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Register a new user0-$pi$ transition driven by magnetic proximity effect in a Josephson junction
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We theoretically study the Josephson effect in a superconductor/normal metal/superconductor ({it S}/{it N}/{it S}) Josephson junction composed of $s$-wave {it S}s with {it N} which is sandwiched by two ferromagnetic insulators ({it F}s), forming a spin valve, in the vertical direction of the junction. We show that the 0-$pi$ transition of the Josephson critical current occurs with increasing the thickness of {it N} along the junction. This transition is due to the magnetic proximity effect (MPE) which induces ferromagnetic magnetization in the {it N}. Moreover, we find that, even for fixed thickness of {it N}, the proposed Josephson junction with the spin valve can be switched from $pi$ to 0 states and vice versa by varying the magnetization configuration (parallel or antiparallel) of two {it F}s. We also examine the effect of spin-orbit scattering on the Josephson critical current and argue that the 0-$pi$ transition found here can be experimentally observed within the current nanofabrication techniques, thus indicating a promising potential of this junction as a 0-$pi$ switching device operated reversibly with varying the magnetic configuration in the spin valve by, e.g., applying an external magnetic field. %with the magnetization configuration in the spin valve. Our results not only provide possible applications in superconducting electronics but also suggest the importance of a fundamental concept of MPE in nanostructures of multilayer {it N}/{it F} systems.
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We study the thermodynamic properties of a superconductor/normal metal/superconductor Josephson junction {in the short limit}. Owing to the proximity effect, such a junction constitutes a thermodynamic system where {phase difference}, supercurrent, temperature and entropy are thermodynamical variables connected by equations of state. These allow conceiving quasi-static processes that we characterize in terms of heat and work exchanged. Finally, we combine such processes to construct a Josephson-based Otto and Stirling cycles. We study the related performance in both engine and refrigerator operating mode.
We theoretically study the magnetism induced by the proximity effect in the normal metal of ferromagnetic Josephson junction composed of two $s$-wave superconductors separated by ferromagnetic metal/normal metal/ferromagnetic metal junction (${S}/{F}/{N}/{F}/{S}$ junction). We calculate the magnetization in the $N$ by solving the Eilenberger equation. We show that the magnetization arises in the ${N}$ when the product of anomalous Greens functions of the spin-triplet even-frequency odd-parity Cooper pair and spin-singlet odd-frequency odd-parity Cooper pair in the ${N}$ has a finite value. The induced magnetization $M(d,theta)$ can be decomposed into two parts, $M(d,theta)=M^{rm I}(d)+M^{rm II}(d,theta)$, where $d$ is the thickness of $N$ and $theta$ is superconducting phase difference between two ${S}$s. Therefore, $theta$ dependence of $M(d,theta)$ allows us to control the amplitude of magnetization by changing $theta$. The variation of $M(d,theta)$ with $theta$ is indeed the good evidence of the magnetization induced by the proximity effect, since some methods of magnetization measurement pick up total magnetization in the ${S}/{F}/{N}/{F}/{S}$ junction.
We investigate the current-phase relation of S/F/S junctions near the crossover between the 0 and the pi ground states. We use Nb/CuNi/Nb junctions where this crossover is driven both by thickness and temperature. For a certain thickness a non-zero minimum of critical current is observed at the crossover temperature. We analyze this residual supercurrent by applying a high frequency excitation and observe the formation of half-integer Shapiro steps. We attribute these fractional steps to a doubling of the Josephson frequency due to a sin(2*phi) current-phase relation. This phase dependence is explained by the splitting of the energy levels in the ferromagnetic exchange field.
The order parameter of superconducting pairs penetrating an inhomogeneous magnetic material can acquire a long range triplet component (LRTC) with non-zero spin projection. This state has been predicted and generated recently in proximity systems and Josephson junctions. We show using an analytically derived domain wall of an exchange spring how the LRTC emerges and can be tuned with the twisting of the magnetization. We also introduce a new kind of Josephson current reversal, the triplet $0-pi$ transition, that can be observed in one and the same system either by tuning the domain wall or by varying temperature.
We theoretically study the Josephson current in Ising superconductor-half-metal-Ising superconductor junctions. By solving the Bogoliubov-de Gennes equations, the Josephson currents contributed by the discrete Andreev levels and the continuous spectrum are obtained. For very short junctions, because the direct tunneling of the Cooper pair dominates the Josephson current, the current-phase difference relation is independent of the magnetization direction, which is the same as the conventional superconductor-ferromagnet-superconductor junctions. On the other hand, when the length of the half-metal is similar to or greater than the superconducting coherence length, the spin-triplet Josephson effect occurs and dominates the Josephson current. In this case, the current-phase difference relations show the strong magnetoanisotropic behaviors with the period pi. When the magnetization direction points to the $pm$ z directions, the current is zero regardless of the phase difference. However, the current has a large value when the magnetization direction is parallel to the junction plane, which leads to a perfect switch effect of the Josephson current. Furthermore, we find that the long junctions can host both the 0 state and pi state, and the $0$-$pi$ transitions can be achieved with the change of the magnetization direction. The physical origins of the switch effect and $0$-$pi$ transitions are interpreted from the perspectives of the spin-triplet Andreev reflection, the Ising pairing order parameter and the Ginzburg-Landau type of free energy. In addition, the influences of the chemical potential, the magnetization magnitude, and the strength of the Ising spin-orbit coupling on the switch effect and $0$-$pi$ transitions are also investigated. Furthermore, the two-dimensional Josephson junctions are also investigated and we show that the spin-triplet Josephson effect can exist always.
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