Twin boundaries provide a convenient defect for investigating vortex dynamics in superconductors. They occur naturally in YBa{sub 2}Cu{sub 3}O{sub 7}, with well defined planar geometries. They are a strong pinning defect, and at the temperature of the melting transition they are the dominant pinning sites in clean crystals. Twin boundaries are easily seen in polarized light, making their location and number directly observable without special equipment. Finally, they present a highly anisotropic pinning potential to the vortices, creating the possibility of interesting new behavior. In this paper, we describe experiments using twin boundaries to probe two effects in vortex dynamics: a new peak effect in the critical current occurring in the solid state just below the melting transition, and anisotropic pinning by planar defects

Crabtree, G. W.

Fendrich, J.

Gardiner, T.

Gunter, D.

Kwok, W. K.

Nikitenko, V. I.

van der Beek, C. J.

Vlasko-Vlasov, V. K.

Welp, U.

UNT Digital Library

NRlM Seminar, Tsukuba, Japan, February 17-18,1995 The Interaction of Vortices with Twin Boundaries* G.W. Crabtree, W.K. Kwok, U. Welp, J. Fendrich, C.J. van der Beek, V.K. Vlasko-Vlasov,s V.I. Nikitenko,* D. Gunter, and T. Gardiner Materials Science Division and Science and Technology Center for Superconductivity Argonne National Laboratory, ,Argonne, Illinois 60439 Tha subnilfed manusalp4 has been authored ty a cantrector of the US. Government under contract No. W-3I-iOSMG38. Aeoordhgtj, lha US. Government mtains a -d&e, myaffy-free licemsto publish or rspoduoe h pubikhedform d this contriknbn. or d b w  dhws lo do 80. for US. Government PU-s. INVITED: International Seminar on Superconductors in High Magnetic Fields, National Research Institute for Metals, Tsukuba, Japan, February 17-18, 1995 DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or respnsi- bility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Refer- ence herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, rccom- mendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. ~ Work supported by the US. Department of Energy, BES-Materials Sciences under contract #W-3 1-109-ENG-38 (GWC, WKK, UW) and the National Science Foundation-Ofice of Science and Technology Centers for Superconductivity under contract #DMR91-2oooO (E, CJvdB, DG, TG). District, 142432 Russia. * $Permanent address: Institute of Solid State Physics, Russian Academy of Sciences, Chemogolovka, Moscow DlSTR1BUTION OF "HIS DOCUMENT IS UNLIMITED - GI+ DISCLAIMER Portions of this document may be illegible in electronic image products. Images are produced from the best available original document. . .  I Invited paper at the International Seminar on Supekonductors in High Magnetic Fields, National Research Institute for Metals, Tsukuba. Japan, February 17-18,1995 THE INTERACTION OF VORTICES WITH TWIN-BOUNDARIES G. W. Crabtree, W. K. Kwok,. U. Welp, J. Fendrich, C. J. van der Beek, V. K. Vlasko-Vlasov,+ V. I. Nikitenko,+ D. Gunter, and T. Gardiner Argonne National Laboratory Argonne, IL 60439 USA Introduction Twin boundaries provide a convenient defect for investigating vortex dynamics in superconductors. They occur naturally in YBa2Cu307, with well defined planar geometries. They are a strong pinning defect, and at the temperature of the melting transition they are the dominant pinning sites in clean .crystals. Twin boundaries' are easily seen in polarized light, making their location and number directly observable without special equipment. Finally, they present a highly anisotropic pinning potential to the vortices, creating the possibility of interesting new behavior. In this paper, we describe experiments using twin boundaries to probe two effects in vortex dynamics: a new peak effect in the a.itical current occurring in the solid .state just below the melting transition, and anisotropic pinning by planar defects; Pre-melting Peak Effect Figure I shows the resistivity of a single crystal of YBCO containing two twin boundaries oriented at 45" to the crystal edges and separated by 140 microns. The current direction is 'parallel to a sample edge in the ab plane, and the field is along the c-axis. The melting transition in this low field of 0.5 T is indicated by an arrow. At low current, the resistivity drops sharply in the liquid state as the temperature is lowered, going -to zero at the freezing transition and remaining zero in the solid state. This behavior is typical of the freezing transition,l and is caused by the strong difference in the dynamic response of the liquid and solid 'phases. Because of the finite shear modulus in the solid state, a given co'nfiguration of pinning defects is much more effective in pinning the solid than in pinning the ,liquid. This change in pinning effectiveness causes the resistivity of the solid to go to zero abruptly at the freezing transition if the transport current is low.. I However, e v e n  t h e  solid