General boundary conditions for quasiclassical theory of superconductivity in the diffusive limit: application to strongly spin-polarized systems

Eschrig, Matthias; Cottet, Audrey; Belzig, Wolfgang; Linder, Jacob

doi:10.1088/1367-2630/17/8/083037

Cited by 118 publications

(149 citation statements)

References 94 publications

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“…Spin-filtering barriers are described by the generalized Kuprianov-Lukichev boundary conditions [50], which include spin-polarized tunneling at the SF interfaces [51,52],…”

Section: Spin-filtering Boundary Conditions Beyond the Quasiclasmentioning

confidence: 99%

Anomalous current in diffusive ferromagnetic Josephson junctions

2017

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We demonstrate that in diffusive superconductor/ferromagnet/superconductor (S/F/S) junctions a finite, anomalous Josephson current can flow even at zero phase difference between the S electrodes. The conditions for the observation of this effect are noncoplanar magnetization distribution and a broken magnetization inversion symmetry of the superconducting current. The latter symmetry is intrinsic for the widely used quasiclassical approximation and prevented previous works based on this approximation from obtaining the Josephson anomalous current. We show that this symmetry can be removed by introducing spin-dependent boundary conditions for the quasiclassical equations at the superconducting/ferromagnet interfaces in diffusive systems. Using this recipe, we consider generic multilayer magnetic systems and determine the ideal experimental conditions in order to maximize the anomalous current.

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“…Spin-filtering barriers are described by the generalized Kuprianov-Lukichev boundary conditions [50], which include spin-polarized tunneling at the SF interfaces [51,52],…”

Section: Spin-filtering Boundary Conditions Beyond the Quasiclasmentioning

confidence: 99%

Anomalous current in diffusive ferromagnetic Josephson junctions

2017

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“…The expressions (21) and (24) define the Josephson phase profile φ(x) which now depends only on φ 0 . To find φ 0 we take into account that in the ground state the total Josephson current I y = 0.…”

Section: Phase Transitions Due To the Shifting Of The Vortexmentioning

confidence: 99%

“…[17][18][19][20] and references therein) or complicated noncollinear distribution of the magnetization (see Refs. [21][22][23] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Anomalous Josephson effect controlled by an Abrikosov vortex

et al. 2017

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The possibility of a fast and precise Abrikosov vortex manipulation by a focused laser beam opens the way to create laser-driven Josephson junctions. We theoretically demonstrate that a vortex pinned in the vicinity of the Josephson junction generates an arbitrary ground state phase which can be equal not only to 0 or π but to any desired ϕ 0 value in between. Such ϕ 0 junctions have many peculiar properties and may be effectively controlled by the optically driven Abrikosov vortex. Also we theoretically show that the Josephson junction with the embedded vortex can serve as an ultrafast memory cell operating at sub THz frequencies. I. INTRODUCTIONJosephson junctions (JJs) with nonzero spontaneous phase difference between the superconducting electrodes in the ground state (the so-called π , ϕ 0 , and ϕ JJs) have become the subject of intensive theoretical and experimental study during the past decade [1,2]. The most striking feature of such junctions is their ability to generate a current in the superconducting circuit, thus acting as a phase battery [3][4][5][6]. In addition, relatively small variation of the system parameters may provoke dramatic changes in the ground state phase difference, which is believed to provide new effective tools for controlling the currents in microelectronic devices (see, e.g., Refs. [7,8]).There are several generic mechanisms leading to the spontaneous appearance of nonzero Josephson phase. The basic one reveals when the superconducting (S) electrodes are separated by a ferromagnetic (F) layer. The exchange field inside the ferromagnet produces the spatial oscillations of the Cooper pair wave function, and depending on the ratio between the oscillation period and the F-layer thickness the ground state phase is equal to 0 or π (these cases are referred as 0 or π JJs, respectively) [9][10][11]. A peculiar situation is realized when the thickness d of the ferromagnet varies along the junction in a way that in some parts of the ferromagnet the value of d corresponds to the 0 state while in other parts to the π state (see Ref. [12] and references therein). If there is only a slight difference between the areas of the "0" and "π " regions the phase frustration can result in the appearance of a state with the spontaneous phase difference φ = ±ϕ = 0,π which is degenerate (ϕ JJ) (see Ref.[13] and references therein). A similar effect takes place in Josephson junctions with the current injectors acting as an effective source of the phase jumps along the junction (see and references therein). One can also obtain a ϕ 0 JJ, where the ground state phase φ = ϕ 0 is not degenerate, e.g., using the JJs with broken inversion symmetry [17]. In this case the superconducting current I through the junction should not be necessarily an odd function of the phase difference φ and can take the form I = I c sin(φ + ϕ 0 ) [17]. Such situation is realized in the S|F|S junctions with strong spin-orbit coupling (see and references therein) or complicated noncollinear distribution of the magnetization (see an...

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“…(7) deals with the long-range ESC transformed adiabatically in space under the action of spin gauge fields. In FM/SC systems with the usual spin-singlet superconductors such correlations can appear only as a result of the nonadiabatic spin-flip which converts MSC into the ESC [26,28,37]. This process occurs within the thin layer near the FM/SC interface and can be described by the effective boundary conditions.…”

Section: Boundary Conditionsmentioning

confidence: 99%

“…So far, proximity and transport calculations in SC/FM hybrids have mostly concentrated on either fully polarized systems, so-called half metals [24][25][26][27][28], or in the opposite limit of weakly polarized systems [23,29], where the difference between spin subbands is completely neglected. However, most FMs have an intermediate exchange splitting of the energy bands of the order of but less than the Fermi energy.…”

Section: Introductionmentioning

confidence: 99%

Gauge theory of the long-range proximity effect and spontaneous currents in superconducting heterostructures with strong ferromagnets

2017

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Gauge theory of the long-range proximity effect and spontaneous currents in superconducting heterostructures with strong ferromagnets Bobkova, I. V.; Silaev, Mikhail Bobkova, I. V., Bobkov, A. M., & Silaev, M. (2017). Gauge theory of the long-range proximity effect and spontaneous currents in superconducting heterostructures with strong ferromagnets. Physical Review B, 96 (9) We present the generalized quasiclassical theory of the long-range superconducting proximity effect in heterostructures with strong ferromagnets, where the exchange splitting is of the order of Fermi energy. In the ferromagnet the propagation of equal-spin Cooper pairs residing on the spin-split Fermi surfaces is shown to be governed by the spin-dependent Abelian gauge field which results either from the spin-orbital coupling or from the magnetic texture. This additional gauge field enters into the quasiclassical equations in superposition with the usual electromagnetic vector potential and results in the generation of spontaneous superconducting currents and phase shifts in various geometries which provide the sources of long-range spin-triplet correlations. We derive the Usadel equations and boundary conditions for the strong ferromagnet and consider several generic examples of the Josephson systems supporting spontaneous currents.

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General boundary conditions for quasiclassical theory of superconductivity in the diffusive limit: application to strongly spin-polarized systems

Cited by 118 publications

References 94 publications

Anomalous current in diffusive ferromagnetic Josephson junctions

Anomalous current in diffusive ferromagnetic Josephson junctions

Anomalous Josephson effect controlled by an Abrikosov vortex

Gauge theory of the long-range proximity effect and spontaneous currents in superconducting heterostructures with strong ferromagnets

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