The equilibrium magnetization of granular high temperature superconductors in low fields

Physica C 174 (1991) 233-241 North-Holland

The equilibrium magnetization of granular high temperature superconductors in low fields I. The Meissner effect o f YBa2 (CUl - xFex) 307_ y

S. Ruppel, G. Michels, H. Geus, J. Kalenborn, W. Schlabitz, B. Roden and D. Wohlleben II. Physikalisches lnstitut, Universitdt zu Ki~ln, W-5000 Ki~ln 41, Germany

Received 20 April 1990 Revised manuscript received 19 November 1990

We report the temperature and field dependence of the DC Meissner effect of sintered pellets of YBa2(Cuj _xFex)307_y with 0
1. Introduction In this p a p e r we report on the spontaneous flux expulsion of sintered pellets of YBa2 (Cu i _xFex) 3 0 7 _ r This system provides a good basis to study as a function o f temperature, field a n d concentration the a n o m a l i e s o f the M e i s s n e r effect found in sintered pellets o f all high t e m p e r a t u r e sup e r c o n d u c t o r s ( H T S C s ) , n a m e l y an i n c o m p l e t e expulsion at H < He1 followed by complete expulsion at H < H m < < H c l [ 2 - 5 ] . We discuss our d a t a in terms o f two e q u i l i b r i u m effects, which were first suggested by Seidler et al. [ 3 ] a n d are analysed in detail in the following p a p e r [ 1 ].

2. Sample preparation and characterization YBa2(Cl_xFex)307_y samples with 0_
in an alumina crucible, again ground in a mortar, a n d then in a ball mill. This procedure was repeated three times to ensure good homogeneity. Then the p o w d e r was pressed with a force o f 12 tons into pellets o f 6.5 m m radius. T h e pellets were then a n n e a l e d for 12 h at 950°C u n d e r flowing oxygen. This was done in April 1988. In N o v e m b e r 1989, after they no longer showed full flux expulsion at the lowest fields (apparently because o f the d i s a p p e a r a n c e o f the weak links by aging, see below), the samples with x = 0 and x = 0 . 0 2 were a n n e a l e d again u n d e r flowing oxygen. X-ray diffraction patterns with C u - K a r a d i a t i o n d i d not show any i m p u r i t y phases for x < 0.2, within the resolution o f about 5%. At 0.025 < x < 0.03, there is an o r t h o r h o m b i c to ( p s e u d o ) t e t r a g o n a l phase transition, as r e p o r t e d e.g. in [6 ]. The lattice constants o f the u n d o p e d sample are a = 3 . 8 2 5 A, b = 3 . 8 8 4 A a n d c = 1 1 . 6 8 5 A. At x = 0 . 0 3 we find a = b = 3 . 8 6 A, a n d a increases to 3.87 A at x = 0 . 2 . The c-axis decreases only slowly, to I 1.65 A at x = 0 . 2 . In the x = 0 . 0 4 sample a small splitting o f the 2 0 0 / 020 reflex i n d i c a t e d the presence o f a small a m o u n t

0921-4534/91/$03.50 © 1991 - Elsevier Science Publishers B.V. (North-Holland)

234

S. Ruppel et al. / The equilibrium magnetization of granular HTSCs in low fields I too 90

o

:

Resistance

:

Meissner

N v

80

~_" 70 o

6o o

5o 0

2

4 x

6

8

10

[at-% Fe]

Fig. 2. Transition temperature To(x) as function of Fe concentration x, as measured by the resistance ( • ) and by the Meissner flux expulsion ( o ).