state c a n  be de-pinned by applying .sufficient current, as occurs  for t h e  higher current values  in Figure 1. In t h e s e  c a s e s ,  t h e  vortex motion in t h e  solid a n d  liquid c a n  be quite different, s ince  elastic forces between vortices tend t o  make  the  solid move as ' s ing le  object th roughou t  the  crystal ,  while the liquid m o v e s  as individual vortices under t h e  influence of viscosity and  friction. T h e  different dynamic mechanisms of t h e  two p h a s e s  are evident in Figure 1 in t h e  non-Ohmic resistivity in t h e  solid a n d  in t h e  different t e m p e r a t u r e  dependences of t h e  resistivity above a n d  below t h e  melting temperature. O-Ool CURREM(A) O-O' 88 88.5 89 89.5 90 90.5 91 91.5 T(K) Figure 1: T h e  resistivity of a crystal of Y B a 2 C u . 3 0 7  containing two twin boundaries  s p a c e d  140 microns apar t  a n d  oriented 45" to the  crystal edge a n d  to the  current, for s eve ra l  applied currents. The measurements  were taken with a four probe technique at a frequency of 17 Hz. Inset: typical I-V curves taken with a dc technique. T h e r e  is o n e  remarkable  fea ture  of the current-dependent resistivity in Figure.  1. At a tempera ture  close to, but below, the melting point, all t h e  c u r v e s  approximate ly  go through. z e r o  resistivity. This a p p'r o xi m at e. z e r o i n d i ca t es t h a t  pi n n i n g b e c o m e s d r am at i ca I I y s t r o n g e r  in t h e  solid jus t  before  melting occurs .  This t rend  is opposi te  to t h e  intuitive expectation that pinning becomes  weaker.  as t h e  temperature  is raised. 'The increase in pinning near  melting c a n  be quantified by  m e a s u r i n g  t h e  critical c u r r e n t .  directly with dc  I-V curves. Typical I-V curves  a r e  shown in .the inset to Figure 1, a n d  the .. . 7-. - . . . . . - -  .- critical transport  current der ived from . s u c h  . c u r v e s  using a voltage criteria of 10-7 V is shown in Figure 2. A sha rp  p e a k  in Jc, amounting to approximately a factor of 2, is s e e n  just prior to melting. This pre- melting peak  effect can  also be s e e n 1  in ' c rys t a l s  with twin boundaries or iented parallel t o  t he  vortex motion, a n d  in untwinned crystals,  though t h e  magnitude of t h e  effect  is less pronounced in t h e  latter case. T h e  - - at H=0.5T I I  c 20 - 10- ' volts criteria 86 87 88 89 90 91 92 T(K) Figure 2: Critical t ransport  current  for  t he  crystal shown in Figure 1. The va lues  of Jc were determined from dc m e a s u r e m e n t s  of the  I-V curve, a s suming  a voltage criterion of 10-7 volts. rigin of the peak  effect c a n  be found .in t he  weakening of the s h e a r  modulus .  prior to melting. Below t h e  peak ,  where  t h e  s h e a r  modulus is strong, t he  moving vortices tend to t a k e  up t h e  structure of the  lattice to minimize their mutual interaction energy.  This leads to elastic flow, where the vortex lattice moves  through the crystal as a single elastic object. As t he  s h e a r  modulus w e a k e n s  near  melting, the  la t t ice  c a n  a c c o m m o d a t e  m o r e  dis tor t ion wi thout  b reak ing  its . structure,  a n d  t h e  vortices se t t l e  d e e p e r  into t he  pinning potential wells which oppose their motion. This accounts  for  the increase  in Jc just prior to melting. At' t he  peak  of' Jc, t h e  s h e a r  modulus becomes so w e a k  tha t  t he  lattice is torn, leading to plastic flow. O n c e  s h e a r  motion is allowed, the most  weakly pinned vort ices  t ea r  f ree  of the  lattice structure, leading to a lower critical current.  In this  picture, t h e  p e a k  in Jc mark's t he  transition from elastic to plastic f1o.w. It signals t h e  weakening of t h e  s h e a r  modulus, a n d  is a precursor to  the melting transition of the vortex solid. ~ c . The defects responsible for the increased pinning at the. peak in Jc are . .  the twin boundaries. This identification is made clear by the angular dependence of the resistivity and critical current shown in Figure 3. The valley in resistivity and the associated peak in Jc are largest when 15 10 h E 'z v 5Q 5 0 Figure 3: Temperature dependence of the resistivity and critical current as the field is rotated away from the twin boundary plane. . the field direction is aligned with the c-axis, parallel to the twin boundary plane. As the field direction is rotated away from the boundary plane, the valley in resistivity and the peak. in Jc become less pronounced, disappearing at a misorientation. of approximately 4". This behavior is characteristic of twin boundary pinning, which is .. -- ,T . -,. 1 .I... . . .