Determination of flux-density gradients in YBa2Cu3O7−δ superconductors using the high-resolution Faraday effect

Physica C 166 ( 1990) 36-48 North-Holland

DETERMINATION OF FLUX-DENSITY GRADIENTS IN YBa2Cu307_6 SUPERCONDUCTORS USING THE HIGH-RESOLUTION FARADAY EFFECT M.R. KOBLISCHKA,

N. MOSER,

B. GEGENHEIMER

a and H. KRONMULLER

MPI ftir Metailforschung, Insliiut ftir Physik, D-7000 Stuttgart 80, Heisenbergstrasse 1. Fed. Rep. German!, a MPl,ftir FestkGrperforschung, D- 7000 Siuitgart 80. Hersenbergstrasse 1. Fed. Rep. Germanic Received

8 December

1989

Domain patterns of magnetic flux penetrated in YBaZCu&_-6 superconductors have been observed by means of a high-resolution Faraday technique. The experimental conditions for observing domain patterns with the high-resolution Faraday effect are discussed. Flux-density profiles and the related flux-density gradients were determined from an analysis of the domain patterns. An analysis of the measured flux-density gradients in single-crystals shows that twin-boundaries are not the strongest acting pinning mechanism at low temperatures. Our results support the assumption that intrinsic pinning determines the flux-density gradients and governs the critical currents. It is shown that the flux-density gradients in grains of the sintered specimens are larger than in single-crystals. The resulting thirty times greater pinning forces are measured both magneto-optically and with a SQUIDmagnetometer. This behaviour may be explained by superimposed extrinsic pinning effects such as grain-boundaries.

of a one-dimensional problem, the equation volume pinning force, f,reduces to

1. Introduction For technical applications, the current carrying capacity of high-T, superconductors is one of the most important parameters. In the vortex state, the critical current density,j,, would be zero if the flux-lines were able to move completely free, thus forming a homogeneous distribution of the flux-density (see e.g. [ll). In type-II superconductors various types of lattice defects such as dislocation lines, point defects, precipitations and magnetic defects corresponding to paramagnetic ions give rise to pinning forces on fluxlines leading to a spatial gradient of the flux-line density within the specimen [ 21. The volume pinning force, f,, acting on the vortex lines in hard superconductors is given by the Lorentz force [ 31 f,=jxB

(1)

with the current density j and the magnetic flux density B. Using Maxwell’s equation VxH=j we obtain

f,=[(bcH(W)XBl.

(2)

On applying a magnetic field in z-direction 0921-4534/90/$03.50 ( North-Holland )

0 Elsevier Science Publishers

in the case B.V.

for the

(3) From measurements

of the magnetization curve for H(B) and from this function the inverse slope of the magnetization curve aH=/aB, is obtained. According to eq. (3) the pinmay then be determined experimenning force, f,,,, tally from measurements of B;(x) and i3Bz(x)/iJx. In general three methods may be applied for the determination of flux-density gradients in type-II superconductors. The first and most sensitive method is the decoration technique. developed by Trluble and Essmann [ 41. However, it is difficult to observe by this technique the long-range arrangement of vortices under an applied external magnetic field. Another method for measuring flux-density gradients was developed by Weber and Riegler [ 5 1, using small Hall probes as sensing elements. The resolution power of this method is restricted to about 500 urn, and therefore is not suitable for measuring local fluxdensity gradients on a scale of l-100 urn which is required in order to determine pinning forces with wavelengths of the order of the flux-line distances. H-=K H,, we may determine

M.R. Koblischka et al. /Determination

Only the magneto-optical Faraday effect combines the requirement of a high resolution (ca. 0.5-0.8 urn; limited by optical restrictions), the possibility of observing extended domain patterns, and their dynamic behaviour. Since the first application of the magneto-optical Faraday effect for the investigation of superconductors by Kirchner [6,7] this method has proved its usefulness and has also been applied to type-II, A 1% superconductors by Habermeier and Kronmtiller [ 8 1. Recently, the high resolution Faraday technique was also applied to high-T, superconductors by Moser et al. [9]. In the present paper we describe the experimental conditions for the observation of the flux-density profiles and their gradients both in YBa2Cu@_8 single-crystals and in sintered specimens. For comparing the results of the flux-density gradients of the high-T, materials with the well-known gradients in conventional superconductors, in addition niobium single-crystals have been investigated.

