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Observation of flux penetration in YBa2Cu3O7−δ superconductors by means of the magneto-optical Faraday effect
Physica C 159 (1989) 117-123 North-Holland, Amsterdam
OBSERVATION OF FLUX PENETRATION IN YBa2Cu3OT_6 SUPERCONDUCTORS BY MEANS OF THE MAGNETO-OPTICAL FARADAY EFFECT N. MOSER, M.R. KOBLISCHKA, H. KRONMULLER, B. GEGENHEIMER * and H. THEUSS
Max-Planck-lnstitut J~r Metallforschung, Institut ffir Physik, Heisenbergstrasse 1, D- 7000 Stuttgart 80, Fed. Rep. Germany •Max-Planck-lnstitutJ~r Festk6rperforschung, Heisenbergstrasse 1, D-7000 Stuttgart 80, Fed. Rep. Germany Received 28 March 1989
The penetration of the Shubnikovphase into both single-crystaland sintered YBaCuOspecimens has been observed by means of the magneto-opticalFaraday effect using the high Verdet constant in thin evaporated films of a mixture of EuS and EuF2. This method allows the direct observation of the flux motion. Aftercyclingmagnetic field from zero, the trapped flux structure in the single crystal consists of large domains which are related to the sample shape, whereas in sintered specimens only a part of the total number of the grains transforms into the Shubnikovphase.
1. Introduction On applying a magnetic field larger than the lower critical field, Hc~, to a superconductor the magnetic flux distribution in the sample consists of an inhomogeneous arrangement of flux lines. These inhomogeneities result from the interaction of flux lines with lattice imperfections. Investigations of the flux distribution are of great interest because of the relation between the magnetic flux density gradient and the pinning forces acting on the flux lines which determine the critical current density of the superconductor. The most sensitive method to detect local flux densities and flux density gradients consists in the direct decoration of the flux line lattice as described by Tr/iuble and Essmann [ 1 ]. This was carried out for high-To superconductors by Gammel, Ourmazd, Osamura, Vinnikov and Dolan [2-7]. However, this method only allows one to observe static effects whereas the Faraday effect allows a dynamic investigation of flux penetration. A number of investigations with the magneto-optical Faraday effect of type I superconductors have been performed since the introduction of the method by Alers [8] and deSorbo [9]. This method has been optimized with respect to the spatial resolution with the thin film technique by Kirchner [ 10,11 ], and has been extended to type II superconductors by Habermeier and
Kronmtiller [ 12-14]. The evaporation of a thin layer (thickness 4095 A) of a EuS/EuF2 mixture allows the study of flux penetration and flux patterns with a spatial resolution limited to 0.5 ~tm which is typical for optical microscopes [ 15,16 ]. The determination of the local volume pinning force, Pv, and the local critical current density, Jc, has been deduced by Friedel, De Gennes and Matricon [ 17 ] on the assumption of a one-dimensional movement of a planar flux boundary as is the case of flux penetration in a superconductor with a homogeneous volume pinning force. Pv and Jc are related by
e v ( x ) = -~o B ( x ) VB(x) =J'~(x)B(x),
( 1)
where B denotes the local flux density, /Zo the vacuum permeability and VB(x) is the flux density gradient. The observation of flux line gradients, dB/dx, by the magneto-optical Faraday effect is due to the variation of the angle of rotation of the plane-polarized light in regions of different flux densities. This allows the calculation of volume pinning forces and critical current densities according to eq. (1). The aim of this work was to determine the experimental conditions required to observe the penetration of the Shubnikov phase using the magneto-optical Faraday effect in high-Tc superconductors and to compare the results with the macroscopic magnetization curves.
0921-4534/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division )
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N. Moser et al. / Flux penetration in YBa:Cu~Oz_~ superconductors
2. Specimen preparation Single-crystals of a rectangular shape with edges of length up to 0.6 mm and 15 ~tm thickness were grown from a partially molten mixture of 70 mol% CuO, 25 mol% BaCO3 and 5 mol% YO15 by a slow cooling method. The starting mixture was heated in air to 1323 K, held at this temperature for 5, and then initially cooled at a rate of 1K/h to 1123 K and finally at 10 K / h to room temperature. The characterization of the as-grown crystals is described in ref. [ 18 ]. On account of the small dimensions of the samples a mechanical polishing could not be carried out. Therefore the specimens had to be used as-grown. The sintered samples were prepared from the powdered oxides Y203, CuO and BaCO3. The components were mixed and pressed at 7 kbar into a pellet of 1 cm diameter. Subsequently, the specimen was reacted in a furnace in a stream of air as described in ref. [ 19 ]. The sintered superconductors were mechanically polished thus resulting in a shiny surface. The magneto-optical thin film was evaporated onto the sample surfaces as a mixture of EuS and EuF2 [20-22] at a pressure of p = 10 -6 mbar and a rate of 4 A/s. The thickness of the layer and the vaporization rate were controlled with a quartz oscillator (Leybold XTM). The evaporation in the electronbeam coating plant was halted at a thickness of ]2 corresponding to 4095 A in order to achieve an enhancement of the magneto-optical contrast due to optimum amplitude and phase conditions as described in refs. [ 10,11 ].