~ . . . . . . . .. . . . - effective only over a narrow angular range of field directions nearly aligned with the boundary plane; Anisotropic Twin Boundary Pinning The pinning action of twin boundaries on vortices can be expected to be anisotropic, due to the planar nature of the boundary. In this respect twin boundaries differ from point defects, whose geometry is independent of angle, and columnar defects, where vortices aligned with the defect are effectively pinned against motion in either transverse direction. Twin boundaries present two different pinning strengths to vortices aligned with the boundary plane: relatively weaker pinning for motion within the plane, and. relatively stronger pinning for motion transverse to the plane. Early transport measurements revealed this anisotropy.? The two different pinning potentials arise from two different aspects . of the twin boundary structure. Transverse to the boundary, there is a strong interaction with vortices associated with the strain field of the boundary. TEM studies suggest that the strain field is 10-50 8, wide, enough to contain one vortex. As indicated by transport measurements and the. flux images shown below, the pinning potential well transverse to the boundary effectively opposes the motion of flux across the boundary. If the boundary were a featureless plane, this transverse potential, would not affect motion of the vortices parallel to the plane. In principle, vortices could move along the valley of the transverse potential, remaining trapped inside the twin boundary as they move. However, the twin. boundary is not featureless along its length. Rather, there is likely to be considerable atomic disorder in the boundary, associated with the mismatch of the relatively perfect structures on the two sides. This atomic disorder creates point pinning defects in the boundary, which are responsible for impeding vortex.motion parallel to and within the boundary. The differing strength of the two pinning. mechanisms can be seen clearly in the flux distributions near twin boundaries, observed by magneto-optical techniques. ' Such magneto-optical flux images can be obtained using the Faraday rotation of the polarization of light in an optically active indicator. film placed on the sample? Figure 4 shows the .physical image of a single crystal of YBa2Cu307 containing a series of parallel twin boundaries, and Figure 5 shows flux images of the same crystal at several applied. fields. The single crystal Is approximately 0.7 mm across. from the left .edge to the point on the right, and 20 microns thick. . Twin boundaries extend vertically along the entire crystal, spaced at intervals of 50 to 300 microns. The difference in pinning potential for motion parallel and perpendicular to the boundary is evident in the magnetic field patterns. Looking first at the bottom edge, where vortices enter the crystal in Figure 4: : Physical image of a single crystal of YBa2Cu307, showing parallel twin boundaries spaced at distances of 50 to 300 microns. . the upward direction, the flux is seen to penetrate further into the twin boundaries than it does into the .neighboring untwinned regions, creating a characteristic "flame" pattern at the boundary. The shielding current density flowing at the edge of the crystal can be estimated. from the field penetration distance, using Maxwell's The greater penetration of the field in the twin 4n aH equation 7 Jc = - ax boundary indicates .that the. critical current density in the boundary is lower than in the surrounding bulk. Thus the twin boundary is a weak link at these temperatures. The shielding current flowing parallel to the edge of the crystal must spread out at the twin boundary in'order to lower its density to the critical value in the boundary. A quantitative model3 of the current distribution near a twin boundary based on 'this V-shaped pattern is in good agreement with the local field values derived from images like *those in .Figure .5. The -- penetration of flux into the twin boundaries and the flame pattern are characteristic of pinning against .vortex motion parallel to and within the twin boundary. A very different pattern of field penetration occurs at the left hand edge of the crystal. Here the twin boundary planes are perpendicular . . . . . _ . I . .  : ,- .. . .  Figure 5: Flux images showing the effect of twin boundaries on the ,local field distribution. Images were taken in the applied fields indicated after zero field cooling to 40 K, and in zero field after applying a field of 855 gauss. to the  flow of flux entering the  crystal. The images show a distinct drop in the vortex density at. the twin boundary, indicating that the boundary acts as a barrier to flux motion. In contrast to the deeper penetration for motion within the boundary, motion transverse to the e. boundary is impeded. This stronger pinning for transverse motion is a, feature of the boundary itself, rather than of the local atomic disorder within the boundary. The local field values adjacent to the twin boundary recovered from images like those in Figure 5 imply that the. drop in vortex density across the