Flux pinning; Magneto-optical effect; Ratchet effect; Superconductors; Finite element method; Ginzburg-Landau theory
Abstract :
[en] Considering a noncentrosymmetric pinning texture composed of a square array of triangular holes, the magnetic flux penetration and expulsion are investigated experimentally and theoretically. A direct visualization of the magnetic landscape obtained using a magneto-optical technique on a Nb film is complemented by a multiscale numerical modeling. This combined approach allows the magnetic flux dynamics to be identified from the single flux quantum limit up to the macroscopic electromagnetic response. Within the theoretical framework provided by time-dependent Ginzburg-Landau simulations, an estimation of the in-plane current anisotropy is obtained and its dependence with the radius of the curvature of hole vertices is addressed. These simulations show that current crowding plays an important role in channeling the flux motion, favoring hole-to-hole flux hopping rather than promoting interstitial flux displacement in between the holes. The resulting anisotropy of the critical current density gives rise to a distinct pattern of discontinuity lines for increasing and decreasing applied magnetic fields, in sharp contrast to the invariable patterns reported for centrosymmetric pinning potentials. This observation is partially accounted for by the rectification effect, as demonstrated by finite-element modeling. At low temperatures, where magnetic field penetration is dominated by thermomagnetic instabilities, highly directional magnetic flux avalanches with a fingerlike shape are observed to propagate along the easy axis of the pinning potential. This morphology is reproduced by numerical simulations. Our findings demonstrate that anisotropic pinning landscapes and, in particular, ratchet potentials produce subtle modifications to the critical state field profile that are reflected in the distribution of discontinuity lines.
Disciplines :
Physics
Author, co-author :
Motta, M. ✱; Universidade Federal de São Carlos, São Paulo, Brazil > Departamento de Física
Burger, Loïc ✱; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Electronique et microsystèmes
Jiang, L.; Northwestern Polytechnical University, Xi’an, China > School of Aeronautics
González Acosta, J. L.; Universidad del Magdalena, Santa Marta, Colombia > Facultad de Ingeniería
Jelic, Z. L.; Nokia Bell Labs, Antwerp, Belgium
Colauto, F.; Universidade Federal de São Carlos, São Paulo, Brazil > Departamento de Física
Ortiz, W. A.; Universidade Federal de São Carlos, São Paulo, Brazil > Departamento de Física
Johansen, T. H.; University of Oslo, Norway > Department of Physics
Miloševic, M. V.; Universiteit Antwerpen, Antwerpen, Belgium > Department of Physics
Cirillo, C.; Università degli Studi di Salerno, Fisciano (Sa), Italy > CNR-SPIN
Attanasio, C.; Università degli Studi di Salerno, Fisciano (Sa), Italy > CNR-SPIN and Dipartimento di Fisica “E.R. Caianiello”
Xue, C.; Northwestern Polytechnical University, Xi’an, China > 0School of Mechanics, Civil Engineering and Architecture, and MIIT Key Laboratory of Dynamics and Control of Complex Systems
Silhanek, Alejandro ; Université de Liège - ULiège > Département de physique > Physique expérimentale des matériaux nanostructurés
Vanderheyden, Benoît ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Electronique et microsystèmes
R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics (Addison-Wesley, Reading, 1963), Vol. 1, Chap. 46.
J. M. R. Parrondo and P. Español, Am. J. Phys. 64, 1125 (1996) AJPIAS 0002-9505 10.1119/1.18393.
M. O. Magnasco, Phys. Rev. Lett. 71, 1477 (1993) PRLTAO 0031-9007 10.1103/PhysRevLett.71.1477.
P. Hänggi and F. Marchesoni, Rev. Mod. Phys. 81, 387 (2009) RMPHAT 0034-6861 10.1103/RevModPhys.81.387.
S. Matthias and F. Müller, Nature (London) 424, 53 (2003) NATUAS 0028-0836 10.1038/nature01736.
G. Mahmud, C. J. Campbell, K. J. M. Bishop, Y. A. Komarova, O. Chaga, S. Soth, S. Huda, K. Kandere-Grzybowska, and B. A. Grzybowski, Nat. Phys. 5, 606 (2009) 1745-2473 10.1038/nphys1306.
X. Jiang, D. A. Bruzewicz, A. P. Wong, M. Piel, and G. M. Whitesides, Proc. Natl. Acad. Sci. 102, 975 (2005) PNASA6 0027-8424 10.1073/pnas.0408954102.
P. Galajda, J. Keymer, P. Chaikin, and R. Austin, J. Bacteriol. 189, 8704 (2007) JOBAAY 0021-9193 10.1128/JB.01033-07.
M. B. Wan, C. J. Olson Reichhardt, Z. Nussinov, and C. Reichhardt, Phys. Rev. Lett. 101, 018102 (2008) PRLTAO 0031-9007 10.1103/PhysRevLett.101.018102.
P. K. Ghosh, V. R. Misko, F. Marchesoni, and F. Nori, Phys. Rev. Lett. 110, 268301 (2013) PRLTAO 0031-9007 10.1103/PhysRevLett.110.268301.
