Magnetic Flux Pumping in Superconducting Loop Containing a Josephson Ψ Junction S
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Magnetic Flux Pumping in Superconducting Loop Containing a Josephson Junction S. Mironov,1 H. Meng,2, 3, 4 and A. Buzdin2, 5 1)Institute for Physics of Microstructures, Russian Academy of Sciences, GSP-105, 603950 Nizhny Novgorod, Russia 2)University Bordeaux, LOMA UMR-CNRS 5798, F-33405 Talence Cedex, France 3)School of Physics and Telecommunication Engineering, Shaanxi University of Technology, Hanzhong 723001, China 4)Shanghai Key Laboratory of High Temperature Superconductors, Shanghai University, Shanghai 200444, China 5)Sechenov First Moscow State Medical University, Moscow, 119991, Russia We demonstrate that a Josephson junction with a half-metallic weak link integrated into the superconducting loop enables the pumping of magnetic flux piercing the loop. In such junctions the ground state phase is determined by the mutual orientation of magnetic moments in two ferromagnets surrounding the half-metal. Thus, the precession of magnetic moment in one of two ferromagnets controlled, e.g., by the microwave radiation, results in the accumulation of the phase and subsequent switching between the states with different vorticities. The proposed flux pumping mechanism does not require the application of voltage or external magnetic field which enables the design of electrically decoupled memory cells in superconducting spintronics. When a superconducting loop is put in the external magnetic field the magnetic flux Φ through the loop is B~ quantized being equal to the integer number of the flux 1 quanta Φ0: Φ = nΦ0 . The interplay between the states with different vorticities n enables the implementation of multiply connected superconducting systems as flux qubits2,3, ultra-sensitive magnetic field detectors4,5, gen- erators of ac radiation6 etc. The flux quantization also Controllable Energy naturally suggests using superconducting loop as topo- switching logically protected memory cell in the devices of the rapid single flux quantum (RSFQ) logics7. The straightforward way to switch the loop between the states with different vorticity n requires application of external magnetic flux Φ ∼ Φ . Even for the loops -1 0 1 ext 0 Φ / Φ of the radius R ∼ 0:1 µm the corresponding magnetic 0 field should be ∼ 0:1 T and it grows / R−2 with the de- crease of the loop size which becomes a serious obstacle FIG. 1. Sketch of the superconducting loop containing a for the miniaturization of the flux-based devices. Thus, Josephson junction which enables the switching between the discovery of the physical phenomena which enable the states with different vorticities by periodic driving of the ground state Josephson phase . the controllable switching of the vorticity n without ap- plication of external flux is strongly desired. One of promising mechanisms allowing the flux- free switching can be realized in the loops containing different vorticity without application of external mag- a Josephson junction with embedded magnetic order netic field. 8{11 and/or broken inversion symmetry . These systems However, in most existing '0 junctions the phase vari- are known to reveal unusual collective dynamics of mag- ation is limited (δ'0 < 2π) and the corresponding flux 12{19 netic and superconducting order parameters. In con- Φ < Φ0 cannot change the vorticity n of the supercon- arXiv:2004.13403v1 [cond-mat.supr-con] 28 Apr 2020 trast to the conventional Josephson systems, such junc- ducting state. Indeed, the junctions with a ferromagnetic tions support the non-zero ground state phase '0 be- (F) layer between the superconducting (S) leads support 25{27 tween the superconducting leads. Being incorporated only π states with '0 = π which allow the design 23 into the loop such '0-junctions play the role of the phase of the environmentally decoupled qubits but are not batteries producing the spontaneous electric current suitable for changing the loop vorticity. The alternat- which corresponds to the magnetic flux Φ = ('0=2π)Φ0 ing F layer thickness (see, e.g., Ref. 28 and references through the loop20{24. One can expect, thus, that con- therein) as well as the presence of the Abrikosov vortex 30{32 trolling the ground state phase '0, e.g., by voltage or or the pair of current injectors in one of S leads may radiation should enable effective tuning of the magnetic produce the second order phase transition with the spon- flux and switching the system between the states with taneous phase '0 gradually changing between zero and 2 FIG. 2. (a) Sketch of the Josephson junction where the weak link consists of a half-metallic layer sandwiched between two ferromagnets. The ground state phase coincides with the angle between the projection of magnetic moments in ferromagnets to the plane perpendicular to the spin quantization axis of half-metal. (b) Sketch of possible experimental setup where circularly polarized radiation controls the rotation