of the orthorhombic phase. Optical migrographs (fig. 1 ) showed a dense polycrystalline structure, without impurity phases for x_<0.06. The sample with x = 0.08 showed small amounts o f CuO. The average size o f the crystallites was 13 I~m for x = 0, 18 ktm for X = 0 . 0 4 and 7 ~tm for x = 0 . 0 6 . Resistivities were measured with a standard AC four-point method, with currents between 0.5 and 0.1 mA. The normal state behaviour was metallic ( d p / d T > O ) for x_<0.04 and semiconducting (dp/ d T < 0) for x >-0.04. Tc o f the undoped sample was 93.0 K (mid-point o f the transition), indicating oxygen deficiency y < 0 . 1 [7]. In the orthorhombic phase we found d T c / d x = - 1.67 [ K / a t % F e ] and in the pseudotetragonal phase d T J d x = - 7 . 3 7 [K/ at%Fe] (fig. 2). For x = 0 and 0.01 the transition widths ( 9 0 - 1 0 % o f p , ) were smaller than 1 K. In the pseudotetragonal phase, they increased roughly linearly with x to about 20 K at x = 0 . 0 8 . The sample with x = 0 . 1 0 and 0.12 showed two transitions. Therefore we did not examine the Meissner effect at x > 0.08. The shift of the Cu-Koedge, the normal state susceptibility and the superconducting shielding effect (ZFC) of these samples are reported elsewhere [ 8,9 ].

~l Fig. 1. (a-e) Optical micrographs of the sintered pellets of YBa2(Cu,_xFex)3OT_ywith x=0, 2, 4, 6 and 8%.. The average grain size is 13 ~tm for x=O, 18 ~tm for x=0.04 and 7 itm for x=0.06.

235

S. Ruppel et al. / The equilibrium magnetization of granular HTSCs in lowfields 1

3. Experimental details A Faraday balance was used for the magnetic measurements in higher fields ( 100 G_
4. Results In figs. 3 and 4 we show the field cooling susceptibility x - M / H as function of temperature, in percent of - 1/4~, for the samples with 0-< x_< 0.08. The following features are observed: i) In our lowest field of 2 0 e , all samples with x_< 0.06 show a full Meissner effect X-- - 1/4~ at suf-

(a)

H[Oe] 0 4000 2°°0

, - - ~

~0

o

20

25

30 ,

i

h

20

b

l

40

l

l

60

Temperature

(b)

o

l

80

iO0

[K]

0 YBa2CuaO -7~

40

H [Oe] iO0 25 ~.o

60

5

20 ~"~

~

80 lO0

2 20

40

60

Temperature

80

100

[K]

Fig. 3. (a) The spontaneous flux expulsion of the pure pellet

(x=0) of YBa2CU3OT_y,in fields between 4000 and 20e, measured before reoxygenation(see text). (b) The spontaneousflux expulsion of the same pellet in fieldsbetween 100 and 20e, measured after reoxigenation. ficiently low temperatures. The sample with x = 0.08 shows only 80% of - 1/4~ in 2 0 e , but is also clearly on its way to full expulsion in still lower fields. ii) Immediately above 2 0 e , the flux expulsion decreases strongly with increasing field, with a point of inflection around 5-10 Oe, followed by a long plateau at (30+ 10)% out to 100 Oe (fig. 5). At still higher fields, the flux expulsion decreases more strongly again (X~ 1/H, see the log-log plot in fig. 6). iii) For the samples in the orthorhombic phase ( x = 0 and 0.02), the flux expulsion remained at (25_+2)% at 2 0 e < H < 200 Oe in those Foner measurements, which were done 1.5 years after the sample preparation (figs. 3(a) and 6 ( b ) ) . After reoxygenation, these samples switched to full flux expulsion at 2 0 e (figs. 3(b) and 6 ( b ) ) , with intermediate low field behaviour similar to all other cases (fig. 6 ( a ) ) . The reoxygenation did not alter the onset of the flux expulsion at To= 93 K, nor the width of the transition, nor x ( T , H ) at H>_ 100 Oe

ooly I 000

S. Ruppel et al. / The equilibrium magnetization of granular HTSCs in low fields I

236

C

LOOO

(a) lO0

|:0

x = 0

~o 500 o

20

~0 200

o

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to

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~

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~°-~~ I/H1 0.,0°o

20 40 50 BO JO0 Temperature [K]

H[eel 20 iO0 25 40 60 t I

25 10 --

80

o .......