A. Guidobaldi, Y. Jeyaram, I. Berdakin, V. V. Moshchalkov, C. A. Condat, V. I. Marconi, L. Giojalas, and A. V. Silhanek, Phys. Rev. E 89, 032720 (2014) PLEEE8 1539-3755 10.1103/PhysRevE.89.032720.
H. Linke, B. J. Alemán, L. D. Melling, M. J. Taormina, M. J. Francis, C. C. Dow-Hygelund, V. Narayanan, R. P. Taylor, and A. Stout, Phys. Rev. Lett. 96, 154502 (2006) PRLTAO 0031-9007 10.1103/PhysRevLett.96.154502.
G. Lagubeau, M. Le Merrer, C. Clanet, and D. Quéré, Nat. Phys. 7, 395 (2011) 1745-2473 10.1038/nphys1925.
C.-S. Lee, B. Jankó, I. Derényi, and A.-L. Barabasi, Nature (London) 400, 337 (1999) NATUAS 0028-0836 10.1038/22485.
J. F. Wambaugh, C. Reichhardt, C. J. Olson, F. Marchesoni, and F. Nori, Phys. Rev. Lett. 83, 5106 (1999) PRLTAO 0031-9007 10.1103/PhysRevLett.83.5106.
J. E. Villegas, S. Savel'ev, F. Nori, E. M. Gonzalez, J. V. Anguita, R. Garcia, and J. L. Vicent, Science 302, 1188 (2003) SCIEAS 0036-8075 10.1126/science.1090390.
V. Rouco, A. Palau, C. Monton, N. Del-Valle, C. Navau, A. Sanchez, X. Obradors, and T. Puig, New J. Phys. 17, 073022 (2015) NJOPFM 1367-2630 10.1088/1367-2630/17/7/073022.
J. Albrecht, A. T. Matveev, J. Strempfer, H. U. Habermeier, D. V. Shantsev, Y. M. Galperin, and T. H. Johansen, Phys. Rev. Lett. 98, 117001 (2007) PRLTAO 0031-9007 10.1103/PhysRevLett.98.117001.
M. Menghini, J. Van de Vondel, D. G. Gheorghe, R. J. Wijngaarden, and V. V. Moshchalkov, Phys. Rev. B 76, 184515 (2007) PRBMDO 1098-0121 10.1103/PhysRevB.76.184515.
D. V. Denisov, A. L. Rakhmanov, D. V. Shantsev, Y. M. Galperin, and T. H. Johansen, Phys. Rev. B 73, 014512 (2006) PRBMDO 1098-0121 10.1103/PhysRevB.73.014512.
P. de Gennes, Superconductivity of Metals and Alloys (Westview, Boulder, CO, 1999).
D. Cerbu, V. N. Gladilin, J. Cuppens, J. Fritzsche, J. Tempere, J. T. Devreese, V. V. Moshchalkov, A. V. Silhanek, and J. Van de Vondel, New J. Phys. 15, 063022 (2013) NJOPFM 1367-2630 10.1088/1367-2630/15/6/063022.
C. Jooss, J. Albrecht, H. Kuhn, S. Leonhardt, and H. Kronmüller, Rep. Prog. Phys. 65, 651 (2002) RPPHAG 0034-4885 10.1088/0034-4885/65/5/202.
L. E. Helseth, R. W. Hansen, E. I. Ilyashenko, M. Baziljevich, and T. H. Johansen, Phys. Rev. B 64, 174406 (2001) PRBMDO 0163-1829 10.1103/PhysRevB.64.174406.
M. Pannetier, R. J. Wijngaarden, I. Fløan, J. Rector, B. Dam, R. Griessen, P. Lahl, and R. Wördenweber, Phys. Rev. B 67, 212501 (2003) PRBMDO 0163-1829 10.1103/PhysRevB.67.212501.
A. V. Silhanek, L. Van Look, S. Raedts, R. Jonckheere, and V. V. Moshchalkov, Phys. Rev. B 68, 214504 (2003) PRBMDO 0163-1829 10.1103/PhysRevB.68.214504.
M. S. Welling, R. J. Wijngaarden, C. M. Aegerter, R. Wördenweber, and P. Lahl, Physica C 404, 410 (2004) PHYCE6 0921-4534 10.1016/j.physc.2003.11.026.
D. G. Gheorghe, M. Menghini, R. J. Wijngaarden, S. Raedts, A. V. Silhanek, and V. V. Moshchalkov, Physica C 437-438, 69 (2006) PHYCE6 0921-4534 10.1016/j.physc.2005.12.021.
M. Motta, Phys. Rev. B 89, 134508 (2014) PRBMDO 1098-0121 10.1103/PhysRevB.89.134508.
F. Colauto, M. Motta, and W. Ortiz, Supercond. Sci. Technol. 34, 013022 (2021) SUSTEF 0953-2048 10.1088/1361-6668/abac1e.
