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Current-Phase Relations of Josephson Junctions with Ferromagnetic Barriers

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Current-Phase Relations of Josephson Junctions with Ferromagnetic Barriers CURRENT-PHASE RELATIONS OF JOSEPHSON JUNCTIONS WITH FERROMAGNETIC BARRIERS BY SERGEY MAKSIMOVICH FROLOV B.S., Moscow Institute of Physics and Technology, 2000 DISSERTATION Submitted in partial ful¯llment of the requirements for the degree of Doctor of Philosophy in Physics in the Graduate College of the University of Illinois at Urbana-Champaign, 2005 Urbana, Illinois CURRENT-PHASE RELATIONS OF JOSEPHSON JUNCTIONS WITH FERROMAGNETIC BARRIERS Sergey Maksimovich Frolov, Ph.D. Department of Physics University of Illinois at Urbana-Champaign, 2005 Dale J. Van Harlingen, Advisor We have studied Superconductor-Ferromagnet-Superconductor (SFS) Nb-CuNi-Nb Josephson junctions that can transition between the 0 junction and the ¼ junction states with temperature. By direct measurement of the current-phase relation (CPR) we have determined that the critical current of some SFS junctions changes sign as a function of temperature, indicating the ¼ junction behavior. The CPR was de- termined by incorporating the junction into an rf SQUID geometry coupled to a dc SQUID magnetometer, allowing measurement of the junction phase di®erence. No evidence for the second-order Josephson tunneling, that was predicted by a number of theories to be observable near the 0-¼ transition temperature, was found in the CPR. In non-uniform 0-¼ SFS junctions with spatial variations in the e®ective bar- rier thickness, our data is consistent with spontaneous currents circulating around the 0-¼ boundaries. These spontaneous currents give rise to Shapiro steps in the current- voltage characteristics at half-integer Josephson voltages when the rf-modulation is added to the bias current. The degree of 0-¼ junction non-uniformity was deter- mined from measurements of the critical current vs. applied magnetic flux patterns. Scanning SQUID Microscope imaging of superconducting arrays with SFS junctions revealed spontaneous currents circulating in the arrays in the ¼ junction state below the 0-¼ transition temperature. iii Acknowledgements I would like to thank Professor Dale Van Harlingen for teaching me everything I know about experimental physics, for introducing me to the fascinating science of superconducting devices and for guiding me through my graduate studies. Dale is an outstanding scientist and mentor, and a wonderful person. Professor Valery Ryazanov was my undergraduate advisor and later became an invaluable collaborator in my graduate work. I thank him for his trust and support, for his expertise and intuition, and for good times in Chernogolovka and Urbana. I am grateful to the members of the DVH group Kevin Osborn, Joe Hilliard, Mar- tin Stehno, Micah Stoutimore, Madalina Colci, David Caplan, Willie Ong, Francoise Kidwingira, Dan Bahr and Adele Ruosi. I would like to especially thank William Neils a.k.a. \physicist formerly known as Bill", Tony Bonetti and Trevis Crane for their patience in training me and helping me with some of the world's most ridicu- lous experimental problems. I also thank students from the Institute of Solid State Physics in Chernogolovka Alexey Feofanov and Vitaliy Bolginov who I collaborated with in studying SFS Josephson junctions. It is di±cult to appreciate enough the contribution of Vladimir Oboznov, a tech- nology expert who fabricated the state-of-the-art samples that allowed us to perform many novel and important experiments on SFS junctions. In Urbana, we are lucky to have Tony Banks as a supervisor of the microfabrication facility and a walking iv encyclopedia on fabrication technology. I thank some of the teachers whom I was fortunate to learn from in the classroom: Mrs. A.V. Gluschenko, Mr. S.V. Sokirko, Mrs. L. Tarasova, Mrs. T.A. Fedulkina, Mrs. N.E. Talaeva, Mrs. O.N. Soboleva, Mrs. T.M. Solomasova, Mrs. V.I. Zhurina, Mrs. M.A. Ismailova, Mrs. V. P. Saliy, Mrs. N.A. Babich, Ms. E.Yu. Kassiadi, Mrs. Y.V. Lyamina, Dr. N.G. Chernaya, Dr. T.V. Klochkova, Dr. V.T. Rykov, Dr. N.H. Agakhanov, Dr. V.V. Mozhaev, Dr. A.S. Dyakov, Professor G.N. Yakovlev, Dr. G.V. Kolmakov, Dr. N.M. Trukhan, Professor F.F. Kamenets, Professor Yu.V. Sidorov, Dr. E.V. Voronov, Dr. S.N. Burmistrov, Dr. M.R. Trunin, Dr. V.N. Zverev, and Professor A.J. Leggett. My family played a crucial role by stimulating me to learn, work and go forward. For that I thank my wife Olya, my parents Nina and Maksim, my grandparents Irina, Roma, Mikhail and Tasya, and my great-grandparents Tatyana and Vladimir. I was doing my ¯rst current-phase relation measurements in the Summer of 2003 feeling that my thesis was going to be an exercise with a predetermined answer. Then came the Spring of 2004, when the group in Chernogolovka discovered another 0-¼ transition at smaller barrier thicknesses, and the group from Grenoble reported half-integer Shapiro steps in SFS junctions. These experiments literally turned the picture upside down, brought back the question of second-order Josephson tunneling and allowed us to explore the beautiful physics of 0-¼ junctions. I therefore feel justi¯ed to thank nature for being more complex than we anticipated, and for willing to play our game even after centuries of interrogation. This work was supported by the National Science Foundation grant EIA-01-21568, the U.S. Civilian Research and Development Foundation grant RP1-2413-CG-02. We also acknowledge extensive use of the Microfabrication Facility of the Frederick Seitz Materials Research Laboratory at the University of Illinois at Urbana-Champaign. v Table of Contents Chapter 1 Josephson Current-Phase Relation . 