100

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(b)~ ~0033

'

X\ I

re?idatt T ~

. aft:r

1000 ~0000

Field

~

JOe]

'

80

2 20 40 60 BO Temperature [K]

~00

20 40 60 80 Temperature [K]

100

0 H[Oe) X = 0 . 0 4 ~

20 40

lOO

60

tO

tO0

.-

0

x =0

,

x=

°,-0.o8

\\\,

___V",'~

0.06

-10

25--

100

1000

Ma g n e ti c F i e l O

80 i

80 x = 0.08

100

20

10

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ol

iO0

0

o

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~ 100

o

lO

.06

20 40 60 80 iO0 Temperature [K]

"~ ~ 40 ~o 60

33

40

60

Temperature

BO ~00 [K]

0

20 40 60 80 tO0 Temperature [K]

Fig. 4. The s p o n t a n e o u s flux expulsion o f the pellets o f YBa2 ( C u ~_xFex) 307-~ with x = 2, 4, 6 a n d 8% between 2000 a n d 2 Oe.

10000

[Oe]

Fig. 6. ( a ) The s p o n t a n e o u s flux expulsion for YBa2Cu3OT_y ( x = 0) near T = 0 as function o f the a p p l i e d field. N o t e the plateau near 25% below 200 O e before r e o x y g e n a t i o n a n d the full expulsion at 2 0 e thereafter. A b o v e 200 Oe, the e x p u l s i o n is inversely p r o p o r t i o n a l to the field in b o t h cases. ( b ) S a m e as fig. 5, but in a l o g - l o g plot.

dependence of Z(T) immediately below T¢, with dx/ dT~ 1/H at the higher fields, but with field inde(compare figs. 3(a) and ( b ) ) . iv) For the orthorhombic samples ( x = 0 and x = 0 . 0 2 ) one observes strictly linear temperature

~00 ~

YBaa(Cu1_xFex)

pendent slope at the lowest fields (figs. 3 and 4). v) In the quasitetragonal phase ( x > 0.03 ), the expulsion curves downward just below T¢ over a temperature interval, whose width increases with x (fig. 4).

aOT_y

n

80 ~\ ~1

o x-O N x=o.o2 + x=0.04

~

60 ~

5. Discussion

, ,-o.o6

40

"~

20 0

20

40

Nagnetic

60 FielO

BO

100

[Oe]

Fig. 5. The s p o n t a n e o u s flux e x p u l s i o n n e a r T = 0 as function o f

the a p p l i e d field. N o t e the plateau a r o u n d 30% a b o v e 20 Oe a n d the final full e x p u l s i o n at 2 0 e .

The lower critical field Hcl of YBa2Cu307_y is a few 100 Oe at least. Therefore the incomplete flux expulsion shown by all samples in figs. 3 and 4 down to H ~ 2 0 e occurs far below He1. This behaviour distinguishes the granular HTSCs from ordinary granular type-II superconductors [ 11 ]. Krusin-Elbaum et al. [12 ] and Kitazawa et al. [ 5 ] attributed it to pinning. On the other hand, Seidler et al. [ 3 ] have interpreted this behaviour in terms of equilibrium

S. Ruppelet al. / The equilibrium magnetization ofgranular HTSCs in lowfields I properties. Their model is worked out in detail in ref. [ l ]. The key observation is that blocks of HTSC material, which are smaller than the penetration depth 2¢ for fields parallel to the CuO plane, cannot expell even arbitrarily small field components lying parallel to these planes. In a pellet, the HTSC material is subdivided into such blocks by defect surfaces with very low conduction electron density. Consequently, at H < H¢~ the induction meanders in nearly full strength through the pellet, running either parallel to the CuO planes or parallel to the defect surfaces. In this "magnetically transparent" state at H>H¢I (T) < 1000 Oe at all temperatures. Under this condition, and because x>> 1, the equilibrium susceptibility z(H, T) of the assembly of grains with random orientation of their c-axes is

