The evolution of flux distribution in MgB₂ single crystals during their remagnetization was imaged with

 magneto-optical technique. Meissner holes, formed as the areas where the annihilation of vortices and

 antivortices takes place, were found at the boundary between oppositely magnetized parts of the crystal. Gradient

 of magnetic induction in the vicinity of Meissner holes was found to be enhanced. Finger-like structures of

 convex shape, formed during the penetration of magnetic flux inside the crystal, were observed and explained as

 an effect of inhomogeneous pinning and demagnetizing field redistribution in the sample

Abal’osheva, I.

Chabanenko, V.

Cortés-Maldonado, R.

Karpinski, J.

Katrych, S.

Kuchuk, Е.

Mikheenko, P.

Puźniak, R.

Pérez-Rodríguez, F.

Yurchenko, V.V.

Zhigadlo, N.D.

Наукова електронна бібліотека періодичних видань НАН України (Vernadsky National Library of Ukraine)

Low Temperature Physics/Fizika Nizkikh Temperatur, 2014, v. 40, No. 7, pp. 801–806 Magnetic field penetration in MgB2 single crystals: pinning and Meissner holes V. Chabanenko1, E. Kuchuk1, V.V. Yurchenko2, P. Mikheenko2, I. Abal’osheva3, R. Cortés-Maldonado4, F. Pérez-Rodríguez4, J. Karpinski5,6, N.D. Zhigadlo5,  S. Katrych6, and R. Puźniak31A. Galkin Dоnetsk Institute for Physics and Engineering, NASU, Donetsk 83114, UkraineE-mail: vikchabanenko@gmail.com 2Department of Physics, University of Oslo, P.O. Box 1048, Blindern 0316, Oslo, Norway3Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, Warsaw 02-668, Poland4Instituto de Física, Benemérita Universidad Autónoma de Puebla, Puebla, México5Laboratory for Solid State Physics, ETH Zurich, Zurich 8093, Switzerland6Institute of Condensed Matter Physics, EPFL, Lausanne 1015, SwitzerlandReceived February 17, 2014, published online May 21, 2014 The evolution of flux distribution in MgB2 single crystals during their remagnetization was imaged with magneto-optical technique. Meissner holes, formed as the areas where the annihilation of vortices and antivortices takes place, were found at the boundary between oppositely magnetized parts of the crystal. Gradient of magnetic induction in the vicinity of Meissner holes was found to be enhanced. Finger-like structures of convex shape, formed during the penetration of magnetic flux inside the crystal, were observed and explained as an effect of inhomogeneous pinning and demagnetizing field redistribution in the sample.  PACS: 74.25.Ha Magnetic properties including vortex structures and related phenomena; 78.20.Ls Magneto-optical effects; 74.25.Wx Vortex pinning (includes mechanisms and flux creep). Keywords: magnetooptic of flux penetration, vortices, antivortices, Meissner holes, inhomogeneous pinning, single crystal MgB2. 1. IntroductionThe magneto-optical imaging (MOI) allows tracking magnetic flux distribution close to the sample surface [1,2]. The numerical inversion of Biot–Savart law gives an integral relation between the current density distributions and the magnetic self-field. It opened up the possibility of finding supercurrent distributions by MOI. The MOI tech-nique permits the investigation of complex problems, such as inhomogeneous and anisotropic current flow, the de-pendence of critical current on the local magnetic field, the current distribution around crystal defects such as grain boundaries and inner interfaces [1] etc. The MOI studies of the vortex dynamics in Nb films [3] and foils [4] reveal stochastic jumps of the flux bundles forming a rough pene-tration front and giant abrupt changes in the magnetic-flux distribution as a result of the collapse of critical state. For MgB2, most of the studies were devoted to the avalanches in thin films [5,6] and limited data only are available on magnetic field penetration into MgB2 crystals [7,8]. This is mainly due to the difficulties in growing large in size per-fect crystals.  Here the magnetic induction patterns at the boundary between oppositely magnetized parts of MgB2 crystals are studied in details. It was found that near the edge of the crystal the field of opposite directions is present and Meissner holes — the areas where the annihilation of neighboring vortices and antivortices occurs and the re-gions free from flux cavity appear [9,10] — are formed (Fig. 1). © V. Chabanenko, E. Kuchuk, V.V. Yurchenko, P. Mikheenko, I. Abal’osheva, R. Cortés-Maldonado, F. Pérez-Rodríguez, J. Karpinski,  N.D. Zhigadlo, S. Katrych, and R. Puźniak, 2014 V. Chabanenko et al. 2. Experiment and samples The magnetic flux distribution was imaged and analyzed using MOI technique during remagnetization of MgB2 crys-tals. This technique provides data for the normal component of magnetic induction Bn close to the sample surface. As the MOI technique is also a sensitive tool for investigations of crystal inhomogeneity associated with the imperfections of structure and composition [2,11], it allowed us to study lon-gitudinal and transverse cross sections of the finger-like structures formed during magnetic flux penetration in weak spots close to the edge of the crystal.  