2. Conditions for observation of flux-density gradients 2.1. Theoretical background In order to deal with a large Faraday rotation all samples were coated with a magneto-optical thin film, as described in [ 9 1. This magneto-optical active film consists of a mixture of EuS and EuF*. After cooling the samples down to T= 10 K, an external magnetic field, H,,,, is applied perpendicular to the specimen surface to produce the Shubnikov phase (see also fig. 1a). Since the magnetic stray field resulting from the flux lines also penetrates the magneto-optical layer, the polarization vector of the monochromatic, linearly polarized light is rotated through an angle a within this film when the light beam is reflected at the surface of the specimen. (Ydepends on the component of the magnetic field, H,, parallel to the light propagation vector according to (Y= 2 VdH,,

(4)

where Vdenotes the Verdet constant and d the thickness of the magneto-optical layer. For a detailed analysis of the domain patterns, the rotation angle

of&x-density

gradients in YBaCuO

31

should be as large as possible. This is obtained using destructive interference between the light reflected at the surface of the magneto-optical layer (MOL) and the light reflected at the surface of the superconductor without the influence of the magnetic stray fields of the vortices. An optimum contrast is thereupon obtained between regions carrying magnetic flux and regions in the Meissner phase. This leads to a phase condition for the thickness of the MOL given by d=

(2n+

1)1/4

(5)

where n is an integer and A corresponds to the wavelength of the light (A=5460 8,). The best effectiveness of the destructive interference is achieved when the amplitudes of the interfering components are equal in size. Due to the transparency of the magneto-optical layer, the intensity of the light reflected at the surface of the magneto-optical film is much smaller than that of the light reflected at the surface of the superconductor, the absorption of light in the layer must be used for equal amplitudes and therefore for optimal extinction. This is the so-called amplitude condition for the thickness. Both conditions can be fullfilled simultaneously with a magneto-optical layer thickness of 3/4 A; this is equal to 4095 A. The thin layer is also a prerequisite for a high resolution of the Faraday technique, because the attainable resolution depends on the thickness of the layer [ 10,111. Since the stray fields strongly diverge, the thickness of the magneto-optical layer should be less than the distance where the stray fields of fluxlines begin to overlap, to use the possibility of the observation of single flux-lines in high-T, superconductors. The quantitative calibration of the angle of rotation, (Y, with respect to the flux density, B,,,surface,at the surface of the specimen is facilitated if (YWHII

(6a)

and H II Jayer -B Il,surface

(6b)

holds over a large range of the applied magnetic field. For the magneto-optical substances - EuS, EuSe and EuF, - the validity of eq. (6a) has been verified by Gtintherodt et al. [ 12 ] and by Suekane et al. [ 131.

M.R. Koblischka et al. /Determination

38

of&x-density

gradients in YBaCuO ---------

Fcosa

-p

F

/

-0 a’ ’ F / ___________~ T;i

b a

v--e-

Flux

y

Lines

Fig. I. (a). Schematic view of the experimental arrangement for the Faraday effect. MOL denotes the magneto-optical layer, SC the superconductor in the Shubnikov phase, which is produced by the external magnetic field, H,,,, and (Y is the rotation angle of the light after the effect. L is the electric vector of the incident light, N the vector of the unrotated light - reflected at the surface the MOL - and F the vector of the rotated light. For clarity, an angle pz 0 of the incident light is represented; in the experiment /7 is zero, e.g. we have vertical incident light. Also, the magnetic stray fields, caused by the flux-lines in the SC, are shown within the MOL. The polarization planes of the light before and after the reflections at the surface of the MOL and at the surface of the SC are represented schematically. Fig. 1. (b). Vector diagram of the destructive interference. It is clearly shown that for optimal extinction, N and Fcos 01have to be equal in size. cy’ denotes the enlarged rotation angle using the destructive interference.

