- Email: [email protected]
Flux-creep and depinning from columnar defects in layered superconductors
Physica C 470 (2010) S898–S899
Contents lists available at ScienceDirect
Physica C journal homepage: www.elsevier.com/locate/physc
Flux-creep and depinning from columnar defects in layered superconductors M. Konczykowski a,*, C.J. van der Beek a, V. Mosser b, M. Li c, P.H. Kes c a
Laboratoire des Solides Irradiés, Ecole Polytechnique, CNRS-UMR 7642 & CEA/DSM/IRAMIS, 91128 Palaiseau, France ITRON, 76 Avenue Pierre Brossolette, 92240 Malakoff, France c Kamerlingh Onnes Laboratorium, Leiden University, P.O. Box 9506, 2300 RA Leiden, The Netherlands b
a r t i c l e
i n f o
Article history: Accepted 6 May 2010 Available online 12 May 2010 Keywords: Vortex lattice Flux pinning and creep Bose-glass Columnar defects
a b s t r a c t Localization of vortex lines on columnar defects introduced in BSCCO:2212 crystals by heavy ion irradiation is supposed to enhance the critical current Jc to the depairing limit [1]. In experiments, the increase of the magnetic irreversibility is not accompanied by suppression of flux creep, even at low temperatures. This impedes the determination of Jc. Using the Hall-array technique, we have determined the dependence of the energy barrier for flux creep U on current density J at various temperatures and applied magnetic fields. On the basis of the functional form of U(J) dependence, we identify three regimes of flux creep: from linear, Kim-Anderson like, at high currents, to logarithmic at intermediate currents, and power law at low currents. Critical currents determined from U(J) variations, lie orders of magnitude below the depairing current, indicating that the mechanism of creep is different from the half-loop nucleation predicted in the Bose-glass model. Ó 2010 Elsevier B.V. All rights reserved.
Flux-creep mediated by half-loop nucleation, expected in the Bose-glass formed by flux lines localized on columnar defects [2] was observed in BSCCO:2212 crystals at high temperatures, close to Tc [3]. This mechanism was identified from the power law dependence of energy barrier U on shielding current U / Ja (where a depends on the defect concentration). In the low temperature region of the phase diagram, at high shielding current, the size of nucleus may be as small as the interlayer spacing and a logarithmic U(J) dependence is expected U(J) / os ln(Jo/J) [1]. Here, o s is the energy necessary to liberate a ‘‘pancake” vortex and Jo is the depairing current. Here, we report on the systematic study of magnetic relaxation in BSCCO:2212 crystal with various densities of columnar defects. Selected, defect free optimally doped crystals were cut to several 200 lm wide rectangles. Samples were exposed to a beam of 5.8 GeV Pb ions at the GANIL facility in Caen, France. The defect concentration, expressed in matching fields B/ ranged from 0.2 to 2 T. The Hall-array technique was used for magnetic measurements. Samples were put on top of a line of 11 sensors of active area 8 8 lm2 each, realized in pseudomorphic GaAlAs heterostructures. Isothermal hysteresis loops of the local gradient of the magnetic induction, @B/@x i.e. the difference between B measured by two adjacent sensors, proportional to shielding current (J) vs. local magnetic induction were measured. Example of magnetic
* Corresponding author. Tel.: +33 1 69334503. E-mail address: [email protected] (M. Konczykowski). 0921-4534/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2010.05.003
hysteresis loops recorded at 40 K on crystals with B/ = 0.5 T and 2 T, are presented in Fig. 1. Surprisingly, @B/@x depends on magnetic induction even at B B/, when the single vortex pinning regime is expected. The relaxations of Bean critical state [5] were recorded in the flux penetration and flux exit modes. In order to emphasize the amplitude of magnetic relaxation, the temporal evolution of @B/@x in the flux exit mode is plotted for several applied fields. We extract the creep energy barrier vs. current relation using the method of Ref. [4]. Using the Maxwell equation: @B/ @t / r E we convert the local Bz(t) to the local electric field R xo 0 Ey ðxo Þ ¼ center @Bz =@tdx . Taking the local gradient @B/@x(xo) as proportional to J(xo) we reconstruct current–voltage relation E(J). The functional form of the E(J) relation is close to exponential indicative of flux creep via thermally activated jumps. The amplitude of the decay of irreversible magnetization is very large and strong dependence of U on magnetic field leads to the intermingling of the variation of U(J) and U(B). For this reason, sensors located close to the sample edge were used in order to reduce the variation of B during relaxation. Alternatively, we have used samples containing a ring shaped irradiated region surrounded by low pinning, pristine material. For the sensor located in the center of the ring E / @B/@t, while J / B Happl. The width of the hysteresis loop and the related shielding current depend on temperature and on the defect concentration. In the low currenthigh temperature limit, a power law variation of U vs. J is observed, in agreement with previous reports [1,3]. With decreasing temperature (i.e. larger currents), U(J) variation turns to logarithmic. At even lower temperatures, linear U(J) variation appears. In order
S899
M. Konczykowski et al. / Physica C 470 (2010) S898–S899
28
Records of magnetic relaxations 1-3000s H =1 to 6 kOe
40
T[K] 50 45 40 35 30 20
26
a
24 20
U/kT + C
B = 2T Φ
0 B =0.5T
22 20
Φ
18 -20
-40 -20000
T=40K
16
BSCCO:2212 optimaly doped irradiated with 5.8 GeV Pb ions -10000
14 0
10000
BSCCO:2212 optimaly doped irradiated with 1 GeV Pb ions B =0.5T
20000
120
B [G]
Φ
flux exit relaxation at H =0.1 T
to increase the range of explored current densities, we proceeded to the annealing of critical state. After recording the magnetic decay for 3000 s, sample was warmed up for a short period of time and cooled back to the initial temperature. Then, the decay was recorded again for several hundreds of seconds. Variations of U/kT vs. J, recorded at different temperatures and the U(J) curve reconstructed following Maley’s method [6] are depicted in Fig. 2. The apparent critical current and energy barrier Uo can be extracted from the linear and logarithmic variations of U(J). In both cases the values of Jc are several orders of magnitude below the depairing current. The energy barrier Uo obtained from linear U(J) is in the range of 0.1 eV, close to os, the energy needed for the depinning of a single ‘‘pancake” vortex from a columnar defect. This indicates that the mechanism of creep is different from halfloop nucleation at low temperatures. Collective pinning of vortex lines may take place at high defect concentrations explored here. In that case, sliding of Josephson vortices along the columnar defects is a possible flux creep process. In summary, we have identified several regimes of flux creep of vortices localized on columnar defects in layered superconductor. The description of the low temperature, high current regime is beyond the accepted Bose-glass model.
a
100
U [meV]
Fig. 1. Magnetic hysteresis loops of local gradient vs. magnetic induction recorded at 40 K on two BSCCO:2212 samples irradiated by 5.8 GeV Pb ions to the fluences corresponding to matching fields B/ = 2 and 0.5 T. Magnetic decays measured in flux exit mode on B/ = 2 T sample are shown.
50K 45K
80
40K 35K
60
30K
40
25K
0
20
40
60
80
dB/dx ∝ J [G/µm] Fig. 2. Energy barrier for flux creep vs. current variation obtained from magnetic relaxation in flux exit mode at B = 0.1 T on BSCCO:2212 sample irradiated with 5.8 GeV Pb ions (B/ = 0.5 T ). Upper panel shows raw records of U(J)/kT for different temperatures, on the lower panel U(J) dependence reconstructed following Maley method [6] is shown.
References [1] C.J. van der Beek, M. Konczykowski, V.M. Vinokur, G.W. Crabtree, T.W. Li, P.H. Kes, Phys. Rev. B 51 (1995) 15492. [2] D.R. Nelson, V.M. Vinokur, Phys. Rev. Lett. 68 (1992) 2398. [3] M. Konczykowski, N. Chikumoto, V.M. Vinokur, M.V. Feigel’man, Phys. Rev. B 51 (1995) 3957. [4] Y. Abulafia, A. Shaulov, Y. Wolfus, L. Burlachkov, Y. Yeshurun, D. Majer, E. Zeldov, V.M. Vinokur, Phys. Rev. Lett. 75 (1995) 2404. [5] C.P. Bean, Phys. Rev. Lett. 8 (1962) 250. [6] M.P. Maley, J.O. Willis, H. Lessure, M.E. McHenry, Phys. Rev. B 42 (1990) 2639.
