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Surface critical currents and activation energies in high-temperature superconductors
PhysicaC 235-240 (1994)2993-2994 North-Holland
PHYS~gA
Surface Critical Currents and Activation Energies in high-temperature superconductors L. Burlachkov ~ and V.M. Vinokur b ~The Jack and Peal Resnick Institute for Advanced Technology and Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel bMaterials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA The critical currents and activation energies related to the surface (Bean-Livingston) barrier are found for high-temperature superconductors. It is shown that the surface barrier does not undergo a temperature (exponential) suppression which is typical of the bulk pinning. Therefore the surface irreversibility dominates over the bulk one at high temperatures T ~ T¢, where the bulk pinning is suppressed by thermal fluctuations. The dependencies of the surface activation energies Usurl on the external field (Us,,~! o¢ H -1/~) and transport current (Us,,~l ¢x j-1/2 for moderate currents) prove to be different from those for Ub~zk. This helps to distinguish between the surface and bulk effects on the transport and magnetization properties of HTSC. The interplay between the surface and the bulk contributions is discussed.
The importance of surface contribution to the magnetic irreversibility in high-T¢ materials has been proved by magnetization and magnetic relaxation experiments [1, 2]. But the transport properties, such as the transport critical current Jc*~, activation energies U(J t~) and, in turn, resistivity R(T, H, j , r ) and the I - V characteristics are conventionally described (as a review see Ref.[3]) in terms of bulk phenomena, such as vortex pinning, vortex lattice melting and glass transition, etc. Meanwhile the surface barriers can compete with the bulk phenomena and, dominate over them, especially at high temperatures
T'x_ T~. In this paper we discuss the importance of surface barriers for transport properties of high-Te superconductors, particularly for YBa2CuaOx. We derive expressions for Je*r and the surface activation energy U~,~I as functions of current, field and temperature, and discuss the competition between the surface and bulk transport resistance. The surface barrier, discussed first by Bean and Livingston [4], prevents vortex penetration at H < Hp, where H v is the penetration field. Generally He1 < Hp < He, where He1 is the lower critical field, He ~- ~ Hcl/ln(~) is the thermodynamic field and ~ = A/~ (A and ~ are the pene-
tration depth and coherence length respectively). For a perfect barrier Hp = He. Large values of ~ 100 in high-To compounds imply He >> H¢1, which makes the surface barrier prominent even if it is partially diminished by surface imperfections. One more reason for its importance is the "persistence" of the surface barrier is the absence [7] of thermal (exponential) renormalization which is typical of the bulk pinning. The latter decreases exponentially above the depinning temperature Tdp [5], which depends on the type of pinning. For the strongest one (by columnar defects) Trip is about 60-70 K for YBa2CuaOx. Therefore, the surface barrier should dominate at high temperatures T > 80 K, that has been proved experimentally [2]. At H > Hp the surface barrier is still active and determines the surface contribution to magnetization. If the bulk pinning can be neglected, we get an asymmetric surface magnetization loop [6] with the ascending branch (flux entry) described by: (1) where H is the external field and B is the magnetic induction inside a superconductor. The de-
0921-4534D4/$07.00 © 1994 - ElsevierScience B.V. All rights reserved. SSDI 0921-4534(94)02062-0
L. Burlachkov, IfM. Vinokur/Physica C 235 240 (1994) 2993 2994
2994
scending branch (flux exit) is described by: me~ = ¢0/16¢rA 2 << Hcl ~ meq,
(2)
where meq =- H - Beq is the equilibrium magnetization. These expressions enable to find the transport critical current J ~ in a simplest geometry, where a superconducting slab of thickness d imbedded into external magnetic field H parallel to its surface. We suggest that all the relaxation processes are over and the system is at equilibrium: B = Beq(H). In this situation the surface is "locked" by a barrier, which is characterized by activation energy (with parameters appropriate for YBa2CuaOx) eq