of magnetic moment in the F2 layer and subsequent variation of the spontaneous Josephson phase . The superconducting electrodes are covered by the reflecting material to minimize heating effects. π (so that δ'0 < π). The situation looks more promis- netic field. ing for the the S/F/S junctions with the broken inversion The described phase accumulation in junctions re- symmetry where the spin-orbit coupling (SOC) produces minds the Berry phase effect45 since the full recovery of the arbitrary spontaneous phase '0 / ν sin θ where θ the initial magnetic state after the one precession period is the angle between the exchange field in the F mate- is accompanied by the 2π change of the Josephson ground rial and the direction of the broken inversion symmetry state phase . Note that this phenomenon contrasts to while the constant ν characterizes the strength of SOC the behavior of the '0 junctions where the recovery of the and the exchange field33{37. However, the parameter ν is exchange field direction (the angle θ) unavoidably results typically small which limits the '0 variations. in the recovery of the spontaneous phase '0 / sin θ. In this Letter we unravel the flux-free mechanism of For the experimental realization of the described the remote control of the superconducting state vortic- radiation-stimulated vorticity switching it is convenient ity in the loop by the Josephson junction in which to use the Josephson junctions of the \overlap" ge- the range of the spontaneous phase variation is not ometry (see Fig. 2b). This design provides a convenient limited (see Fig. 1). The weak link of the basic junc- access to the surface of the F2 layer for the circularly tion consists of the layer of half-metal (HM) sandwiched polarized electromagnetic wave. At the same time, the between two ferromagnets (Fig. 2a). If the magnetic superconducting electrodes should be covered by the suit- moments in the three magnetic layers are non-coplanar able reflecting material to prevent parasitic heating ef- the current-phase relation of the junction takes the form fects. The recent experiments have demonstrated the active control of triplet supercurrents in different types I(') = Ic sin(' − ) where the spontaneous phase and 46{50 the critical current I are controlled by the directions of of S/F/S junctions including the Josepshon systems c with half-metallic layers.51,52 which provides the guid- the magnetic moments M1 and M2 in the F1 and F2 layers. Specifically, for the spin quantization axis in the ance for the appropriate choice of materials and their half-metal directed along the z-axis the phase coincides parameters. To demonstrate the controllable switching of vorticity with the angle between the projection of M1 and M2 to the xy-plane while the critical current I / sin α sin α and the magnetic flux pumping we consider the supercon- c 1 2 ducting loop of inductance L interrupted by the Joseph- where α1 (α2) is the angle between M1 (M2) and the z- axis.38{43. The geometry of the junction favorable for son junction characterized by the the current-phase the control of the loop vorticity requires the direction of relation I = Ic sin(' − ) where Ic is the critical current (see Fig. 1). The dynamics of the Josephson phase ' is M1 to be fixed along the y-axis and the F2 layer to have 1 the easy-plane (xy) magnetic anisotropy. In this case described by the sine-Gordon equation : radiating the F layer with the circularly polarized elec- 2 2 @ ' 1 @' 1 2πIc tromagnetic wave with the magnetic field rotating in the 2 + + ' + sin [' − (t)] = 0; (1) @t RN C @t LC Φ0C xy plane should cause the precession of M2 around the 44 z-axis resulting in the unlimited accumulation of the where C and RN are the capacity and normal state resis- spontaneous phase . If the described junction is inte- tance of the Josephson junction, respectively. Consider- grated in the superconducting loop such phase accumu- ing the case of identical easy-axis anisotropy of magneti- lation gives rise to the switching between the states with zation in both F layers of the junction we assume that different vorticities and subsequent pumping of magnetic in the absence of external driving (t) = 0. To analyze flux through the loop without actual application of mag- the system dynamics it is convenient to introduce the di- 3 p mensionless time τ = !pt where !p = 2πIc=Φ0C is the p plasma frequency, the quality factor Q = R 2πIcC=Φ0 2 (a) Stable state sin ϕ and the normalized loop inductance λ = 2πLIc=Φ0. In the absence of external driving the number of equi- 0 librium superconducting states in the loop is controlled Saddle −ϕ/λ by the loop inductance. At small λ the equation sin ' = -2 point −ϕ/λ defining the equilibrium states has only one triv- -6 -4 -2 0 2 4 6 ial solution ' = 0. When increasing λ at the threshold ϕ/π values λ = λn one gets the sequential emergence of addi- tional pairs of the stable states ' = ±'n (n = 1; 2; 3:::) 2 (b) sdl and the nearby saddle points ' = ±'n (see Fig.