The measurements were performed at the temperature range of ~ 3–40 K during the magnetization process in magnetic field up to 100 mT and during reversal magneti-zation with the change of direction of the field. The studied crystals were grown from a MgB2 solution at the pressure of 15 kbar and the temperature of 1800 °C in a special high-pressure chamber, which allowed the growth of samples at pressure up to 35 kbar and temperatures up to 2200 °C [12]. Here we show data obtained on the crystal S1 of the approximate dimensions 860×660×250 µm that has the c-axis normal to the platelets and on disc-shaped crystal S2 with 500 µm in diameter and thickness of ~150 µm. The external magnetic field was applied in direction perpendicu-lar to the sample surface. Figure 2 shows electron microscope images of MgB2 plate-like sample S1 with fine details of the shape and the structure of the crystal, presented with enhanced magnifi-cations in Figs. 2(b)–(d). According to the above images sample S1 has a complex shape with nonplanar sides. The steps seen in the crystal may be a source of significant pin-ning of magnetic flux.  3. Results and discussion 3.1. Magnetization process Figure 3 shows penetration of magnetic field into the crystal S1. Magneto-optical imaging is an effective tool in revealing field distribution in the surrounding of defects, while not all defects (inhomogeneities) can be detected by the optical or electron microscope imaging. Summarizing obtained results: At the 20 K (Fig. 3(c)), we can find the regions of the crystal (see, red square), where the penetra-tion of the field inside of the sample is more or less uni-form, almost homogeneous until the middle of the sample. Here, the crystal is quite perfect, pinning centers are weak, and the critical current is low. Areas on the right and the left side of the crystal are characterized by highly inhomo-geneous penetration, and in some places (black areas), al-most complete shielding appear. Here, crystal defects act as strong pinning centers and therefore, significant critical Fig. 1. Magnetic field lines during the penetration of flux of op-posite orientation, occurring when the external field H is de-creased again after it had first been increased to the field of full penetration Hp. Meissner holes show on a normally remagnetized plate (after E.H. Brandt [10]). Fig. 2. Electron microscope images of MgB2 plate-like crystal S1. The steps between the plates of the crystal are clearly seen. 802 Low Temperature Physics/Fizika Nizkikh Temperatur, 2014, v. 40, No. 7 Magnetic field penetration in MgB2 single crystals: pinning and Meissner holes currents exceeding 5–10 times of the value in the red square area may appear. In the left part of the crystal, close to its top edge, there are spots with weak reduced superconducting parameters, where magnetic flux enters the sample easier than in other places. After entering, magnetic flux propagates in a dif-fuse manner forming finger-like patterns that are clearly seen near the top edge of the sample in Fig. 3. These pat-terns remind those seen in superconducting films with quite strong pinning and in YBa2Cu3Ox crystals [11]. It reveals significant pinning in the crystal. The origin of pinning could be in the attraction of vortices due to the steps seen in Fig. 2. One can also see that top left part of the sample remains in Meissner state. The penetration of the field in right part is quite homogeneous and this area was used for investiga-tion of the process of magnetization and demagnetization of the sample applying positive and then negative magnetic field. In a specific range of the field, transverse (t-direction, Fig. 3(a)) and longitudinal (l-direction) profiles of the magnetic induction were analysed in a finger-like struc-tures shown in Fig. 3. The profiles recorded in the increas-ing positive field are shown in Fig. 4. One can see that the distribution of magnetic flux has a convex dome-like shape both in longitudinal and transverse directions. Increase of the field leads to increase of both height and width of the domes. The gate, or the weak spot, where flux enters the crystal becomes wider with the increase of the field. Fig. 3. (Color online) The magnetic flux penetration into the crys-tal S1. The flux profile in the area of finger-like penetration is analyzed in direction perpendicular to the sample surface (l-direction) and along top edge of the sample (t-direction).  Fig. 4. (Color online) Profiles of magnetic induction B in l- (b) and t-directions (c) of the finger-like structure shown in the upper panel (a). Low Temperature Physics/Fizika Nizkikh Temperatur, 2014, v. 40, No. 7 803 V. Chabanenko et al. The formation and growth of dome-like areas contain-ing magnetic flux reflects presence of edge defects and reasonably strong pinning inside the crystal, which restricts further motion of magnetic fluxes. The similar induction profiles observed in YBa2Cu3Ox crystals [11] were inter-preted as flow of flux into central zone, characterized by weak pinning. When magnetic field further increases, the flux moves into the central part erasing the flux free area. 3.2. Flux trapping and remagnetization in negative field Figure 5 shows typical magneto-optical images record-ed at temperature of 3.66 K. Flux trapped as a result of magnetization of the sample in 85 mT and switching off the field to H = 0 is shown in Fig. 5(a). The images 5(b) and (c) show distribution of