[1]

237

with any smearing of T¢. Equation ( 1 ) also predicts correctly the 1 / H dependence of Z( T, H ) at H-> 500 Oe (fig. 6). From the initial slopes of the :~(T, H ) curves in fig. 3(a) at the higher fields (500 to 4000 Oe), we extract CtHc~(0) = (240 _+5 ) Oe via eq. ( 1 ). If we use the values of z ( T = 0 , H ) instead, we find otH~ (0)~, 125-140 Oe at the same fields. This may reflect some hindrance of the flux expulsion by pinning as T-,0 at higher fields [12,5]. However, it could also be caused by some temperature dependence of x;, near T¢, 2 ( T ) approaches and surpasses the average distance between the defect planes and of the crystallites, while ~ does not. In any case, by the initial slope just below T~, v~e are evaluating data in the reversible regime. We therefore take otHc~ (0) = 240 Oe as the equilibrium value for x = 0. For YBa2Cu3OT_y values between 300 and 1000 Oe have been reported for H¢~ (0) with the field parallel to the c-axis [ 13-15 ], and a record H¢~ = 1600 Oe was reported for a single crystal of TmBa2Cu306. 9 [16]. With ot~ 1/2-1/3, our value of 500 < H¢1 (0) < 800 Oe at x = 0 is in the range for good

polycrystalline YBa2Cu307_y. 5.2. 1/3 Flux expulsion at low fields (Hm2c), only 1/3 of the full flux expulsion is expected at low temperatures in fields which are smaller than H¢1(0) [1,3]: Z= - ( 1 / 4 ~ ) ( 1 / 3 ) ( 1 -- 32a/{q¢ } )1/2

(2)

--(l/4n)(l/3)y (H
z(H, T ) = M ( H , T ) / H - (ot/8n) (He1 (0) ( 1 - ( T / T ¢ ) 2 ) / H ) - (ct/4n)Hc, (0) ( 1 - ( T / T c ) ) / H (H~I(T)<
(1)

0.3
For the samples in the orthorhombic phase ( x = 0 and 0.02), the high field curves indeed trace out roughly what is expected for H¢~ (T). The width of the transition of z ( T ) from Tc to the low temperature plateau near T J 2 has therefore nothing to do

T<< T¢, 2,Jq 1/2 << 1 ) .

y is a correction factor, which takes into account the penetration of the field components perpendicular to the CuO planes to depth 2~ along the circumference of the blocks with cross-section q¢~ d 2. The tendency to saturation at 1/3 expulsion is apparent in figs. 3, 4 and 6 below about 200 Oe, most clearly in figs. 3(a) and 6(a), where no crossover occurs to full flux expulsion at very low fields. In figs. 3(a) and 6(a), the saturation occurs actually somewhat below 33%. We shall evaluate the correction factor y

238

S. Ruppelet al. / The equilibrium magnetization of granular HTSCs in lowfields I

after extracting the block size q¢ from the data. 5.3. Extraction of the block size from z(T) near T~ at low fields The average cross-section {qc} of the blocks for fields perpendicular to the CuO planes determines the final, field independent slope of X(T) just below T~ in small fields [ 1 ] via {qc} = ( d z / d T ) (4~T~2~(0) 2) (3//~y) ( (Tc - T)/T~ < (22~(0))2/{qc } << 1,

(3)