boundary is approximately constant, independent of temperature. From this drop, the shielding current flowing at the boundary can be inferred, approximately 0.1 A. The anisotropy in twin boundary pinning against motion within and across the boundary is illustrated dramatically by comparing the behavior of boundaries at the lower left corner and near the middle of the left edge. At the lower left, vortices enter the crystal'from the bottom and these boundaries act as weak links, . producing .the characteristic flame pattern. . Near the . middle of .the left edge, vortices enter from the left, and the same boundaries act as barriers. to ,motion. Thus the anisotropy in pinning is a .generic feature, independent of the structural details of individual boundaries. Figure 5 reveals one other interesting feature which sheds light on the behavior of boundaries at orientations intermediate between parallel and perpendicular to the motion direction. The upper right edge of the . crystal makes a 45" angle with the other crystal edges and with the twin boundaries. There is one twin boundary which extends vertically throughout the crystal, perpendicular to the edge -of the crystal at the bottom, 'and oriented at 45" to the 'upper right edge. At the bottom this twin boundary exhibits the flame pattern characteristic of a weak link, as expected for vortex motion parallel to and within. the boundary. However at the upper right, there is no flame pattern, in spite of the fact that the motion direction (perpendicular- to the edge), has a component along .the boundary plane. Close examination of the images in Figure 5 reveals that there is a slight barrier effect, with a shadow region behind the boundary where the vortex density is slightly lower than in front of the boundary. A reduced barrier effect can be expected for intermediate angles, since there is a path from the crystabedge to the shadow region that does not cross the twin boundary. Thus, unlike the case of boundaries perpendicular to the motion, it is possible for vortices to move into the shadow region by a curved trajectory which avoids the boundary altogether. Such a curved trajectory would be driven by the repulsive interaction between vortices, which tends to create a constant vortex density throughout the crystal. Summary Twin boundaries are a naturally occurring strong pinning defect which can be used to .investigate. and illustrate -the basic features of vortex * behavior in superconductors. This paper discusses twin boundary behavior in the context of two phenomena: the pre-melting peak effect, and anisotropic pinning. The pre-melting peak effect is a new feature of the vortex solid state, associated with the relaxation of vortices more deeply into their pinning potential wells as the shear modulus weakens prior to melting. Twin boundary pinning emphasizes the effect, since these defects are the dominant pinning sites in these crystals near the melting temperature. A pre-melting peak effect can also be seen in untwinned crystals, but with smaller magnitude than is shown here. The phenomenon of anisotropic pinning can be naturally investigated in twin boundaries, since their planar geometry contains two pinning mechanisms of different strength: strong .pinning against motion transverse to the boundary, due to the strain'field associated with the boundary itself, and weak pinning against motion .*parallel to and within the boundary, caused by atomic disorder' occurring at the boundary. The weaker pinning for motion along the boundary allows greater penetration of the field into the boundary than into the neighboring untwinned regions, and produces a characteristic flame pattern in magneto-optical flux images. A quantitative model of the shielding current based on this pattern has been derived. For motion perpendicular to the twin boundary, the boundary acts as a barrier, producing a drop in vortex density across the boundary plane. This work was supported by the U. S. Department of Energy, Basic Energy Sciences-Materials Science under contract #W-31-109-ENG-38 (GWC, WKK, UW) and by the U. S. National Science Foundation-Office of Science and Technology Centers under contract #DMR 91-20000--. (VKV, JF, CJvdB, DG, and TG). Ref e re n ces + Permanent address: Institute of Solid State Physics, Russian Academy of Sciences, Chernogolovka, Moscow district, 142432 Russia 1. W. K. Kwok, J. A. Fendrich, C. J. van der Beek, and G. W. Crabtree, Phys. Rev. Lett. 73,2614 (1 994). 2. W. K. Kwok, U. Welp, G. W. Crabtree, K. G. Vandervoort, R. Hulscher, and J. Z. Liu, Phys. Rev. Lett. 64, 966 (1990). 3. U. Welp, T. Gardiner, D. Gunter, J. Fendrich, G. W. Crabtree, V. K. Vlasko-Vlasov, V. 1. Nikitenko, Physica C 235-241, 241 (1994). .. 

The interaction of vortices with twin boundaries

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The interaction of vortices with twin boundaries

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