O.-A. Adami, Ž. L. Jelić, C. Xue, M. Abdel-Hafiez, B. Hackens, V. V. Moshchalkov, M. V. Milošević, J. Van de Vondel, and A. V. Silhanek, Phys. Rev. B 92, 134506 (2015) PRBMDO 1098-0121 10.1103/PhysRevB.92.134506.
J. Van de Vondel, V. N. Gladilin, A. V. Silhanek, W. Gillijns, J. Tempere, J. T. Devreese, and V. V. Moshchalkov, Phys. Rev. Lett. 106, 137003 (2011) PRLTAO 0031-9007 10.1103/PhysRevLett.106.137003.
J. R. Clem and K. K. Berggren, Phys. Rev. B 84, 174510 (2011) PRBMDO 1098-0121 10.1103/PhysRevB.84.174510.
A. V. Silhanek, M. V. Milošević, R. B. G. Kramer, G. R. Berdiyorov, J. Van de Vondel, R. F. Luccas, T. Puig, F. M. Peeters, and V. V. Moshchalkov, Phys. Rev. Lett. 104, 017001 (2010) PRLTAO 0031-9007 10.1103/PhysRevLett.104.017001.
L. Embon, Y. Anahory, Ž. L. Jelić, E. O. Lachman, Y. Myasoedov, M. E. Huber, G. P. Mikitik, A. V. Silhanek, M. V. Milošević, A. Gurevich, and E. Zeldov, Nat. Commun. 8, 85 (2017) 2041-1723 10.1038/s41467-017-00089-3.
D. Y. Vodolazov and F. M. Peeters, Phys. Rev. B 76, 014521 (2007) PRBMDO 1098-0121 10.1103/PhysRevB.76.014521.
W. V. Pogosov, V. R. Misko, H. J. Zhao, and F. M. Peeters, Phys. Rev. B 79, 014504 (2009) PRBMDO 1098-0121 10.1103/PhysRevB.79.014504.
I. Charaev, T. Silbernagel, B. Bachowsky, A. Kuzmin, S. Doerner, K. Ilin, A. Semenov, D. Roditchev, D. Yu. Vodolazov, and M. Siegel, Phys. Rev. B 96, 184517 (2017) 2469-9950 10.1103/PhysRevB.96.184517.
A. Badía-Majós and C. López, Supercond. Sci. Technol. 25, 104004 (2012) 10.1088/0953-2048/25/10/104004.
A. Badía-Majós and C. López, Supercond. Sci. Technol. 28, 024003 (2015) 10.1088/0953-2048/28/2/024003.
Y. B. Kim, C. F. Hempstead, and A. R. Strnad, Phys. Rev. Lett. 9, 306 (1962) PRLTAO 0031-9007 10.1103/PhysRevLett.9.306.
J. I. Vestgarden, D. V. Shantsev, Y. M. Galperin, and T. H. Johansen, Phys. Rev. B 84, 054537 (2011) PRBMDO 1098-0121 10.1103/PhysRevB.84.054537.
E. H. Brandt, Phys. Rev. B 52, 15442 (1995) PRBMDO 0163-1829 10.1103/PhysRevB.52.15442.
L. Prigozhin and V. Sokolovsky, Supercond. Sci. Technol. 31, 055018 (2018) SUSTEF 0953-2048 10.1088/1361-6668/aab75d.
J. I. Vestgarden, F. Colauto, A. M. H. de Andrade, A. A. M. Oliveira, W. A. Ortiz, and T. H. Johansen, Phys. Rev. B 92, 144510 (2015) PRBMDO 1098-0121 10.1103/PhysRevB.92.144510.
M. Motta, F. Colauto, R. Zadorosny, T. H. Johansen, R. B. Dinner, M. G. Blamire, G. W. Ataklti, V. V. Moshchalkov, A. V. Silhanek, and W. A. Ortiz, Phys. Rev. B 84, 214529 (2011) PRBMDO 1098-0121 10.1103/PhysRevB.84.214529.
R. J. Watts-Tobin, Y. Krähenbühl, and L. Kramer, J. Low Temp. Phys. 42, 459 (1981) JLTPAC 0022-2291 10.1007/BF00117427.
A. Bossavit, IEEE Proc. A 135, 493 (1988) 10.1049/ip-a-1.1988.0077.
L. Burger, C. Geuzaine, F. Henrotte, and B. Vanderheyden, COMPEL 38, 1441 (2019) CODUDU 0332-1649 10.1108/COMPEL-11-2018-0488.
F. Henrotte, B. Meys, H. Hedia, P. Dular, and W. Legros, IEEE Trans. Magn. 35, 3 (1999) IEMGAQ 0018-9464 10.1109/20.767235.
C. Geuzaine and J.-F. Remacle, Int. J. Numer. Methods Eng. 79, 1309 (2009) IJNMBH 0029-5981 10.1002/nme.2579.
P. Dular, C. Geuzaine, F. Henrotte, and W. Legros, IEEE Trans. Magn. 34, 3395 (1998) IEMGAQ 0018-9464 10.1109/20.717799.