3. Experimental procedure The magneto-optical detection system consists of a Reichert-Jung Polyvar polarization microscope and an optical cryostat. The single-crystals were first mounted on a fiat copper block and then glued in good thermal contact with the cooling block inside the cryostat, whereas the sintered specimens were fixed directly. A canal system passes though the block to ensure good thermal contact with the liquid helium. The velocity of flow of the helium is controlled by a pumping system on the gaseous side of the cryostat and a pressure unit on the liquid helium side as shown in fig. 1. In addition to this configuration
microscope
He pump
Iiit//,
I vcacuum
Fig. 1. Optical cryostat. 1: specimens; 2: coverglass; 3: O-ring;4: magnetic shielding tube; 5: lenses; 6: coolingblock; 7: magnetic coil. a bifilar heater wound on the cooling block enables the temperature to be varied over the range 6 K to 300 K. The temperature of the cooling table is determined with a Pt resistor and that of the samples with a thermocouple fixed to the copper sheet with the specimen under investigation. The vacuum system is sealed by a cover glass of 1 mm thickness and of 35 mm diameter which is about 1 mm above the samples. This arrangement allows one to investigate up to seven specimens without ventilating the cryostat. The magnetic coil is connected to the cryostat in such a way as to produce a magnetic field perpendicular to the sample surface; the values are within the range 0 < #oHex~<0.23 T. The optical polarization light microscope used was a Reichert-Jung microscope with a resolution of about 0.8 pm. The polarizer and analyser consist of polarizer foils fabricated by Kaesemann which can be rotated separately, so as to obtain optimum extinction conditions. To achieve a maximum contrast of the domains, the cover glass of the cryostat is made of a low magneto-optical active material (Schott BK7, with the Verdet constant V= 0.02 angular min/ G cm at room temperature). This technique reduces depolarization effects markedly compared to the Herasil glass which is usually used. Lenses with long working distances of up to 3.8 mm were used because of the large distance between specimen surface
N. Moser et aL / Flux penetration in YBa2CusO7_a superconductors
and the upper side of the cover glass. To eliminate depolarization effects due to the magnet, the lenses were shielded from the magnetic field by a mu-metal tube. A TV camera system is connected to the Reichert-Jung polarization light microscope to transfer the pictures to an image processing system. The grabbed and processed frames can finally be stored in the frame-buffer of the computer. By means of the image processing system it is possible to drastically reduce the noise of the images by a continuous integration. An additional real-time background subtraction of the integrated image without flux penetration from the integrated image with flux penetrating into the specimen gives pictures of high contrast. These can be analysed with respect to the grey values corresponding to the flux line gradients. The image processing system is represented schematically in fig. 2. The measurements of the magnetization curves and the transition curve to the superconducting state are performed using a SQUID magnetometer. Because of the small dimensions of the YBaCuO single-crystal, the sample was fixed on an A1203 sheet of 0.2
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m m thickness showing a very low background magnetic moment. This configuration allows one to measure the magnetization curve in the same geometrical arrangement of the sample surface with respect to the magnetic field as the flux penetration was observed by the Faraday effect.
4. Experimental results 4.1. Y B a C u O single crystals
From measurements of the magnetization curves of YBaCuO single-crystals the lower critical field, given by (2)
#oH'c~ = ( 1 - D ) #oHc~ ,
(D denotes the demagnetization factor and/zoH~, is the uncorrected value) is determined from these measurements to be 45 _+3 m T as represented in fig. 3. At H'¢~ the magnetization curve starts to deviate from the "Meissner line" indicating the beginning of magnetic flux penetration into the specimen. The Meissner and Shubnikov patterns coexist up to ~He~t ~<#oH~2. The transition curve to superconductivity is shown in fig. 4 indicating a Tc of 87 K. In fig. 5a the shape of the YBaCuO single-crystal is represented without an applied external magnetic field, #oHext. Figures 5b to 5e show the flux penetration for increasing applied fields. The figures represent the remanent magnetic flux patterns, i.e., the
0 0singlecrystal [ ~ ,--, 6 YBaCuO ~Z 5OO T=5OK '
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Fig. 3. Magnetization curve of a YBaCuO single-crystal measured at 5 K. poH'c~ (5 K) is determined to 45+3 mT as the deviation of the measured points from the "Meissner curve". Additionally, the magnetization curve up to 2 T is represented.