T
U,u~S(v)lkZ, ~ - - ~ . 10 4 for both vortex entry and exit, where 7- = (To T ) / T e . The transport current J*~, flowing along the slab, leads to a difference A H =_ He,~ - He,: = (4rr/c)J `~
(3)
between the fields Hen and He~ at the sides of the slab. Of course Her, > He~:, so that vortices enter the slab (by thermoactivation surmounting of the surface barrier) from the side He,~. Note that in [7] jt~ denoted the mean density of the current; here we prefer to use jt~ for a total current through a slab. From the condition A H ( B ) < men(B) - m a x ( B ) we get [7]: + B 2-
B
~ 8rrH"
(4)
In order to find the activation energy U,~,,.I as a function of jt~ at j~r < j~r, we have to combine the expressions for the activation energies Uen, Uex [8] derived for magnetization experiments (in the expression for Uen and Uex [8] we should use respectively He,~ and H , , instead of H) with Eq.(3) under the condition Uen = Ue~ U~u,'I. The latter condition provides the continuity of the vortex flux through the slab. As a result we gett U
,d,~,
¢0A __3/2 / ~ 1
=
V
¢
1
AH
(5)
(where 3' is the anisotropy) for A H _= (47r/c)J t~ > rneq. This condition is almost always satisfied at current densities greater than 1 0 3 A / c m 2 and usual samples with d >_ 0.1 rnm. A more complicate formula in the opposite limit A H < meq we present elsewhere. In the case where a bulk pinning is present altogether with a surface barrier, the vortices should successively surmount the surface and the bulk barriers. Therefore the role of the activation energy U will play the largest of U,~,~] and UbulkIf U , ~ f > Ub~,Ik, then a small applied current jt~ should flow along the surfaces only, thus U depends on the total current Jt~. In the opposite case, where U,~,~.r < Ub~,lk, jt~ is distributed over the bulk, and U depends on the current density, Jt~/d. In the case where samples of different thicknesses d are available from the same batch, this can provide a convenient tool to distinguish between the surface and bulk barriers. L.B. is grateful to the support from the Raschi Foundation and the Israel Academy of Science. V.M.V. acknowledges the support from the Argonne National Laboratory through U.S. Department of Energy, BES-Materials Sciences, under contract No. W-31-109-ENG-38. REFERENCES 1. V.N. Kopylov, A.E. Koshelev, I.F. Schegolev and T.G. Togonidze, Physica C 170, 291 (1990). 2. M. Konczykowski, L. Burlachkov, Y. Yeshurun and F. Holtzberg, Phys. Rev. B 43, 13707 (1991). 3. G. Blatter, M. Feigelman, V. Geshkenbein, A.I. Larkin and V.M. Vinokur, to be published in Rev. Mod. Phys. 4. C.P. Bean and J.D. Livingston, Phys. Rev. Lett. 12, 14 (1964). 5. D.R. Nelson and V. Vinokur, Phys. Rev. Lett. 68, 2398 (1992). 6. J.R. Clem, LTI3, (Plenum, NY, 1974) vol. 3, p. 102. 7. L. Burlachkov and V.M. Vinokur, Physica B 194-196, 1819 (1994). 8. L. Burlachkov, Phys. Rev. B 47, 8056 (1993).
PHYS~gA
Surface Critical Currents and Activation Energies in high-temperature superconductors L. Burlachkov ~ and V.M. Vinokur b ~The Jack and Peal Resnick Institute for Advanced Technology and Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel bMaterials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA The critical currents and activation energies related to the surface (Bean-Livingston) barrier are found for high-temperature superconductors. It is shown that the surface barrier does not undergo a temperature (exponential) suppression which is typical of the bulk pinning. Therefore the surface irreversibility dominates over the bulk one at high temperatures T ~ T¢, where the bulk pinning is suppressed by thermal fluctuations. The dependencies of the surface activation energies Usurl on the external field (Us,,~! o¢ H -1/~) and transport current (Us,,~l ¢x j-1/2 for moderate currents) prove to be different from those for Ub~zk. This helps to distinguish between the surface and bulk effects on the transport and magnetization properties of HTSC. The interplay between the surface and the bulk contributions is discussed.
