Width of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>0</mml:mn><mml:mtext>−</mml:mtext><mml:mi>π</mml:mi></mml:mrow></mml:math>phase transition in diffusive magnetic Josephson junctions

Shomali, Zahra; Zareyan, Malek; Belzig, Wolfgang

doi:10.1103/physrevb.78.214518

Cited by 3 publications

(5 citation statements)

References 41 publications

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“…This phase diagram is similar to the 0 − π Josephson couplings phase diagram of a homogenous F contact between two superconductors, see Ref. [49]. As we show in the inset of Fig.…”

Section: S1f1f2s2 Junctionsupporting

confidence: 85%

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Spin supercurrent in Josephson contacts with noncollinear ferromagnets

2011

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We present a theoretical study of the Josephson coupling of two superconductors which are connected through a diffusive contact consisting of noncollinear ferromagnetic domains. The leads are conventional s-wave superconductors with a phase difference of ϕ. First, we consider a contact with two domains with magnetization vectors misoriented by an angle θ. Using the quantum circuit theory, we find that in addition to the charge supercurrent, which shows a 0−π transition relative to the angle θ, a spin supercurrent with a spin polarization normal to the magnetization vectors flows between the domains. While the charge supercurrent, is odd in ϕ and even in θ, the spin supercurrent is even in ϕ and odd in θ. Furthermore, with asymmetric insulating barriers at the interfaces of the junction, the system may experience an antiferromagnetic-ferromagnetic phase transition for ϕ = π. Secondly, we discuss the spin supercurrent in an extended magnetic texture with multiple domainwalls. We find the position-dependent spin supercurrent. While the direction of the spin supercurrent is always perpendicular to the plane of the magnetization vectors, the magnitude of the spin supercurrent strongly depends on the phase difference between the superconductors and the number of domain walls. In particular, our results reveal a high sensitivity of the spin-and charge-transport in the junction to the number of domain walls in the ferromagnet. We show that superconductivity in coexistence with non-collinear magnetism, can be used in a Josephson nanodevice to create a controllable spin supercurrent acting as a spin transfer torque on a system. Our results demonstrate the possibility to couple the superconducting phase to the magnetization dynamics and, hence, constitutes a quantum interface e.g. between the magnetization and a superconducting qubit. Spin supercurrent inJosephson contacts with noncollinear ferromagnets 2 (b) x=0 (a) θ S 2 S 1

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“…This phase diagram is similar to the 0 − π Josephson couplings phase diagram of a homogenous F contact between two superconductors, see Ref. [49]. As we show in the inset of Fig.…”

Section: S1f1f2s2 Junctionsupporting

confidence: 85%

“…Note that in general for any phase difference φ, the resulting Green's functions vary from one node to another, simulating the spatial variation along the F contact (see Ref. [49]). From the resulting Green's functions and Eq.…”

Section: Model and Basic Equationmentioning

confidence: 99%

Spin supercurrent in Josephson contacts with noncollinear ferromagnets

2011

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“…( 3) and the boundary conditions iteratively, the initial value is refined until the Green's functions are computed with the desired accuracy for each of the n nodes. The technique is fully described in the work by Shomali et al [20,21,58]. Finding the Green's function of the systems, the components of the spin supercurrent and the STT are computed via the following formulas,…”

Section: A Diffusive Mosfet Spinmentioning

confidence: 99%

“…In general, a node inside F c is characterized by a Green's function Ǧi , which is an energy-dependent 4 × 4-matrix in the Nambu and spin spaces. The technique is fully described in the work by Shomali et al [20,21,58]. Finding the Green's function of the systems, the components of the spin supercurrent and the STT are computed via the following formulas,…”

Section: Diffusive Mosfet Spinmentioning

confidence: 99%

Spin transfer torque and exchange coupling in Josephson junctions with ferromagnetic superconductor reservoirs