A schematic view of the experimental arrangement is given in fig. 1a: fig. 1b shows the vector diagram of the destructive interference. 2.2. Experimental conditions Look-up

A description of the sample preparation and of the coating of the samples with the magneto-optical layers is given in [ 91. In order to satisfy eq. ( 5 ), the evaporation in the electron-beam coating plant was stopped at a thickness of 4095 A. This value gives a suitable compromise between the amplitude and phase conditions, as pointed out in section 2.1. By polarization optics an optical contrast, K(r), due to the Faraday rotation (Y(Y), is produced which leads to a spatial distribution of the light intensity, I(r). This intensity is recorded by the video camera and transferred to the image processing system. K(r) and Z(r) are related to each other by a look-up table, which can be selected by the image processor. Our most used look-up table is represented in fig. 2. This intensity is directly related to the local density of the magnetic field and can be calibrated experimentally. For the calculation of the volume pinning force, .h,, the local flux-density as well as the flux-density gradient must be known. The determination of B,(x) cannot yet be performed quantitatively but will be done in a forthcoming paper by comparing the grey

/nten.sity/input

table

Car b. units1

-

Fig. 2. The most used look-up table in our experiments. This lookup table represents a relation between the rotation angle. 01, and the intensity-output of the image-processing system. A value of zero corresponds to “black” and a value of 255 to “white”.

values of a calibration specimen in a selected magnetic field with the values of the sample under investigation. The experimental set-up consists of a polarization light microscope and of an optical cryostat, as described by Moser et al. [ 9 1. A TV camera is connected to the microscope to transfer the “grabbed” frames to an image-processing system. This system consists of a personal computer with a video-processing inboard for analyzing purposes and a Ha-

MR. Koblischka et al. /Determination

mamatsu video processor for the real-time subtraction. The camera pictures were digitalized and then integrated, in order to reduce the noise drastically. All the video information was then transformed into a scale of 256 grey values, influenced by the optional look-up table (here the grey value of 0 corresponds to black and 255 to white). The frames of the image processing system consist of an array of 5 12 X 5 12 pixels. These pixel distances have to be calibrated in real lengths. The frames which have been so calibrated can now be analyzed using the analyzing functions of the computer’s video-inboard. An additional background subtraction in real-time can be performed so as to obtain only the information of interest. Some of the effects shown in section 3 can be observed with much higher contrast by means of this background subtraction, particularly at the sintered YBazCu30,_6 specimens.

offlux-density gradients in YBaCuO

39

3.2. Flux-density projiles of Nb single-crystals To compare the flux-density profiles, two typical pictures of Nb single-crystals with penetrated flux are shown in figs. 3 and 4a. In fig. 3a the niobium singlecrystal is shown while increasing the external magnetic field to He,,=70 mT. The marked line in fig. 3a is analyzed in fig. 3b, where the intensity of the light as a function of the penetration depth is shown. This state is characterized by the sharp step of the magnetic flux at the edge of the crystal, followed by a long, almost linear decay and then a second sharp step towards the centre of the crystal. Nearly the same domain pattern results in fig. 4a., but the external magnetic field had been reduced from 90 mT to zero. In fig. 4b., the profile of this remanent state is shown. The sharp steps at both ends of the intensity profile have vanished, the maximum intensity is somewhat smaller and the gradient turns outwards from the sample. The temperature in both cases was 5 K.

3. Experimental results 3.1. Sample preparation

The niobium single-crystals had the form of flat cylinders with a diameter of 4 mm and a thickness of 2 mm and were spark-cut from long, zone-melted niobium rods and then mechanically polished thus resulting in a shiny, planar surface. The YBaCuO single-crystals with an edge-length up to 0.6 mm and thicknesses of 15 urn were grown using a slow cooling method. The process itself and the characterization of the samples was described earlier [ 9,141. Due to the small dimensions of the samples it was not possible to polish the specimen surfaces and therefore the single-crystals had to be used “as-grown”. The sintered samples of YBa2Cuj0,_6 were reacted in a furnace, starting from a mixture of the powdered oxides YZOJ, BaCO, and CuO. These samples were cylinders of 4 mm in diameter and 2 mm in thickness. The transition temperature, T,, of the sintered samples is about 91 K and that of the single-crystals 89 K.

3.3. Flux-density profiles of YBa2Cu307_-6 singlecrystal In all experiments with YBaCuO the temperature applied was 10 K. In fig. 5a, a domain pattern is represented for an external magnetic field of 150 mT. Fig. 6a shows the remanent state after applying an external magnetic field of 150 mT. The bright regions of the surface are those where flux has penetrated, and the dark region on the surface corresponds to the remaining flux-free superconducting part of the single-crystal (Meissner phase). Figures 5b and 6b show the related intensity profiles along the white line indicated on the surface. The behaviour of the profile at the boundary of the crystal in fig. 5b is similar to that of fig. 3b. In both cases a step of the flux-density is observed which shows a much larger gradient for YBaCuO. However, the obtained intensity of the polarized light is much smaller than that obtained for the niobium crystals. The sharper step compared with that of niobium is due to the greater acting pinning forces in YBaCuO. The remanent state (figs. 6a and 6b) shows a maximum of the flux-density near the border of the flux-zone with a smaller gradient for the inner part of the sample. Figure 7 represents the dependence of the inten-

