.23 0.20 0.25 0.28 0.29 0.29 0.29 0.31 0.30 0.35 0.39 0.53
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M. Dgiumling / The reversible magnetization of YBa2Cu307_a
Simonov [23] showed that for fields > 10Hal the vortices line up with the applied field for essentially all orientations of the crystal axis with respect to the field. Therefore only for very low fields is there a tendency of the vortices to align themselves with the a, b planes. Secondly, it is assumed that the magnetization of our fairly small-grained sample is identical to that of an infinite specimen. This is approximately the case since for example there is a 50% difference in grain size for the samples in fig. 5, but the extracted values for H~(0) and x are quite similar. Another aspect is the accuracy of the numerical solution used to compute the magnetization as a function of x and the applied field H. In order to obtain a comparison this fit program was used to fit the digitized data o f H a o et al. The parameters extracted are virtually identical to the ones given by Hao et al. themselves. Therefore there are only minor differences between these two different numerical solutions [ 2,3 ] of the Ginzburg-Landau equations. The numerical behavior of the fit program used is regular up to very high values of x. A more sophisticated theoretical approach should include a distinction of the different x parameters [ 18 ], also using their temperature dependence. This might also lead to a change in the temperature dependence of the thermodynamic critical field. Since the main goal of this work was to establish trends and since the approach currently used yielded very good results a more sophisticated fit was not used.
5.3. Fully oxygenated sample Tlieuss and Kronmiiller [24] also made measurements of M, ev on polycrystalline specimens. However, the magnetizations given here at a given temperature and field (for example 86.5 K and 1 T) are three times larger than theirs, and have a different field dependence. Unfortunately there is very little information on specimen preparation and oxygenation in their article, so that comparisons are rather difficult. Using a similar fitting method Hao et al. [ 3 ] obtain a x value of 55 for a nominally fully oxygenated single crystal with HIIc. Their value for He(0) is smaller than the value" obtained here. As the specimen was a single crystal, the irreversibilities were much larger than for our polycrystalline specimens,
thus making the reversible regime very small. In addition, the agreement between fit and data in their paper is significantly worse than in this work. Other measurements on single crystals produced in a similar fashion were made by Welp et al. [ 5 ] for both Hllc and H l c . They did not carry out a fitting procedure, but temperature and field dependence of their magnetizations were quite similar to the values obtained by Hao et al. In comparison to previous measurements values for the GL parameter x are found that are very high, even considering the possible errors due to the fact that the specimens are randomly oriented polycrystals. However, the magnetization of the polycrystalline specimens cannot be fitted using the single crystal parameters of Hao et al. This is due to the temperature dependence of the magnetization at lower temperatures (around 75 K). Unless a quite different temperature dependence for He is used, a fit with x = 55 creates a curvature, whereas the data is essentially straight in this regime. The high x values lead to very high values of the upper critical field slope, and thus to a very small coherence length, even for HIIc (see table 1 ). There should be no physical reason why the present results disagree with those of others. It therefore must be due to the material or specimen preparation. It is well-known that most single crystals contain fairly large amounts of gold in the structure (up to 10% substitution on the Cu chain sites). Gold increases the Tc value by up to 2 K [25 ], and may significantly influence x and the upper critical field. Palstra et al. [26] measured an upper critical field slope (using a thermomagnetic method) of about 8 T / K for H]lc on a crystal that did not contain gold. Unfortunately, no magnetizations were measured. Another issue is oxygenation. In the ceramic the is well-known because the times that are required to oxygenate them to equilibrium are small, and the oxygen content can be analyzed directly. That is not so in single crystals because of their small size. Due to long diffusion distances and the low mobility of O at the oxygenation temperature it must be expected that single crystals are somewhat oxygen deficient. Indeed, our oxygen deficient specimens show lower values of x and He, leading to a lower upper critical field slope. However, T¢ is below 90 K, which
M. Diiumling/ The reversiblemagnetization of YBa2CusO7_6 does not seem to be the case for the single crystals.
5.4. Oxygen deficient specimens As pointed out earlier [ 10 ], some variability in the magnetization was encountered with oxygen deficient specimens. According tO a recent phase diagram [ 12 ] specimens quenched from high temperature are most homogeneous, since a single phase field is predicted. At room temperature a two phase field is predicted for most stoichiometries, which makes the specimens metastable at room temperature. The increase of Tc after room (or slightly elevated) temperature annealing that has been observed by Veal et al. [27] may be a result of this metastability. Our specimens were measured days or weeks after the quench from the oxygenation temperature. No changes in the magnetization with time for times of the order of weeks were observed. For the specimens with ~=0.43 and 0.5 one more complication arises. The initial anneal takes place in a regime where the equilibrium structure is tetragonal [ 28 ] (nonsuperconducting). At room temperature the equilibrium structure is orthorhomic (superconducting). Thus the specimen has to transform its structure during the quench. In order to obtain an equilibrium state both of these specimens were postannealed. Therefore there is the possibility that the specimens are not single phase, which would make the results of the fitting procedure dubious.
5.5. Specific heat Specific heat measurements have been carried out on both single crystals [22 ] and polycrystalline ceramics [29,30]. Since Tc is high phononic contributions to the specific heat are high as well, leading to a small jump at T~ on top of a large background. Both thermal fluctuations and sample inhomogeneities tend to lower and broaden the specific heat jump. Typical values for the zero field jump Ac/Tc range from 50 to 60 m J / ( K 2 mol) for nominally fully oxygenated specimens. Good agreement between calculated and measured values if oxygen deficiencies J around 0.06 are assumed for most specimens in the literature. This is rather sensible since it is not difficult to achieve this oxygen content even in a fully dense specimen using typical oxygenation treat-
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ments. Junod et al. [ 30 ] measured the specific heat j u m p as a function of oxygen deficiency. They find a strong dependence of the j u m p on t$. The highest value for Ac/T¢ that they measured was 67 m J / (K 2 mol). The same trend is certainly also found in this work. For fully oxygenated specimens even higher jumps in the specific heat are expected. However, these very small g values ( ~<0.02) are only expected in specimens that are oxygenated as a powder, or in ceramics where the pores are connected.
6. Conclusions The reversible magnetization in ceramic specimens of YBa2Cu3OT_a with 0.02 ~ ~< 0.5 was measured in magnetic fields up to 5.5 T. The magnetization fits very well to calculated values obtained using Ginzburg-Landau theory. However, for the fully oxygenated specimen values of x and He in the literature cannot fit the magnetization curves. Much higher values of x (between 170 and 300) have to be used to obtain a satisfactory fit. Resulting from the high x very high values of the upper critical field are obtained, leading to a very short coherence length even for the HIIc orientation. Both x and Hc values decrease with increasing ~. Specific heat jumps at Tc were computed from the temperature dependence of He, and quantitative agreement with measurements from the literature is obtained. It is predicted that fully oxygenated specimens with ~< 0.02 should exhibit a larger specific heat jump at T~ than what has been measured so far.
Acknowledgements I thank T.M. Shaw, L.E. Levine and L. Civale for discussions, T.McGuire for the use of the magnetometer, and M.M. Plechaty for performing the oxygen analysis. The starting powders of YBa2Cu3OT_6 were provided by E. Olsson and P. Duncombe. The work was partially funded by DARPA under constract No. N00014-89-0112.
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