The importance of surface contribution to the magnetic irreversibility in high-T¢ materials has been proved by magnetization and magnetic relaxation experiments [1, 2]. But the transport properties, such as the transport critical current Jc*~, activation energies U(J t~) and, in turn, resistivity R(T, H, j , r ) and the I - V characteristics are conventionally described (as a review see Ref.[3]) in terms of bulk phenomena, such as vortex pinning, vortex lattice melting and glass transition, etc. Meanwhile the surface barriers can compete with the bulk phenomena and, dominate over them, especially at high temperatures
T'x_ T~. In this paper we discuss the importance of surface barriers for transport properties of high-Te superconductors, particularly for YBa2CuaOx. We derive expressions for Je*r and the surface activation energy U~,~I as functions of current, field and temperature, and discuss the competition between the surface and bulk transport resistance. The surface barrier, discussed first by Bean and Livingston [4], prevents vortex penetration at H < Hp, where H v is the penetration field. Generally He1 < Hp < He, where He1 is the lower critical field, He ~- ~ Hcl/ln(~) is the thermodynamic field and ~ = A/~ (A and ~ are the pene-
tration depth and coherence length respectively). For a perfect barrier Hp = He. Large values of ~ 100 in high-To compounds imply He >> H¢1, which makes the surface barrier prominent even if it is partially diminished by surface imperfections. One more reason for its importance is the "persistence" of the surface barrier is the absence [7] of thermal (exponential) renormalization which is typical of the bulk pinning. The latter decreases exponentially above the depinning temperature Tdp [5], which depends on the type of pinning. For the strongest one (by columnar defects) Trip is about 60-70 K for YBa2CuaOx. Therefore, the surface barrier should dominate at high temperatures T > 80 K, that has been proved experimentally [2]. At H > Hp the surface barrier is still active and determines the surface contribution to magnetization. If the bulk pinning can be neglected, we get an asymmetric surface magnetization loop [6] with the ascending branch (flux entry) described by: (1) where H is the external field and B is the magnetic induction inside a superconductor. The de-
0921-4534D4/$07.00 © 1994 - ElsevierScience B.V. All rights reserved. SSDI 0921-4534(94)02062-0
L. Burlachkov, IfM. Vinokur/Physica C 235 240 (1994) 2993 2994
2994
scending branch (flux exit) is described by: me~ = ¢0/16¢rA 2 << Hcl ~ meq,
(2)
where meq =- H - Beq is the equilibrium magnetization. These expressions enable to find the transport critical current J ~ in a simplest geometry, where a superconducting slab of thickness d imbedded into external magnetic field H parallel to its surface. We suggest that all the relaxation processes are over and the system is at equilibrium: B = Beq(H). In this situation the surface is "locked" by a barrier, which is characterized by activation energy (with parameters appropriate for YBa2CuaOx) eq
T
U,u~S(v)lkZ, ~ - - ~ . 10 4 for both vortex entry and exit, where 7- = (To T ) / T e . The transport current J*~, flowing along the slab, leads to a difference A H =_ He,~ - He,: = (4rr/c)J `~
(3)
between the fields Hen and He~ at the sides of the slab. Of course Her, > He~:, so that vortices enter the slab (by thermoactivation surmounting of the surface barrier) from the side He,~. Note that in [7] jt~ denoted the mean density of the current; here we prefer to use jt~ for a total current through a slab. From the condition A H ( B ) < men(B) - m a x ( B ) we get [7]: + B 2-
B
~ 8rrH"
(4)
In order to find the activation energy U,~,,.I as a function of jt~ at j~r < j~r, we have to combine the expressions for the activation energies Uen, Uex [8] derived for magnetization experiments (in the expression for Uen and Uex [8] we should use respectively He,~ and H , , instead of H) with Eq.(3) under the condition Uen = Ue~ U~u,'I. The latter condition provides the continuity of the vortex flux through the slab. As a result we gett U
,d,~,
¢0A __3/2 / ~ 1
=
V
¢
1
AH
(5)
(where 3' is the anisotropy) for A H _= (47r/c)J t~ > rneq. This condition is almost always satisfied at current densities greater than 1 0 3 A / c m 2 and usual samples with d >_ 0.1 rnm. A more complicate formula in the opposite limit A H < meq we present elsewhere. In the case where a bulk pinning is present altogether with a surface barrier, the vortices should successively surmount the surface and the bulk barriers. Therefore the role of the activation energy U will play the largest of U,~,~] and UbulkIf U , ~ f > Ub~,Ik, then a small applied current jt~ should flow along the surfaces only, thus U depends on the total current Jt~. In the opposite case, where U,~,~.r < Ub~,lk, jt~ is distributed over the bulk, and U depends on the current density, Jt~/d. In the case where samples of different thicknesses d are available from the same batch, this can provide a convenient tool to distinguish between the surface and bulk barriers. L.B. is grateful to the support from the Raschi Foundation and the Israel Academy of Science. V.M.V. acknowledges the support from the Argonne National Laboratory through U.S. Department of Energy, BES-Materials Sciences, under contract No. W-31-109-ENG-38. REFERENCES 1. V.N. Kopylov, A.E. Koshelev, I.F. Schegolev and T.G. Togonidze, Physica C 170, 291 (1990). 2. M. Konczykowski, L. Burlachkov, Y. Yeshurun and F. Holtzberg, Phys. Rev. B 43, 13707 (1991). 3. G. Blatter, M. Feigelman, V. Geshkenbein, A.I. Larkin and V.M. Vinokur, to be published in Rev. Mod. Phys. 4. C.P. Bean and J.D. Livingston, Phys. Rev. Lett. 12, 14 (1964). 5. D.R. Nelson and V. Vinokur, Phys. Rev. Lett. 68, 2398 (1992). 6. J.R. Clem, LTI3, (Plenum, NY, 1974) vol. 3, p. 102. 7. L. Burlachkov and V.M. Vinokur, Physica B 194-196, 1819 (1994). 8. L. Burlachkov, Phys. Rev. B 47, 8056 (1993).