40

M.R. Kobllschka

et al. / Deiermnaiion

qfflux-densit),

gradrents

rn YBaC‘uO

Fig. 3. (a). Domain pattern of a Nb smgle-crystal in an external magnetic field of H,,,= 70 mT (7‘~ 5 K). The white line denotes the line which is analyzed in fig. 3 (b). 0 corresponds to the beginning of the analysis. (b) Intensity profile along the straight line marked in fig. 3 (a). Sharp steps are observed at the edge of the crystal and towards the centre of the crystal.

sity profiles on the external magnetic field; all profiles were taken for the same straight line in the remanent state (see also figs. 5a and 6a). By increasing the magnetic field, the position of the maximum of the flux profiles is not shifted whereas the flux-density of the maximum of the flux profile grows. Figure 8a represents a remanent domain pattern after applying an external magnetic field of 150 mT. In fig. 8a a quadratic area at the specimen boundary is marked with white lines and the edges of this area are labeled “A” to “D”. A polarization micrograph of this area is given in fig. 8b. On some parts of the specimen the magneto-optical layer peeled off - after the photographs were

taken - revealing a highly twinned, dark region. The outlined area is identical to that of fig. 8a. The twinboundaries in ( 1IO)-direction are represented by the dark straight lines, starting at the border of the crystal and pointing to the inner side of the crystal. The twin-boundaries on which the flux-penetration is analyzed as shown in fig. 8c are marked by arrows. The rest of the sample is still covered with the magneto-optical thin film, represented by the brighter area in fig. 8b. In fig. 8c the analysis of the penetrated flux within the marked area is shown. In this three-dimensional plot only a moderate relation between the twinboundaries (their direction is represented by the in-

MR. Koblischka et al. /Determination

1000

500 penetration depth [pm1

-

offlux-density gradients in YBaCuO

41

Fig. 4. (a). Domain pattern of a Nb single-crystal in the remanent state, after applying an external magnetic field of H,,,= 90 mT and reducing it to zero ( T= 5 K). (b) Intensity profile of the remanent state. The maximum intensity achieved is somewhat smaller and the sharp steps have vanished due to the flux escaping from the sample.

3.4. Sintered specimens serted frames) and the penetrated flux can be found additionally to the normal flux distribution as shown by the profile in fig. 6b. No retardation of the flux-zone is found in the twinned region compared with the twin-free regions. The pinning effect of the twin-boundaries seems to be visible by “valleys” which modify the normally observed flux-density profiles. Therefore, for the penetrating flux, twin-boundaries do not act as strong pinning centres because the usually obtained penetration depth is also observed in the twinned area.

Our investigation reveals that only a few grains are visible which had been penetrated by the flux after increasing the magnetic field to 0.23 T and then reducing it to zero. This is indicated by the bright grains, as represented in fig. 9a. All other grains which have not been influenced by the magnetic flux are completely subtracted by the digital subtraction method, thus leading to a homogeneous grey background and to higher contrast of the domain patterns of the grains [ 91. The flux-density gradients within single grains show maxima in the middle of the grains in the perpendicular direction and a plateau-like be-

42

M.R. Koblischka et al. /Determination ofjlux-densitv gradients in YBaC‘uO

0

50 penefra~ion

100 depth

150

Cpml -

haviour parallel to the longitudinal direction of the grains. Figure 9b shows the analysis of a grain marked in fig. 9a. The analysis of a line labeled “11” shows three maxima of intensity at two “holes” in the grain, which result from the polishing procedure. The dashed line represents the flux-density for the undisturbed region of the grain. The analysis along the line labeled “ I ” shows a maximum in the middle of the grain. In fig. 9c, a three-dimensional plot of the magnetic flux-distribution is represented. In contrast to the single-crystal, the grains are completely penetrated by the magnetic flux at an external magnetic field of 0.23 T. In fig. 9a, three holes are visible leading to