N. Moser et al. / Flux penetration in YBa2Cu307_~ superconductors
120
4.2. Sintered YBaCuO specimens
rE
0
20
40
60
80
100
T [K] Fig. 4. Transition from the normal state to the superconducting state ofa YBaCuO single-crystal. The specimen was cooled in the presence of a magnetic field PoH~xt = 2 mT,
flux which is trapped after applying external magnetic fields, #OHext of 0.1 T, 0.14 T, 0.16 T and 0.23 T and reducing each successive value to zero at the observation temperature of 10 K. The penetration of the magnetic flux appears to be stable and remains unchanged under these conditions. This characteristic behaviour corresponds to strong irreversible effects in the magnetization curve. The dark areas on the white border are partly due to a contamination of the as-grown single-crystal. These regions are indicated in fig. 5a. On increasing the external magnetic field, the first penetration of flux around the circumference of the specimen became observable at #oHg" = 52.5 mT (c, denotes measurements parallel to the c axis). The depth, L, of this penetration increases with field and is represented in fig. 6. The penetration field, /ZoHg II, is found to be higher than those obtained from the macroscopic magnetization curve: #0H~," (Faraday)>poH~li (magnetization). The features of the initial penetration of the specimen are nearly uniform with a retardation on the right hand side of the sample. The well-known phenomenon of edges acting as centres of primary flux penetration described by Baird [ 27 ] was not observed in the present investigations. The penetrated flux remained stable and did not move outwards for a given magnetic file within the limits of experimental error, as is expected in the case of an ideal superconductor. Since it is not possible to increase the applied field beyond 0.23 T, the flux penetration can only be observed up to a penetration depth of 150 ~tm.
The low- and high-field magnetization measurements performed at 5 K on sintered samples of dimensions 3 m m diameter and 2 m m height are represented in fig. 7. The low-field magnetization curve shows a primary maximum of 3.5 m T of the negative polarization at an external magnetic field of 4 mT. A second maximum is observed in the high-field curve at 200 mT. The analysis of the magnetization curves yields a value of 30 m T for the lower critical field, H'cl. The observation of the penetrated flux into the sintered YBaCuO specimen is only possible with help of the image processing system due to the low contrast between the Meissner phase and the mixed phase. The subtraction of the stored background frame of the specimen in the Meissner state from the real-time frame of the sample in the Shubnikov state shows the flux which has penetrated into the grains. On account of an optimum contrast of the frame, fig. 8 represents the remanent state after increasing the applied field to 0.23 T and then reducing to zero. At zero field depolarization effects will not disturb the minimum contrast between the two phases. The investigation reveals that only a few grains are visible which have been penetrated by the flux. This is indicated by the black grains. All other grains which have not been influenced are completely subtracted, thus leading to a homogeneous grey background.
5. Discussion The penetration field of, ~ H g t~, of 52.5 m T as determined by the magneto-optical Faraday effect corresponds to a much higher value than the lower critical field of #oH~ II=45 + 3 mT of the single-crystal as determined from the magnetization curves. This latter value agrees with the results reported in ref. [23 ]. The difference between these values, may be due to the existence of an energy barrier near the surface [16,24]. This barrier is due to the attractive force of the flux line to the surface and an increasing line energy of the vortex with increasing distance, x, from the surface. In addition to this contribution there is also a repulsive force acting on the vortex from the surface produced by the interaction of the
N. Moser et a L / Flux penetration in YBa2Cu3Oz_6 superconductors
121
Fig. 5. (a) As-grown YBaCuO single-crystal, in zero field. ( b ) - (e) Domain structures of superconducting YBaCuO single-crystal at 10 K, showing remanent flux after applying an external magnetic field. The Shubnikov phase is bright and the Meissner phase dark. (b) /zoHe~ =0.14 T; (c) /~oH~xt=0.16 T; (d) #oHext =0.23 T.
122
N. Moser et al. / Flux penetration in YBa2Cus07_ ~superconductors
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Fig. 6. Dependence of the penetration depth, L, for the Shubnikov phase on the external magnetic field lzoH~,,.The field at which flux penetration begins,/~oHp,is about 52.5 roT. Fig. 8. Domain structure of the sintered YBaCuO specimen. The remanent flux is shown after applying an external field of 0.23 T at 10 K. The grains into which flux has penetrated ("Shubnikov phase") are dark. For clarity some grains are outlined.