flux after application of nega-tive fields of H = –17 mT and –28.9 mT, respectively. Brighter intensity in these images corresponds to a higher normal component of magnetic induction (Bn) and the darker one to lower Bn. The white arrow in Fig. 5(a) shows the direction along which the magnetic flux distribution was analyzed. The remagnetization front reveals Meissner hole as a dark line around the perimeter of the sample, as it is shown in the panels of Fig. 5. With increase of negative field, Meissner hole moves inside the crystal and its width de-creases (Fig. 6). The Meissner hole in zero magnetic field (Fig. 5(a)) occurs due to finite demagnetization factor of the crystal and to the ability of the crystal to trap magnetic field. Figure 7 shows the profiles of the normal magnetic induction Bn for different applied fields along the direction marked by the white line in Fig. 5(a). It appears that in the vicinity of the parts of Meissner hole (squares in the fi-gure) the derivative dBn/dx is increased by 2–3 times com-pared to its value in the bulk, controlled by the pinning. This is in agreement with model developed in Ref. 9 (Fig. 4(a)) and Ref. 10, showing that the Meissner hole Fig. 5. Magneto-optical images of MgB2 crystal S1 at T = 3.66 K during remagnetization in negative fields H, mT: 0 (a); –17 (b); –28.9 (c). The boundary between up () and down ( ⊕ ) magne-tized areas is near of the crystal edges (c). Fig. 6. Effect of increasing negative magnetic field on Meissner hole displacement inside the crystal (a) and on its width (b). 804 Low Temperature Physics/Fizika Nizkikh Temperatur, 2014, v. 40, No. 7 Magnetic field penetration in MgB2 single crystals: pinning and Meissner holes displaces magnetic flux to the periphery [9 (Fig. 3(a))] of the area where annihilation of vortices and anti-vortices takes place. The displaced flux increases Bn in the area close to the hole. 3.3. Nut-like structure distribution of magnetic flux in the crystal Figure 8(a) shows nut-like structure formed by Meissner holes in crystal S2. Presented image was obtained by ex-posing sample to magnetic field of a value above full pene-tration field. After that the direction of the field was re-versed setting its absolute value somewhat below the value of previous field. This procedure was repeated several times, finally reducing field to 17 mT. The structure in Fig. 8(a) is similar to that obtained in YBa2Cu3Ox crystal in the presence of the ac field [10]. The Meissner holes in such a structure separate domains with opposite directions of magnetic field. An example of the profile of the absolute value of induction in the vicinity of one of the holes is shown in Fig. 8(b). Image is taken along the line marked by large red arrow in Fig. 8(a). As in Fig. 7(b), there is increase in the gradient of induction in the vicinity of the hole. The nut-like structure in Fig. 8(a) shows several areas with strong pinning separated by areas of weaker pinning. Such a structure deserves further investigation of its local magnetic properties in combination with structural analysis. 4. Conclusions As a result of the application of MOI technique to MgB2 single crystals it was found that:  — Meissner holes are formed along the edge of the crystal in the trapped magnetic field or in the field of the opposite polarity to the field used for magnetization; — in agreement with available models, Meissner holes are shifted towards the centre of the crystal; — the derivative of magnetic induction dBn/dx in the vicinity of Meissner hole is 2–3 times larger than the bulk value, controlled by pinning; — structure formed by Meissner holes in a bulk crystal is similar to “fingerprints”, unlike that one of thin films, where dendritic structures are dominant; Fig. 7. (a) Profile of trapped magnetic flux after magnetization in H = 85 mT at T = 3.66 K; (b) Absolute value of magnetic induction in the vicinity of right “projection” of Meissner hole in panel (a). Fig. 8. (a) Nut-like pattern in crystal S2 constituted by Meissner holes in field of 17 mT; (b) Magnetic induction profile (absolute value) along the line shown by large arrow in (a). The structure of induction around the Meissner hole is marked by square. Low Temperature Physics/Fizika Nizkikh Temperatur, 2014, v. 40, No. 7 805 V. Chabanenko et al. — the induction profiles of finger-like structures in longitudinal and transverse directions have a convex dome-like shape; — the gates, through which magnetic flux enters the crystals widen with an increase of external magnetic field. Acknowledgments This work was partially supported by SEP-CONACYT (Mexico) under grant CB-2012-01-183673, by the National Science Centre of Poland based on decision No. DEC-2013/08/M/ST3/00927, and by Swiss National Science Foundation. J.K and S.K acknowledge support of Europe-an Community FP7 Project Super-Iron. Authors wish to thank V.V. Burkhovetskii for electron microscope images of crystals.   1. A. 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Magnetic field penetration in MgB₂ single crystals: pinning and Meissner holes

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Magnetic field penetration in MgB₂ single crystals: pinning and Meissner holes

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