H < He, (T) (22o(T))Z/{q¢ } ) Without weak links (Hm~0), fl= 1, and with, fl= 2 (at H < H m ) [1]. We first evaluate the case x = 0 . In the data of fig. 3 (a), we observe saturated expulsion near 25°/0 and no crossover to full expulsion as in figs. 3(b) and 4, down to our lowest field of 2 Oe. These data were taken 1.5 years after the sample preparation and before reoxygenation; the absence of a crossover to full flux expulsion indicates Giaever barriers between the blocks, or a very wide mesh of the Josephson loops (Hm--'0 [1]). The susceptibility is independent of H within AT.~2 K for H_<10 Oe, with dz/ dT=0.0117 K -~. W i t h ; t a ( 0 ) = 1 4 0 0 A [13,17], eq. (3) gives {q~}= (1.8 lxm) 2. The mean cross-section of the crystallites ranges from 50 to 350 ~tm2 (fig. l ), about two orders of magnitude larger. {q~}= ( 1.8 ~tm) 2 must then be the cross-section of blocks bordered by nearly insulating planar defects within the crystallites. Such defects may e.g. be twin planes [ 19,20]. Twinning can be seen in the optical micrograph for x = 0 in fig. l (a), where it occurs in checkerboard fashion within the crystallites. Because of the field penetration to depth 2a into the blocks, the actual size of the blocks is larger than the magnetically measured qc. Using the correction factor ~, for square shaped blocks and 2a(0) = 1400 A, we find {q'~}~ (2.0 ~tm) 2. With this eq. (2) gives ),= 0.77, predicting the observed expulsion of ~ 25%. Note that {q~} ~ (2.0 !xm)2~2¢2. If the dctual distance between the intersections of defect surfaces with the CuO planes were smaller than 2¢, a maximum distance of order 2e between surfaces with out of plane components Be would be energetically cheaper

than a distribution with finite Be at every defect surface. {q~} ~22 is then consistent with minimum kinetic energy in the Meissner loops at maximum volume with B parallel to the CuO planes!. The data of fig. 3 (b), taken after reoxygenation, do not differ from those in fig. 3(a), except at the lowest fields, where significant changes are caused by the reestablishment of weak links across the defect surfaces. The initial slope of :t(T) at 2 Oe has grown to d z / d T = 0.025 K - 1, to twice the value measured in fig. 3 (a) in the (near) absence of weak links, consistent with the expectation that for Ho--,0, fl= 1, while for H < Ho, fl = 2 (eq. ( 3 ) ). This shows that the block size {q~} and H¢~(0) did not change during reoxygenation, to high accuracy. 5.4. Size of the Josephson loops from the crossover to full flux expulsion For a pellet with Josephson barriers (weak links) connecting the blocks, the average cross-section {ql} of the Josephson loops is measured by the field H a half way along the crossover from 1/ 3 to full flux expulsion [ 1 ]

{q~}~ ~o/(9~oHm).

(4)

In fig. 3 (b), the data show a crossover at H ~ 5 0 e , similar to all other data with x > 0 (fig. 4). For Hm= 5 Oe, eq. (4) gives {q~}~ (0.7 p-m) 2, 8-10 times smaller than the area {q~ } of the blocks, and about 1000 times smaller than the cross-section of the crystallites. Clearly these loops must be within the crystallites (case ii) in section 5 of [ 1 ] ). The area of these loops is in fact quite close to the cross-section 22a(O){q'e}l/2..~0.56 lxm2 of the field penetration along the planar defects around the rim of a square shaped {q~} = (2 ~tm) 2. In other words, the flux is expelled from the pellet entirely, when the Josephson loops around the defect surfaces with average area {q~}~ 22a{qc}~/2 "pinch off" the fields running along the defect planes and grain boundaries at fields, which puts less than one quantum of flux onto these loops [1]. Note that the data in fig. 3 before and after reoxygenation give the same To, the same field and temperature dependence at high fields, the same saturation of the flux expulsion near 25% at intermediate fields, and the same average cross-section {q~} of the