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Fig. 7. The magnetization curve of a sintered YBaCuO specimen at 5 K. The deviation from the Meissner curve leads to a value of #oH'c~= 30 mT (symbolized by the dashed line). The magnetization curve measured up to 2 T is represented in the inset. external field decreasing inside the specimen according to H e -aL/x (2L denotes the p e n e t r a t i o n d e p t h ) with the magnetic field o f the flux line which has the same sign. The a d d i t i o n o f these two contributions gives a m a x i m u m o f the vortex energy as a function o f x . On increasing the external field, flux starts to penetrate the s u p e r c o n d u c t o r at H f f but cannot spread spontaneously into the r e m a i n d e r of the specimen. The flux lines are concentrated at a distance o f the order o f 0.3 g m [ 5 ] from the edge o f the sample which corresponds to the value o f ~-L. In this case, the p e n e t r a t e d flux cannot be observed by the microscope because its resolution is l i m i t e d to 0.8 gm. W i t h increasing external field the energy barrier to flux p e n e t r a t i o n vanishes at #oHm;LIand the
flux enters spontaneously into the r e m a i n d e r o f the sample. Therefore one observes the invasion o f the S h u b n i k o v phase beginning at this penetration field /~oH~II> #oH~i LI. After reducing the external field to zero, the flux remains t r a p p e d within the single-crystal. This irreversibility is due to pinning o f the vortices at grain boundaries, chemical inhomogeneities and crystal-lattice defects. Surface energy barriers also prevent the flux from escaping from the specimen until the a p p l i e d field is reduced to zero. Even with the present resolution o f the microscope, at 10 K no relaxation effects o f the p e n e t r a t e d flux could be observed, as has previously been reported by Yeshurun [25]. The evaluation o f the volume pinning forces, Pv, a n d the critical current density, Jc, on the a s s u m p t i o n o f a linear flux density gradient and a local flux density o f B = 0 . 2 3 T at L = 0 yields via eq. ( 1 ) a value for Pv of 1.9× 108 N / m 3 and a critical current density o f 9 × 10 s A / m 2. The lower critical field o f the sintered specimen, #oH'c~ = 30 - 3 mT, is in the range o f ~toH~i bl= 9 +_ 1 mT~
N. Moser et al. / Flux penetration in YBa eCu 3O z_a superconductors
riety of different orientations of these grains in the superconductor. Those grains with the orientation of their c axes perpendicular to the applied field will be the first to be penetrated by the S h u b n i k o v phase because of the lower entry field. O n the other hand, the very small d i m e n s i o n s of the grains, of 5 to 10 ~tm length and 1 to 3 ~tm width, which are comparable to the penetration depth 2ab=0.8 ~tm (2 ab corresponds to the penetration depth in the a - b plane) [23] lead to a complete intrusion of the mixed state. Both the orientation and the d i m e n s i o n a l i t y effect contribute to a complete penetration of the mixed state into the grains. All other grains are either nonsuperconducting or misoriented with respect to the incident light beam.
6. Conclusions The observation of the flux penetration in YBaCuO single-crystals was successfully performed by means of the magneto-optical Faraday effect. The investigations revealed a nearly isotropic flux penetration which could be observed dynamically a n d recorded. This technique was also applied to sintered YBaCuO supercondctors, where flux penetration was observed in i n d i v i d u a l grains. The observation of the flux penetration into the sintered specimens, in addition to the study of flux penetration into individual grains, will be performed in the future. F u r t h e r investigations are in progress on thin superconducting films.
Acknowledgements We acknowledge valuable discussions with H.U. Habermeier, E.H. Brandt, U. EBmann and J. Parisi. Also we wish to thank H. W a l d m a n n for the design of the cryostat, R. Reisser for his assistance during the measurements with the S Q U I D magnetometer, R. Henes for preparing the sintered YBaCuO specimens and P. Keppler for coating the samples with the magneto-optical active films. The authors wish
123
also to thank H. Blythe for critical reading the manuscript.