1 1.1 The Josephson e®ects . 1 1.2 Negative critical currents - ¼ junctions . 7 1.3 Non-sinusoidal current-phase relations . 16 Chapter 2 ¼ Junctions in Multiply-Connected Geometries . 21 2.1 ¼ junction in an rf SQUID . 21 2.2 ¼ junction in a dc SQUID . 27 2.3 Arrays of ¼ junctions . 33 Chapter 3 Proximity E®ect in Ferromagnets . 38 3.1 Order parameter oscillations in a ferromagnet . 38 3.2 SFS Josephson junctions . 44 Chapter 4 Fabrication and Characterization of SFS Junctions. 50 4.1 Magnetism of CuNi thin ¯lms . 50 4.2 Fabrication procedures . 54 4.3 Transport measurements procedure . 58 4.4 Critical current vs. barrier thickness . 61 4.5 Critical current vs. temperature . 64 Chapter 5 Phase-Sensitive Experiments on Uniform SFS Junctions . 69 5.1 Measurement technique . 71 5.2 Current-phase relation data and analysis . 79 5.3 E®ects of residual magnetic ¯eld . 84 Chapter 6 Experiments on Non-Uniform SFS 0-¼ Junctions. 89 6.1 Di®raction patterns of 0-¼ junctions . 89 6.2 Spontaneous currents in 0-¼ junctions . 101 6.3 Half-integer Shapiro steps in 0-¼ junctions . 108 Chapter 7 Search for sin(2Á) Current-Phase Relation . 114 vi Chapter 8 Experiments on Arrays of SFS Junctions . 120 8.1 Imaging arrays with a scanning SQUID microscope . 121 8.2 Spontaneous currents in SFS ¼ junction arrays . 127 References . 136 Author's Biography . 142 vii CURRENT-PHASE RELATIONS OF JOSEPHSON JUNCTIONS WITH FERROMAGNETIC BARRIERS Sergey Maksimovich Frolov, Ph.D. Department of Physics University of Illinois at Urbana-Champaign, 2005 Dale J. Van Harlingen, Advisor We have studied Superconductor-Ferromagnet-Superconductor (SFS) Nb-CuNi- Nb Josephson junctions that can transition between the 0 junction and the ¼ junc- tion states with temperature. By direct measurement of the current-phase relation (CPR) we have determined that the critical current of some SFS junctions changes sign as a function of temperature, indicating the ¼ junction behavior. The CPR was determined by incorporating the junction into an rf SQUID geometry coupled to a dc SQUID magnetometer, allowing measurement of the junction phase di®erence. No evidence for the second-order Josephson tunneling, that was predicted by a number of theories to be observable near the 0-¼ transition temperature, was found in the CPR. In non-uniform 0-¼ SFS junctions with spatial variations in the e®ective bar- rier thickness, our data is consistent with spontaneous currents circulating around the 0-¼ boundaries. These spontaneous currents give rise to Shapiro steps in the current- voltage characteristics at half-integer Josephson voltages when the rf-modulation is added to the bias current. The degree of 0-¼ junction non-uniformity was deter- mined from measurements of the critical current vs. applied magnetic flux patterns. Scanning SQUID Microscope imaging of superconducting arrays with SFS junctions revealed spontaneous currents circulating in the arrays in the ¼ junction state below the 0-¼ transition temperature. Chapter 1 Josephson Current-Phase Relation 1.1 The Josephson e®ects The superconducting state of matter was originally identi¯ed through the total loss of electrical resistance by certain metals (Hg, Pb, Nb, Al) cooled to su±ciently low temperatures (» 1 ¡ 10 K) [1]. The analogy can be drawn to the frictionless flow of liquid, the phenomenon known as the superfluidity. In 4He, below the \lambda temperature", which is approximately 2:17 K at the atmospheric pressure, the Bose- Einstein condensation takes place: an anomalously large number of molecules occupy the ground state and do not participate in the energy exchange with the environment. The di®erence from the case of metals is that helium liquid consists of diatomic mole- cules, which are bosons, but the electrical current in metals is created by electrons, which are fermions. Fermions cannot undergo the Bose-Einstein condensation due to the Pauli exclusion principle. Instead, at zero temperature electrons occupy all avail- able states up to the Fermi energy, which is determined by the density of conduction electrons. However, two electrons in a metal can couple via a mechanism known as the 1 Cooper pairing. An electron moving through a lattice of ions creates vibrations (phonons), which can be absorbed by another electron. The interaction that arises as a result can be attractive provided the electron-phonon coupling is strong enough.
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