S. Ruppel et aL / The equilibrium magnetization of granular HTSCs in Iow fields I

blocks. Reoxygenation should of course not change the size of the grains, but apparently it did not change the number of planar defects either, nor, most importantly, the intragrain properties such as Te and Hot(0). The only effect of reoxygenation was apparently an improvement of the electrical contact across the barriers, turning them from Giaever to Josephson type! This allowed us to separate deafly the magnetic transparency of an assembly of sufficiently small blocks, i.e. the saturation of the expulsion near , 4 n X ~ 1/3 (fig. 3 ( a ) ) , from the final flux expulsion by the superconducting loops at Hm ~ 5 0 e (fig. 3(b)) Not surprisingly, the crossover field to full flux expulsion varies somewhat with x (figs. 5 and 6). In fact, the samples with x = 0 . 0 4 and 0.02 expell more flux in the region H,~
5.5. Temperature and field dependence of x for smeared Tc In the previous sections we have assumed identical Te's in all grains, independent of the grain size. With this assumption, X(T) should vary linearly just below Te, without and with weak links [ 1 ]. Experimentally we find that in YBa2Cu3OT_y the steep increase o f x ( T ) below Te is indeed linear (fig. 3), except for some rounding within 0.2 K of T¢, which was barely detectable within our experimental resolution (and is not apparent here). On the other hand, the downwards curvature of the initial flux expulsion becomes important in the quasitetragonal phase at x > 0.02 (fig. 4). This cur-

239

(a) 0

wo

-B

-1; 5O

60

70

Temperature (b)

15

. . . . .

80 [K]

/

'

12

B 4 ~o

Oh" . 0

. . . . . . . . 2 4 6 8 x

I0

[at-% Fe]

Fig. 7. (a) Construction of the transition width ATe(x) from the rounding of the flux expulsion just below Tc (data from x=0.06 at H = 100 Oe). (b) ATe(x) as defined in (a), extracted from the data in fig. 4.

vature appears at all fields. The width of the region of curvature is independent of the field within the scatter of the data, but increases strongly with x. In fig. 7(a) we give a construction by which we define the intrinsic width ATe(x) and in fig. 7(b) the corresponding values, as extracted from the data in fig. 4. The Tc(x) from the flux expulsion, defined in the inset of fig. 7(a), is plotted in fig. 2, together with the resistive T~(x). The rounding can be explained by a superposition of susceptibility curves with sharp but different Te's, i.e. with a distribution of Tjs over the grains, whose width is approximately given by ATe(x). The linear magnetization curves from grains with different Tjs then add up over the temperature interval ATe(x). At lower temperatures, all grains are superconducting. If they are then still all in the linear region of their individual x ( T ) curves, they will produce an intermediate total linear X(T) over a finite temperature interval ( x = 0.04). If not, there will be merely a point of inflection of x ( T ) , as for x = 0 . 0 6 and x=0.08.

240

S. Ruppel et aL / The equilibrium magnetization of granular HTSCs in lowfields I

The fact that all samples tend towards full flux expulsion below a crossover field of order 5 Oe implies that all crystallites are fully superconducting near T = 0: while we have a distribution of Tjs, this distribution does not include a significant fraction of nonsuperconducting blocks, not even nonsuperconducting regions within the crystaUites. The fact that all grains are fully superconducting at low temperatures is suggested independently by the clear plateau of the flux expulsion around 30% (eq. (3)). We point out that the linear parts of z ( T ) have smaller slopes at finite x than at x = 0 at the same field. For H > H0, when the slopes are proportional to H~ ( O ) / H (eq. ( 1 ) ), this is expected for smaller H~ (0). A decrease of H~ (0), or equivalently, an increase of 2a (0), is expected when the effective mass m* of the carriers increases (due to elastic scattering in the CuO planes), a n d / o r when the carrier density no decreases. Both effects are expected when doping YBa2Cu307_y with Fe impurities. A decrease of Hc~ (0) with increasing x can also be seen in fig. 6 (b), where the lines with slope - 1 at H > 200 Oe move to the left with increasing x (Her(0) is two times smaller at x = 0 . 0 6 than at x = 0 ) . The only sample which may be suspected of not being fully superconducting at T--.0 is the one width x=0.08, since it shows only 15-20% flux expulsion on the plateau between 20 and 100 Oe, and since full flux expulsion could not be documented with our lowest field of 2 Oe (fig. 5). However, even in that case the data are consistent with 100% superconducting volume: a decrease of Hc ~(0) of the x = 0.06 with respect to the x = 0 sample by a factor of 2 implies an increase of 2 a ( 0 ) by the factor 1.41. The correction factor in eq. (3) then predicts only 22% flux expulsion (without weak links and at equal block size), again close to the observation. In fig.8 we give the flux expulsion at 100 Oe as function ofx. It shows a nearly linear decrease in the pseudotetragonal phase, from 30% at x = 0 . 0 3 to zero at x=0.14. Since for d/ka(0) << 1 Z ~ ).,~(0) - 2 ~. ltono (0) e 2 / m *, this result suggests that for x>_0.03, no(O)/rn* decreases linearly with increasing x. We wish to point out an important correlation of our data with specific heat measurements on the YBa2(Cul_xFex)307_y system [21]. The specific heat anomaly was found to be large and relatively