Fig. 5. (a) Domain pattern of a YBaCuO single-crystal whde increasing the magnetic field to H,,,= 150 mT (T= IO K). (b) Intensity profile along the white line of fig. 5 (a). The intensity achieved is smaller than in niobium; due to the greater pinning forces in YBaCuO the steps are not so sharp as in niobium.

an accumulation of flux around these defects. This behaviour is also represented in the 3D-plot of fig. 9c. The black planes labeled D, to D3 depict these “holes”. Furthermore, constrictions of a wavelength of about 1.5 urn are superimposed on the total fluxdensity distribution which may result from the interaction of the flux-lines with the twin-boundaries in the grains. The penetration of the Shubnikov phase into these grains takes place spontaneously, because the London penetration depth, AL, is of the same order of magnitude as the grain dimensions (A, z 0.15 pm, grain size z 2.10 urn’) [ 15,161. The obtained first penetration field is of the order of H,,,z30 mT.

M.R. Koblischkaet al. /Determination offlux-density gradients in YBaCuO

OF.,,,I,,,,I,,,,I,,,,I 0

50 penetration

100

150

depth Cpml ---+

When the external magnetic field is reversed, the same domain patterns result, but in contrast to the other side, e.g. if the Shubnikov phase was bright, the Shubnikov phase will now be dark and vice versa. 3.5. Determination

of pinning forces

In addition to the magneto-optical investigations we have performed measurements with a commercial SQUID-magnetometer. From the magnetization data the pinning forces are calculated using the critical state model as developed by Bean [ 17 ] f,=l.SAMB/(p,,R).

(7)

43

Fig. 6. (a). Domain pattern of the remanent state in a singlecrystal of YBaCuO, after applying an external magnetic field of 150 mT and then reducing it to zero ( T= 10 K). (b) Intensity profile along the white line of fig. 6. (a). Again, a maximum near the middle of the flux-zone is observed (see e.g. figs. 4 (a, b) ) with gradients turning in- and outwards from the sample.

In eq. (7) AA4 denotes the difference between the magnetization measured for increasing and decreasing magnetic field, H, and R the diameter of the coherent superconducting region. For fields well above H,, in the case of the sintered specimens this diameter will be the grain size [ 181, in the case of the single-crystals R corresponds to an effective diameter because only a part of the total crystal size becomes superconducting. In figs. 10a and lob the volume pinning force is plotted against the magnetic flux density. Figure 10a shows a maximum at a magnetic field of 1.2 T. In the case of the sintered specimens this maximum is not yet reached within the range of the available mag-

44

M. R. Koblrschka

et al. / Deterrninar~on

i_IdYLCLIY--d.ililii& 0

50

penetration

100 depth

150

Cpm 1 -

q/:fllc.u-densir!)

gradirnrs

ning forces in the high-T, materials compared with niobium. In deformed niobium disks and in the A 1Scompounds like Nb$n flux-density gradients similar to that of YBaCuO were obtained [ 20,2 11. The remanent state is characterized by flux-density profiles with a maximum near the middle of the flux-zone, caused by flux escaping from the sample. This behaviour leads to the flux-creep phenomenon. While increasing the external magnetic field. this step is somewhat sharper, but even now the strong pinning forces also cause a profile comparable with that of the remanent state. 4. I. YBa2Cu30,_s

Fig. 7. Dependence of the intensity profiles on the external magnetic field ( T= 5 K). All profiles were taken from the same line in the remanent state. On increasing the magnetic field, the maximum is not shifted, but the maximum value ofthe profile grows.

netic field [ 191. The values of the pinning forces obtained from the magnetization measurements are in the same range as the data obtained by a simple estimation from our magneto-optical observations. The gradients SB/Sx were taken from the fluxdensity profiles, and a simple calibration was performed with the assumption that the maximum of intensity corresponds to the applied external magnetic field, corrected with the demagnetization factor of the sample. This evaluation of the volume pinning force yields via eq. (3) in the case of the YBaCuO single-crystal .fP= 1.8.10’ N/m’ for an external field of B=O. 15 T and f,= 3 x lo8 N/m’ for B= 0.23 T. For the sintered sample, eq. (3 ) yields a value off,= 8 x 1O9 N/m’ for an external magnetic field of 0.23 T. In the case of the sintered specimens our values for & are comparable with the data of Wordenweber et al. [ 191.