References [ 1] H. Tr~iubleand U. Essmann, Phys. star. sol. 25 (1968) 395. [2] P.L. Gammel, D.J. Bishop, G.J. Dolan, J.R. Kwo, C.A. Murray, L.F. Schneemeyerand J.V. Waszczak, Phys. Rev. B36 (1987) 2592. [3]A. Ourmazd, J.A. Rentschler, W.J. Skocpol and D.W. Johnson Jr., Phys. Rev. B 36 (1987) 8914. [4] K. Osamura, Y. Tomii, N. Matsukara and S. Ochiai, Jap. J. Appl. Phys. 27 (1988) L860. [5] L.Ya. Vinnikov, L.A. Gurevich, G.A. Emel'chenko and Yu.A. Osipyan, JETP Lett. 47 (1988) 131. [6] L.Ya. Vinnikov, L.A. Gurevich, G.A. Emel'chenko and Yu.A. Osipyan, Solid State Comm. 67 (1988) 421. [7] G.J. Dolan, G.V. Chandrasekhar, T.R. Dinger, C. Feild and F. Holtzberg, Phys. Rev. Len. 62 (1989) 827. [8] P.B. Alers, Phys. Rev. 105 (1957) 104. [9] W. deSorbo, Phys. Rev. Len. 4 (1960) 406. [10] H. Kirchner, Phys. Lett. A 30 (1969) 437. [ 11 ] H. Kirchner, Phys. star. sol. (a) 4 ( 1971 ) 531. [ 12] H.U. Habermeier, R. Aoki and H. Kronmiiller, Phys. star. sol. (a) 50 (1978) 187. [13] W. Klein and H. Kronmtiller, Phys. stat. sol. (a) 67 (1987) 109. [ 14 ] R. Potratz, W. Klein, H.U. Habermeier and H. Kronmiiller, Physl. stat. sol. (a) 60 (1980) 417. [ 15 ] R.P. Huebener,R.T. Kampwirthand V.A. Rowe, Cryogenics 12 (1972) 100. [ 16] R.P. Hiibener,MagneticFlux Structures in Superconductors (Springer Verlag, Berlin, 1979). [ 17] J. Friedel,P.G. deGennesand H. Matricon,Appl. Phys. Lett. 2 (1963) 119. [ 18] C. Thomsen, M. Cardona, B. Gegenheimer, R. Liu and A. simon, Phys. Rev. B 37 (1988) 9860. [19] N. Moser, A. Hofmann, P. Schiile, R. Henes and H. Kronmtiller, Z. Phys. B 71 (1988) 37. [20 ] P. Laeng and L. Rinderer, Cryogenics 12 ( 1972 ) 315. [21 ] G. Giinterodt, Phys. cond. mat. 18 (1974) 37. [22] J. Schoenes,Z. Phys. B20 (1975) 345. [23] A. Umezawa, G.W. Crabtree and J.Z. Liu, Physica C 153155 (1988) 1461. [24] C.P. Bean and J.D. Livingston, Phys. Rev. Lett. 12 (1964) 14. [25] Y. Yeshurun and A.P. Malozemoff, Phys. Rev. Lett. 60 (1988) 2202. [26] Y. Isikawa, Physica C 153-155 (1988) 1471. [27] D.C. Baird, Can. J. of Physics 42 (1964) 1682.
OBSERVATION OF FLUX PENETRATION IN YBa2Cu3OT_6 SUPERCONDUCTORS BY MEANS OF THE MAGNETO-OPTICAL FARADAY EFFECT N. MOSER, M.R. KOBLISCHKA, H. KRONMULLER, B. GEGENHEIMER * and H. THEUSS
Max-Planck-lnstitut J~r Metallforschung, Institut ffir Physik, Heisenbergstrasse 1, D- 7000 Stuttgart 80, Fed. Rep. Germany •Max-Planck-lnstitutJ~r Festk6rperforschung, Heisenbergstrasse 1, D-7000 Stuttgart 80, Fed. Rep. Germany Received 28 March 1989
The penetration of the Shubnikovphase into both single-crystaland sintered YBaCuOspecimens has been observed by means of the magneto-opticalFaraday effect using the high Verdet constant in thin evaporated films of a mixture of EuS and EuF2. This method allows the direct observation of the flux motion. Aftercyclingmagnetic field from zero, the trapped flux structure in the single crystal consists of large domains which are related to the sample shape, whereas in sintered specimens only a part of the total number of the grains transforms into the Shubnikovphase.
1. Introduction On applying a magnetic field larger than the lower critical field, Hc~, to a superconductor the magnetic flux distribution in the sample consists of an inhomogeneous arrangement of flux lines. These inhomogeneities result from the interaction of flux lines with lattice imperfections. Investigations of the flux distribution are of great interest because of the relation between the magnetic flux density gradient and the pinning forces acting on the flux lines which determine the critical current density of the superconductor. The most sensitive method to detect local flux densities and flux density gradients consists in the direct decoration of the flux line lattice as described by Tr/iuble and Essmann [ 1 ]. This was carried out for high-To superconductors by Gammel, Ourmazd, Osamura, Vinnikov and Dolan [2-7]. However, this method only allows one to observe static effects whereas the Faraday effect allows a dynamic investigation of flux penetration. A number of investigations with the magneto-optical Faraday effect of type I superconductors have been performed since the introduction of the method by Alers [8] and deSorbo [9]. This method has been optimized with respect to the spatial resolution with the thin film technique by Kirchner [ 10,11 ], and has been extended to type II superconductors by Habermeier and
Kronmtiller [ 12-14]. The evaporation of a thin layer (thickness 4095 A) of a EuS/EuF2 mixture allows the study of flux penetration and flux patterns with a spatial resolution limited to 0.5 ~tm which is typical for optical microscopes [ 15,16 ]. The determination of the local volume pinning force, Pv, and the local critical current density, Jc, has been deduced by Friedel, De Gennes and Matricon [ 17 ] on the assumption of a one-dimensional movement of a planar flux boundary as is the case of flux penetration in a superconductor with a homogeneous volume pinning force. Pv and Jc are related by
e v ( x ) = -~o B ( x ) VB(x) =J'~(x)B(x),
( 1)
where B denotes the local flux density, /Zo the vacuum permeability and VB(x) is the flux density gradient. The observation of flux line gradients, dB/dx, by the magneto-optical Faraday effect is due to the variation of the angle of rotation of the plane-polarized light in regions of different flux densities. This allows the calculation of volume pinning forces and critical current densities according to eq. (1). The aim of this work was to determine the experimental conditions required to observe the penetration of the Shubnikov phase using the magneto-optical Faraday effect in high-Tc superconductors and to compare the results with the macroscopic magnetization curves.