BOI[ YBa2 (CUt_xFex) aO7_y '~ 40~" o ~ _ ~

0

t

0

i

.eissner

'lO00erstedt.

,

i

4 8 12 x [at-~ Fe]

16

Fig. 8. The spontaneous flux expulsion in 100 Oe at low temperature as a function ofx.

sharp at x = 0 and x=0.01 (in the orthorhombic phase). In this phase we also find sharp T~'s (ATe< 1 K). However, at x=0.04, i.e. in the quasitetragonal phase, the anomaly was strongly depressed and broadened and became hard to distinguish from the smooth phononic background. This result is consistent with the broadening of T¢ measured by the flux expulsion (fig. 7 ( b ) ) : downward curvature of the initial flux expulsion and smearing of the specific heat anomaly go together! There must of course be a specific heat anomaly with the proper entropy in the tetragonal phase; after all, we find that all these alloys are fully superconducting near T = O, albeit with decreasing no~m*. However, because of the smearing of To, the specific heat anomaly will be rounded off. Because of its smooth variation with temperature, it can no longer be separated from the phononic background specific heat, whose smooth variation with temperature is not shown independently.

6. Conclusions Our analysis of the dependence of the spontaneous flux expulsion of sintered pellets of YBa2(Cu~_xFex)307_y on temperature, field and concentration shows that an interpretation of the incomplete flux expulsion at fields H m < H < H c ~ (0) in terms of magnetic transparency and of the final complete expulsion at H < H m in terms of less than one quantum of flux on the Josephson loops can be carried through successfully. Both effects occur in thermodynamic equilibrium [ 1,3]. Sufficiently far below T¢, all pellets of

S. Ruppel et al. / The equilibrium magnetization of granular HTSCs in low fields I

YBa2(CUl_xFex)307_y are f o u n d to be superconducting over nearly their entire volume. F r o m the field a n d temperature dependence o f the spontaneous flux expulsion, we find an average cross-section of the superconducting blocks in the C u O planes of {qc)2 ~ 4 $tm2 ~ 22 at x = 0. These blocks lie within the much larger crystallographic grains a n d are bordered by defect surfaces. Superconducting loops a r o u n d these surfaces with cross-section 22¢2a ~ 0.5 ktm2 are responsible for the final flux expulsion in fields H < H m < 5 0 e . In the o r t h o r h o m b i c phase (x-< 0.03 ) the intrinsic width of the transition is less than 1 K, in the average over all grains. In the tetragonal phase, however, there is an intrinsic width, which increases linearly with x for 0.04_
Acknowledgements

This work was supported by the B u n d e s m i n i s t e r f'tir Forschung u n d Technologic through B M F T contract ~13N5494A a n d by the Deutsche Forschungsgemeinschaft through SFB 34 I. We t h a n k U. Callies for providing the X-ray data, G. Dietz a n d N. Wild for access to a n d help with the F o n e r magnetometer, a n d K. Baberschke, W. Braunisch, K. Kitazawa a n d B. Schliepe for discussions.

References

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