4. Discussion The flux-density gradients in the YBaCuO superconductors show the same behaviour as is generally expected from type-II superconductors. Due to the strong pinning forces in these materials, the initial state of the flux-penetration shows a four times sharper boundary than in conventional type-II superconductors. This is a result of the rather large pin-

in YBaC’rrO

single-crystals

In the case that twin-boundaries correspond to strong pinning centres, the gradient analysis should reveal a sharp discontinuity if the flux penetrates through a twin-boundary and the maximum obtained penetration-depth of the flux in a heavily twinned region should be considerably smaller than in the rest of the sample. Our analysis of a twinned region of the YBaCuO single-crystal shows the usually obtained penetration depth of the magnetic flux also in the twinned regions; the pinning effect of the twin-boundaries causes only a slightly modified flux-density profile. Therefore, this flux-density profile shows clearly that at low temperatures - as applied in our experiments - an additional pinning mechanism must act in our samples in the given arrangement with the c-axis parallel to the applied magnetic field. Dinger et al. [22] have pointed out recently that locally the flux-density on the twin-boundaries exceeds that of the external magnetic field. In fig. 8c. the highest maxima of intensity are found near the middle of the obtained penetration depth (see also fig. 6b), and the flux-density is only little modified at the twin-boundaries. Schimmele et al. [23] have proposed and described theoretically an intrinsic, or collective, pinning mechanism for the flux-lines. This mechanism acts if the energy of a flux-line depends on its position relative to the crystal lattice. For small coherence lengths 5 of the order of a few lattice constants the flux-lines are moving in the discrete crystal lattice. The line energy in this case depends periodically on the position of the flux-line.

p

twin-boundaries

+xsner-phase

Fig. 8. (a) Domain pattern of single-crystal YBaCuO in the remanent state (T= 10 K) after applying H,,, = 150 mT. The analyses of the area labeled “A” to “D” are given in figs. 8 (b, c ) . (b ) Polarization micrograph of the labeled area. On some parts of the specimen the magneto-optical layer peeled off revealing a highly twinned, dark region. The twin-boundaries in ( 1lO)-direction are visible as dark lines. The twin-boundaries, on which the tluxpenetration is analyzed as shown in fig. 8 (c), are marked by arrows. The rest of the sample is still covered with the magnetooptical thin film, represented by the brighter area. (c) Three-dimensional plot of the penetrated flux in the labeled area. The direction of the twin-boundaries shown in fig. 8 (b) is marked by the inserted frame. The usually observed penetration-depth is maintained also in the twinned region. The normal flux-density profile is found to be slightly modified by the pinning effect of the twin-boundaries, leading to “valleys” in the 3D-plot.

46

,W.K. Koblrschka

PI al. / Deterrnrnalron

oJ/lur-densri),

gradrents

in YBaC’uO

Fig. 9. (a). Domain pattern of sintered YBaCuO in the remanent state (T= 10 K; after applying an external field H,,,=230 mT and reducing it to zero). Only a few grains are visible which were penetrated by the flux. The white lines labeled “I/” and “1” are analyzed in fig. 9 (b), beginning at the point 0. D, to D3 are pointing to the holes on the surface of the grain. (b) Intensity profiles of sintered YBaCuO. The analysis of the line labeled “II” shows three maxima of intensity at two “holes” in the grain. The dashed line represents the flux-density profile neglecting the effect ofthe holes. (c) Three-dimensional plot ofthe magnetic flux-distribution (Shubnikov phase 1 in a selected grain of a sintered specimen. The same grain is also analyzed in fig. 9 (b); the thicker lines are the traces of the intensity profiles. The dark inserts labeled D, to D3 correspond to the holes on the grain, as they are visible in fig. 9 (a). The flux-density is enhanced around three macroscopic defects. The repeating constrictions may result from the interaction of the magnetic flux with twinboundaries modulating the flux-density profile.