Contents lists available at ScienceDirect
Physica C journal homepage: www.elsevier.com/locate/physc
Flux-creep and depinning from columnar defects in layered superconductors M. Konczykowski a,*, C.J. van der Beek a, V. Mosser b, M. Li c, P.H. Kes c a
Laboratoire des Solides Irradiés, Ecole Polytechnique, CNRS-UMR 7642 & CEA/DSM/IRAMIS, 91128 Palaiseau, France ITRON, 76 Avenue Pierre Brossolette, 92240 Malakoff, France c Kamerlingh Onnes Laboratorium, Leiden University, P.O. Box 9506, 2300 RA Leiden, The Netherlands b
a r t i c l e
i n f o
Article history: Accepted 6 May 2010 Available online 12 May 2010 Keywords: Vortex lattice Flux pinning and creep Bose-glass Columnar defects
a b s t r a c t Localization of vortex lines on columnar defects introduced in BSCCO:2212 crystals by heavy ion irradiation is supposed to enhance the critical current Jc to the depairing limit [1]. In experiments, the increase of the magnetic irreversibility is not accompanied by suppression of flux creep, even at low temperatures. This impedes the determination of Jc. Using the Hall-array technique, we have determined the dependence of the energy barrier for flux creep U on current density J at various temperatures and applied magnetic fields. On the basis of the functional form of U(J) dependence, we identify three regimes of flux creep: from linear, Kim-Anderson like, at high currents, to logarithmic at intermediate currents, and power law at low currents. Critical currents determined from U(J) variations, lie orders of magnitude below the depairing current, indicating that the mechanism of creep is different from the half-loop nucleation predicted in the Bose-glass model. Ó 2010 Elsevier B.V. All rights reserved.
Flux-creep mediated by half-loop nucleation, expected in the Bose-glass formed by flux lines localized on columnar defects [2] was observed in BSCCO:2212 crystals at high temperatures, close to Tc [3]. This mechanism was identified from the power law dependence of energy barrier U on shielding current U / Ja (where a depends on the defect concentration). In the low temperature region of the phase diagram, at high shielding current, the size of nucleus may be as small as the interlayer spacing and a logarithmic U(J) dependence is expected U(J) / os ln(Jo/J) [1]. Here, o s is the energy necessary to liberate a ‘‘pancake” vortex and Jo is the depairing current. Here, we report on the systematic study of magnetic relaxation in BSCCO:2212 crystal with various densities of columnar defects. Selected, defect free optimally doped crystals were cut to several 200 lm wide rectangles. Samples were exposed to a beam of 5.8 GeV Pb ions at the GANIL facility in Caen, France. The defect concentration, expressed in matching fields B/ ranged from 0.2 to 2 T. The Hall-array technique was used for magnetic measurements. Samples were put on top of a line of 11 sensors of active area 8 8 lm2 each, realized in pseudomorphic GaAlAs heterostructures. Isothermal hysteresis loops of the local gradient of the magnetic induction, @B/@x i.e. the difference between B measured by two adjacent sensors, proportional to shielding current (J) vs. local magnetic induction were measured. Example of magnetic
* Corresponding author. Tel.: +33 1 69334503. E-mail address: [email protected] (M. Konczykowski). 0921-4534/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2010.05.003
hysteresis loops recorded at 40 K on crystals with B/ = 0.5 T and 2 T, are presented in Fig. 1. Surprisingly, @B/@x depends on magnetic induction even at B B/, when the single vortex pinning regime is expected. The relaxations of Bean critical state [5] were recorded in the flux penetration and flux exit modes. In order to emphasize the amplitude of magnetic relaxation, the temporal evolution of @B/@x in the flux exit mode is plotted for several applied fields. We extract the creep energy barrier vs. current relation using the method of Ref. [4]. Using the Maxwell equation: @B/ @t / r E we convert the local Bz(t) to the local electric field R xo 0 Ey ðxo Þ ¼ center @Bz =@tdx . Taking the local gradient @B/@x(xo) as proportional to J(xo) we