0921-4534/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division )
118
N. Moser et al. / Flux penetration in YBa:Cu~Oz_~ superconductors
2. Specimen preparation Single-crystals of a rectangular shape with edges of length up to 0.6 mm and 15 ~tm thickness were grown from a partially molten mixture of 70 mol% CuO, 25 mol% BaCO3 and 5 mol% YO15 by a slow cooling method. The starting mixture was heated in air to 1323 K, held at this temperature for 5, and then initially cooled at a rate of 1K/h to 1123 K and finally at 10 K / h to room temperature. The characterization of the as-grown crystals is described in ref. [ 18 ]. On account of the small dimensions of the samples a mechanical polishing could not be carried out. Therefore the specimens had to be used as-grown. The sintered samples were prepared from the powdered oxides Y203, CuO and BaCO3. The components were mixed and pressed at 7 kbar into a pellet of 1 cm diameter. Subsequently, the specimen was reacted in a furnace in a stream of air as described in ref. [ 19 ]. The sintered superconductors were mechanically polished thus resulting in a shiny surface. The magneto-optical thin film was evaporated onto the sample surfaces as a mixture of EuS and EuF2 [20-22] at a pressure of p = 10 -6 mbar and a rate of 4 A/s. The thickness of the layer and the vaporization rate were controlled with a quartz oscillator (Leybold XTM). The evaporation in the electronbeam coating plant was halted at a thickness of ]2 corresponding to 4095 A in order to achieve an enhancement of the magneto-optical contrast due to optimum amplitude and phase conditions as described in refs. [ 10,11 ].
3. Experimental procedure The magneto-optical detection system consists of a Reichert-Jung Polyvar polarization microscope and an optical cryostat. The single-crystals were first mounted on a fiat copper block and then glued in good thermal contact with the cooling block inside the cryostat, whereas the sintered specimens were fixed directly. A canal system passes though the block to ensure good thermal contact with the liquid helium. The velocity of flow of the helium is controlled by a pumping system on the gaseous side of the cryostat and a pressure unit on the liquid helium side as shown in fig. 1. In addition to this configuration
microscope
He pump
Iiit//,
I vcacuum
Fig. 1. Optical cryostat. 1: specimens; 2: coverglass; 3: O-ring;4: magnetic shielding tube; 5: lenses; 6: coolingblock; 7: magnetic coil. a bifilar heater wound on the cooling block enables the temperature to be varied over the range 6 K to 300 K. The temperature of the cooling table is determined with a Pt resistor and that of the samples with a thermocouple fixed to the copper sheet with the specimen under investigation. The vacuum system is sealed by a cover glass of 1 mm thickness and of 35 mm diameter which is about 1 mm above the samples. This arrangement allows one to investigate up to seven specimens without ventilating the cryostat. The magnetic coil is connected to the cryostat in such a way as to produce a magnetic field perpendicular to the sample surface; the values are within the range 0 < #oHex~<0.23 T. The optical polarization light microscope used was a Reichert-Jung microscope with a resolution of about 0.8 pm. The polarizer and analyser consist of polarizer foils fabricated by Kaesemann which can be rotated separately, so as to obtain optimum extinction conditions. To achieve a maximum contrast of the domains, the cover glass of the cryostat is made of a low magneto-optical active material (Schott BK7, with the Verdet constant V= 0.02 angular min/ G cm at room temperature). This technique reduces depolarization effects markedly compared to the Herasil glass which is usually used. Lenses with long working distances of up to 3.8 mm were used because of the large distance between specimen surface
N. Moser et aL / Flux penetration in YBa2CusO7_a superconductors
and the upper side of the cover glass. To eliminate depolarization effects due to the magnet, the lenses were shielded from the magnetic field by a mu-metal tube. A TV camera system is connected to the Reichert-Jung polarization light microscope to transfer the pictures to an image processing system. The grabbed and processed frames can finally be stored in the frame-buffer of the computer. By means of the image processing system it is possible to drastically reduce the noise of the images by a continuous integration. An additional real-time background subtraction of the integrated image without flux penetration from the integrated image with flux penetrating into the specimen gives pictures of high contrast. These can be analysed with respect to the grey values corresponding to the flux line gradients. The image processing system is represented schematically in fig. 2. The measurements of the magnetization curves and the transition curve to the superconducting state are performed using a SQUID magnetometer. Because of the small dimensions of the YBaCuO single-crystal, the sample was fixed on an A1203 sheet of 0.2
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m m thickness showing a very low background magnetic moment. This configuration allows one to measure the magnetization curve in the same geometrical arrangement of the sample surface with respect to the magnetic field as the flux penetration was observed by the Faraday effect.