Also, in recent works [ 22,24-261 another so-called intrinsic or defect pinning mechanism is proposed to be active at low temperatures; this is caused by an oxygen defect distribution in the CuO-planes. In conventional superconductors, effective pinning sites are typically of the size of the coherence length ( [ 271. According to this criterion, pinning defects in the

high-T, superconductors have to be some angstrijms in size [ 28 1. Therefore, we agree with Dinger et al. [22] and Schimmele et al. [23], that intrinsic collective and defect pinning is active in the high-T, superconductors at low temperatures. The determination of the volume pinning forces from the SQUID-measurements using the critical

M.R. Koblischka et al. /Determination

14 ext.mcgnetic

field

BIT] -

YBaCuO sintered T: 10K

b

I

0

+-

2.0 ext. magnetic

6.0 field BIT] -

Fig. 10. (a) Field dependence of the volume pinning force, f,, of single-crystal YBaCuO, determined from measurements with a SQUID-magnetometer using the critical state model developed by Bean [ I7 ] (T= 5 K). A maximum of the pinning force is found at B= 1, 2 T. (b) Field dependence of the volume pinning force of sintered YBaCuO at T= 5 K. The maximum is not yet reached within the range of available magnetic fields.

state model of Bean yields comparable values for f,, as they were estimated from the magneto-optically measured flux-profiles. A further calibration of the intensity will show more details.

ofjlux-density gradients in YBaCuO

47

flux-density gradients parallel and perpendicular to the longitudinal direction of the crystallite reveals nearly identical values. The flux-density profile is modified in the surroundings of macroscopic defects like “holes” as represented in figs. 9a-9c, leading to an increase of a factor of three of the flux-density gradient. Hereby it is shown that macroscopic defects are effective pinning centres. The flux-density gradients, which are much larger in the sintered, polycrystalline samples (see e.g. figs. 6b and 9b) lead to pinning forces which are correspondingly larger than in the single-crystals. This result is obtained both magneto-optically and from the SQUID-measurements. The pinning forces which are some thirty times larger than in the single-crystals (see figs. 1Oa, b) are estimated to arise not only from intrinsic effects but also from extrinsic effects. These superimposed pinning forces may result from grain boundary and grain-size effects, since the flux-density gradients are influenced by the surface of the small grains. A similar behaviour of the pinning forces dependent on the grain-size is observed for NB,Sn by Potratz et al. [ 2 11. They found that the pinning force,f,, is inversely proportional to the grain diameter. The penetration of flux into the sintered specimens occurs in three steps [ 29,301. In the first step, the shielding of the complete sample is broken at a critical field, Hc,comp. In the second step, the Josephson junctions are penetrated and in the last step, the grains themselves were penetrated by the flux at HC,I). The magneto-optical investigations show only this last step and the so obtained first penetration field, JY_ is of the same magnitude as the critical field derived from the deviation from the linear initial magnetization curve [ 9 1.

4.2. YBa2Cu307_6 sintered specimens

5. Conclusions

The main difference between sintered specimens and single-crystals corresponds to the almost spontaneous penetration of the flux into a superconducting grain because the London penetration-depth AL is comparable to the grain diameter (2, r 0.15 urn, grain size ~3.10 pm* [l&16]). Furthermore, the grains are completely in the Shubnikov phase in contrast to the single-crystals. The investigation of the

The method of the magneto-optical Faraday effect has been found to be a suitable method for determining flux-density gradients in the high-T, superconductors. The influence of twin-boundaries on the penetrated flux-density in single-crystals could be observed as a modulation of the overall flux-density gradient. The flux-density gradient may be governed

48

M. R. Kobhschka

et al. / Determrnation

by an intrinsic defect or collective pinning mechanism as described by Schimmele et al. and Dinger et al. The grains of sintered specimens are - in contrast to single-crystals - completely penetrated by the magnetic flux. The flux-density profiles of the grains are influenced by their dimensions. This leads to a maximum in the middle of the grain of the flux-density perpendicular to the longitudinal direction and to a plateau of flux-density in the parallel direction. A modulation of the flux-density profiles occurs due to macroscopic defects like holes and possibly by twin-boundaries. Due to the magnetic phase transition of EuS at 16.9 K in this paper only observations in the temperature range from 4 to 15 K have been performed. With a better magneto-optical compound observations of the domain structures at higher temperatures will be possible. Further work is planned on the magnetooptical observation of the flux-creep phenomenon in the high-T, superconductors and on observation of the domain structure in thin films.

Acknowledgements

We acknowledge valuable discussions with E.H. Brand& L. Schimmele and U. Essmann. We also wish to thank H. Theuss for his assistance during the measurements with the SQUID-magnetometer, R. Henes for preparing the sintered YBaCuO specimens and P. Keppler for coating the samples with the magnetooptical active films. The authors also wish to thank H.J. Blythe for critically reading the manuscript. This publication was subsidized by the Bundesminister fur Forschung und Technologie (Kenzeichen 13 N 57005 ). The authors are responsible for the content of the publication.

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