Shomali

Asgari

2019

J. Phys.: Condens. Matter

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In this paper, the spin transfer torque (STT) and the exchange coupling of the Josephson junctions containing the interesting cases of diffusive/ballistic-triplet/singlet ferromagnetic superconductor (FS) materials together with the diffusive Josephson junction of the form S1/F1/I1/N/I2/F2 with I being the insulating barrier are investigated. Using the Nazarov quantum circuit theory, it is found that for the diffusive FS1/N/FS2 structure the STT only appears in the normal direction to the plane of the exchange fields of the F1 and F2. This results in the antiparallel/parallel or vice versa parallel/antiparallel transition of the favorable exchange coupling depending on the considered parameters of the system, including the nonmagnetic spacer thickness, the superconducting phase difference, the length and the exchange field of the ferromagnets. Furthermore, the analyze of the width of the transitions, the phase difference interval in which an interlayer length-induced antiparallel/parallel transition can be occurred, is performed. For instance, as the exchange field or the temperature increases, the interval of phase difference gets larger. On the other hand, the ballistic Josephson junction containing the triplet ferromagnetic superconductor reservoirs solving the 16×16 Bogoliubov-de-Gennes equation is studied. It is found that although the exchange fields of the FS are laid in the z and y direction, the STT interestingly exists in all three directions of x, y and z. This exciting finding suggests that the favorable equilibrium configuration concerning the least exchange coupling occurs in the relative exchange field direction different from 0 or π. To the best of our knowledge it is for the first time that the occurrence of the in-plane STT is reported. Moreover, the occurrence of the beat like behavior with two oscillation period for the out-of-plane STT is interestingly acquired.

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“…Superconductivity is a coherent state of spontaneously broken U(1)-symmetry. So, the Josephson effect is a response of the mentioned coherent state to an inhomogeneity, say the variation of phase, over the junction [1][2][3]. Also, analogous non-superconducting effect is predicted to exist in the magnetic tunnel barrier between two ferromagnets with the SO(3) symmetry-breaking coherent states [4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 97%

Josephson junctions with chiral p-wave ferromagnetic superconductor reservoirs in presence of spin-orbit coupling interaction

Shomali¹

2022

Supercond. Sci. Technol.

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The spin transfer torque (STT), is studied in new cases of Josephson junctions containing triplet p-wave chiral ferromagnetic superconductor reservoirs (FS). To be more precise, FS$_1$|spin orbit coupling layer (SOC$_1$)|Normal metal (N)|SOC$_2$|FS$_2$ materials have been investigated. Specifically, FS$_1$|N|FS$_2$ structure with one layer of SOC at FS$_1$|N interface and also two layers of SOC at both FS$_1$|N and N|FS$_2$ interfaces are investigated. For the structures including two SOC layers, both symmetric and asymmetric cases with respectively equal and different potential strengths are studied. The ballistic Josephson junctions are studied solving the Bogoliubov-de-Gennes equation. In particular, the cases with short normal metal contacts with thickness much smaller than the superconducting coherence length, $\psi$, are studied. It is obtained for the case with only one SOC layer, while the absolute value of the out-of-plane STT remains almost unchanged, its direction reverses for lower values of $\alpha$, the angle between exchange fields of the two ferromagnetic superconductors. Also, the nanosystem in presence of two similar SOCs, exhibits lower out-of-plane STT. This is justified as the unit vector along the interface normal for the SOC$_1$ is in the opposite direction of the second SOC$_2$ layer. Hence, one can expect that these potentials fade the effect of each other. When the SOCs are not the same and have different values of potential strength, the out-of-plane STT reduces less which is attributed to slighter cancellation due to unequal potential strength. Moreover, the barrier strength is varied. It has been shown that the barrier strength increment changes the behavior of the STT. Particularly, it is found that it results in sign and value change of the STT. Further, the emergence of in-plane STTs in presence of SOC are confirmed and investigated for various systems.

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Width of the0−πphase transition in diffusive magnetic Josephson junctions

Cited by 3 publications

References 41 publications

Spin supercurrent in Josephson contacts with noncollinear ferromagnets

Spin supercurrent in Josephson contacts with noncollinear ferromagnets

Spin transfer torque and exchange coupling in Josephson junctions with ferromagnetic superconductor reservoirs

Josephson junctions with chiral p-wave ferromagnetic superconductor reservoirs in presence of spin-orbit coupling interaction

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