4. Experimental results 4.1. Y B a C u O single crystals
From measurements of the magnetization curves of YBaCuO single-crystals the lower critical field, given by (2)
#oH'c~ = ( 1 - D ) #oHc~ ,
(D denotes the demagnetization factor and/zoH~, is the uncorrected value) is determined from these measurements to be 45 _+3 m T as represented in fig. 3. At H'¢~ the magnetization curve starts to deviate from the "Meissner line" indicating the beginning of magnetic flux penetration into the specimen. The Meissner and Shubnikov patterns coexist up to ~He~t ~<#oH~2. The transition curve to superconductivity is shown in fig. 4 indicating a Tc of 87 K. In fig. 5a the shape of the YBaCuO single-crystal is represented without an applied external magnetic field, #oHext. Figures 5b to 5e show the flux penetration for increasing applied fields. The figures represent the remanent magnetic flux patterns, i.e., the
0 0singlecrystal [ ~ ,--, 6 YBaCuO ~Z 5OO T=5OK '
j
400
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300
PC
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1 Fig. 2. Image processing system.
~i -' ~
200
.
..................
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o0
I
20
40
-2~0o=......................... o soo io~
60 80 /.zoHext [mTl
mc~
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Fig. 3. Magnetization curve of a YBaCuO single-crystal measured at 5 K. poH'c~ (5 K) is determined to 45+3 mT as the deviation of the measured points from the "Meissner curve". Additionally, the magnetization curve up to 2 T is represented.
N. Moser et al. / Flux penetration in YBa2Cu307_~ superconductors
120
4.2. Sintered YBaCuO specimens
rE
0
20
40
60
80
100
T [K] Fig. 4. Transition from the normal state to the superconducting state ofa YBaCuO single-crystal. The specimen was cooled in the presence of a magnetic field PoH~xt = 2 mT,
flux which is trapped after applying external magnetic fields, #OHext of 0.1 T, 0.14 T, 0.16 T and 0.23 T and reducing each successive value to zero at the observation temperature of 10 K. The penetration of the magnetic flux appears to be stable and remains unchanged under these conditions. This characteristic behaviour corresponds to strong irreversible effects in the magnetization curve. The dark areas on the white border are partly due to a contamination of the as-grown single-crystal. These regions are indicated in fig. 5a. On increasing the external magnetic field, the first penetration of flux around the circumference of the specimen became observable at #oHg" = 52.5 mT (c, denotes measurements parallel to the c axis). The depth, L, of this penetration increases with field and is represented in fig. 6. The penetration field, /ZoHg II, is found to be higher than those obtained from the macroscopic magnetization curve: #0H~," (Faraday)>poH~li (magnetization). The features of the initial penetration of the specimen are nearly uniform with a retardation on the right hand side of the sample. The well-known phenomenon of edges acting as centres of primary flux penetration described by Baird [ 27 ] was not observed in the present investigations. The penetrated flux remained stable and did not move outwards for a given magnetic file within the limits of experimental error, as is expected in the case of an ideal superconductor. Since it is not possible to increase the applied field beyond 0.23 T, the flux penetration can only be observed up to a penetration depth of 150 ~tm.
The low- and high-field magnetization measurements performed at 5 K on sintered samples of dimensions 3 m m diameter and 2 m m height are represented in fig. 7. The low-field magnetization curve shows a primary maximum of 3.5 m T of the negative polarization at an external magnetic field of 4 mT. A second maximum is observed in the high-field curve at 200 mT. The analysis of the magnetization curves yields a value of 30 m T for the lower critical field, H'cl. The observation of the penetrated flux into the sintered YBaCuO specimen is only possible with help of the image processing system due to the low contrast between the Meissner phase and the mixed phase. The subtraction of the stored background frame of the specimen in the Meissner state from the real-time frame of the sample in the Shubnikov state shows the flux which has penetrated into the grains. On account of an optimum contrast of the frame, fig. 8 represents the remanent state after increasing the applied field to 0.23 T and then reducing to zero. At zero field depolarization effects will not disturb the minimum contrast between the two phases. The investigation reveals that only a few grains are visible which have been penetrated by the flux. This is indicated by the black grains. All other grains which have not been influenced are completely subtracted, thus leading to a homogeneous grey background.
5. Discussion The penetration field of, ~ H g t~, of 52.5 m T as determined by the magneto-optical Faraday effect corresponds to a much higher value than the lower critical field of #oH~ II=45 + 3 mT of the single-crystal as determined from the magnetization curves. This latter value agrees with the results reported in ref. [23 ]. The difference between these values, may be due to the existence of an energy barrier near the surface [16,24]. This barrier is due to the attractive force of the flux line to the surface and an increasing line energy of the vortex with increasing distance, x, from the surface. In addition to this contribution there is also a repulsive force acting on the vortex from the surface produced by the interaction of the
N. Moser et a L / Flux penetration in YBa2Cu3Oz_6 superconductors
121
Fig. 5. (a) As-grown YBaCuO single-crystal, in zero field. ( b ) - (e) Domain structures of superconducting YBaCuO single-crystal at 10 K, showing remanent flux after applying an external magnetic field. The Shubnikov phase is bright and the Meissner phase dark. (b) /zoHe~ =0.14 T; (c) /~oH~xt=0.16 T; (d) #oHext =0.23 T.