reconstruct current–voltage relation E(J). The functional form of the E(J) relation is close to exponential indicative of flux creep via thermally activated jumps. The amplitude of the decay of irreversible magnetization is very large and strong dependence of U on magnetic field leads to the intermingling of the variation of U(J) and U(B). For this reason, sensors located close to the sample edge were used in order to reduce the variation of B during relaxation. Alternatively, we have used samples containing a ring shaped irradiated region surrounded by low pinning, pristine material. For the sensor located in the center of the ring E / @B/@t, while J / B Happl. The width of the hysteresis loop and the related shielding current depend on temperature and on the defect concentration. In the low currenthigh temperature limit, a power law variation of U vs. J is observed, in agreement with previous reports [1,3]. With decreasing temperature (i.e. larger currents), U(J) variation turns to logarithmic. At even lower temperatures, linear U(J) variation appears. In order
S899
M. Konczykowski et al. / Physica C 470 (2010) S898–S899
28
Records of magnetic relaxations 1-3000s H =1 to 6 kOe
40
T[K] 50 45 40 35 30 20
26
a
24 20
U/kT + C
B = 2T Φ
0 B =0.5T
22 20
Φ
18 -20
-40 -20000
T=40K
16
BSCCO:2212 optimaly doped irradiated with 5.8 GeV Pb ions -10000
14 0
10000
BSCCO:2212 optimaly doped irradiated with 1 GeV Pb ions B =0.5T
20000
120
B [G]
Φ
flux exit relaxation at H =0.1 T
to increase the range of explored current densities, we proceeded to the annealing of critical state. After recording the magnetic decay for 3000 s, sample was warmed up for a short period of time and cooled back to the initial temperature. Then, the decay was recorded again for several hundreds of seconds. Variations of U/kT vs. J, recorded at different temperatures and the U(J) curve reconstructed following Maley’s method [6] are depicted in Fig. 2. The apparent critical current and energy barrier Uo can be extracted from the linear and logarithmic variations of U(J). In both cases the values of Jc are several orders of magnitude below the depairing current. The energy barrier Uo obtained from linear U(J) is in the range of 0.1 eV, close to os, the energy needed for the depinning of a single ‘‘pancake” vortex from a columnar defect. This indicates that the mechanism of creep is different from halfloop nucleation at low temperatures. Collective pinning of vortex lines may take place at high defect concentrations explored here. In that case, sliding of Josephson vortices along the columnar defects is a possible flux creep process. In summary, we have identified several regimes of flux creep of vortices localized on columnar defects in layered superconductor. The description of the low temperature, high current regime is beyond the accepted Bose-glass model.
a
100
U [meV]
Fig. 1. Magnetic hysteresis loops of local gradient vs. magnetic induction recorded at 40 K on two BSCCO:2212 samples irradiated by 5.8 GeV Pb ions to the fluences corresponding to matching fields B/ = 2 and 0.5 T. Magnetic decays measured in flux exit mode on B/ = 2 T sample are shown.
50K 45K
80
40K 35K
60
30K
40
25K
0
20
40
60
80
dB/dx ∝ J [G/µm] Fig. 2. Energy barrier for flux creep vs. current variation obtained from magnetic relaxation in flux exit mode at B = 0.1 T on BSCCO:2212 sample irradiated with 5.8 GeV Pb ions (B/ = 0.5 T ). Upper panel shows raw records of U(J)/kT for different temperatures, on the lower panel U(J) dependence reconstructed following Maley method [6] is shown.
References [1] C.J. van der Beek, M. Konczykowski, V.M. Vinokur, G.W. Crabtree, T.W. Li, P.H. Kes, Phys. Rev. B 51 (1995) 15492. [2] D.R. Nelson, V.M. Vinokur, Phys. Rev. Lett. 68 (1992) 2398. [3] M. Konczykowski, N. Chikumoto, V.M. Vinokur, M.V. Feigel’man, Phys. Rev. B 51 (1995) 3957. [4] Y. Abulafia, A. Shaulov, Y. Wolfus, L. Burlachkov, Y. Yeshurun, D. Majer, E. Zeldov, V.M. Vinokur, Phys. Rev. Lett. 75 (1995) 2404. [5] C.P. Bean, Phys. Rev. Lett. 8 (1962) 250. [6] M.P. Maley, J.O. Willis, H. Lessure, M.E. McHenry, Phys. Rev. B 42 (1990) 2639.