122
N. Moser et al. / Flux penetration in YBa2Cus07_ ~superconductors
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o
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Fig. 6. Dependence of the penetration depth, L, for the Shubnikov phase on the external magnetic field lzoH~,,.The field at which flux penetration begins,/~oHp,is about 52.5 roT. Fig. 8. Domain structure of the sintered YBaCuO specimen. The remanent flux is shown after applying an external field of 0.23 T at 10 K. The grains into which flux has penetrated ("Shubnikov phase") are dark. For clarity some grains are outlined.
. : .. 1
YBaCuO sintered T= 5.0K
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]
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Fig. 7. The magnetization curve of a sintered YBaCuO specimen at 5 K. The deviation from the Meissner curve leads to a value of #oH'c~= 30 mT (symbolized by the dashed line). The magnetization curve measured up to 2 T is represented in the inset. external field decreasing inside the specimen according to H e -aL/x (2L denotes the p e n e t r a t i o n d e p t h ) with the magnetic field o f the flux line which has the same sign. The a d d i t i o n o f these two contributions gives a m a x i m u m o f the vortex energy as a function o f x . On increasing the external field, flux starts to penetrate the s u p e r c o n d u c t o r at H f f but cannot spread spontaneously into the r e m a i n d e r of the specimen. The flux lines are concentrated at a distance o f the order o f 0.3 g m [ 5 ] from the edge o f the sample which corresponds to the value o f ~-L. In this case, the p e n e t r a t e d flux cannot be observed by the microscope because its resolution is l i m i t e d to 0.8 gm. W i t h increasing external field the energy barrier to flux p e n e t r a t i o n vanishes at #oHm;LIand the
flux enters spontaneously into the r e m a i n d e r o f the sample. Therefore one observes the invasion o f the S h u b n i k o v phase beginning at this penetration field /~oH~II> #oH~i LI. After reducing the external field to zero, the flux remains t r a p p e d within the single-crystal. This irreversibility is due to pinning o f the vortices at grain boundaries, chemical inhomogeneities and crystal-lattice defects. Surface energy barriers also prevent the flux from escaping from the specimen until the a p p l i e d field is reduced to zero. Even with the present resolution o f the microscope, at 10 K no relaxation effects o f the p e n e t r a t e d flux could be observed, as has previously been reported by Yeshurun [25]. The evaluation o f the volume pinning forces, Pv, a n d the critical current density, Jc, on the a s s u m p t i o n o f a linear flux density gradient and a local flux density o f B = 0 . 2 3 T at L = 0 yields via eq. ( 1 ) a value for Pv of 1.9× 108 N / m 3 and a critical current density o f 9 × 10 s A / m 2. The lower critical field o f the sintered specimen, #oH'c~ = 30 - 3 mT, is in the range o f ~toH~i bl= 9 +_ 1 mT~
N. Moser et al. / Flux penetration in YBa eCu 3O z_a superconductors
riety of different orientations of these grains in the superconductor. Those grains with the orientation of their c axes perpendicular to the applied field will be the first to be penetrated by the S h u b n i k o v phase because of the lower entry field. O n the other hand, the very small d i m e n s i o n s of the grains, of 5 to 10 ~tm length and 1 to 3 ~tm width, which are comparable to the penetration depth 2ab=0.8 ~tm (2 ab corresponds to the penetration depth in the a - b plane) [23] lead to a complete intrusion of the mixed state. Both the orientation and the d i m e n s i o n a l i t y effect contribute to a complete penetration of the mixed state into the grains. All other grains are either nonsuperconducting or misoriented with respect to the incident light beam.
6. Conclusions The observation of the flux penetration in YBaCuO single-crystals was successfully performed by means of the magneto-optical Faraday effect. The investigations revealed a nearly isotropic flux penetration which could be observed dynamically a n d recorded. This technique was also applied to sintered YBaCuO supercondctors, where flux penetration was observed in i n d i v i d u a l grains. The observation of the flux penetration into the sintered specimens, in addition to the study of flux penetration into individual grains, will be performed in the future. F u r t h e r investigations are in progress on thin superconducting films.
Acknowledgements We acknowledge valuable discussions with H.U. Habermeier, E.H. Brandt, U. EBmann and J. Parisi. Also we wish to thank H. W a l d m a n n for the design of the cryostat, R. Reisser for his assistance during the measurements with the S Q U I D magnetometer, R. Henes for preparing the sintered YBaCuO specimens and P. Keppler for coating the samples with the magneto-optical active films. The authors wish
123
also to thank H. Blythe for critical reading the manuscript.
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