“…Eq. (21). With this model for the scattering matrices S a and S b , a typical plot of the supercurrent at φ = π/2 as a function of θ is shown in Fig.…”
Section: Numerical Resultsmentioning
confidence: 99%
“…This is a very suggestive result, as it was recently predicted that the Josephson current should be very sensitive to the angle θ between the two magnetic moments. 20,21 In what follows, we refrain from calculating the full equilibrium torque but concentrate on it φ-dependent part, the rationale being that it is precisely the φ-dependent part that can be viewed as the supercurrent induced torque. As we shall see, the φ-dependent part of the torque only has contributions from energies within ∆ 0 of the Fermi energy and can, therefore, be calculated from the scattering properties of the junction at and near the Fermi level.…”
Section: Spin Current and Spin Torquementioning
confidence: 99%
“…14,19 Josephson junctions with two magnetic layers were studied in Refs. 20,21, where it was shown that the supercurrent for antiparallel alignment of the magnetic moments can be larger than for parallel alignment.…”
We show that a Josephson current flowing through a ferromagnet-normal-metal-ferromagnet trilayer connected to two superconducting electrodes induces an equilibrium exchange interaction between the magnetic moments of the ferromagnetic layers. The sign and magnitude of the interaction can be controlled by the phase difference between the order parameters of the two superconductors. We present a general framework to calculate the Josephson current induced magnetic exchange interaction in terms of the scattering matrices of the different layers. The effect should be observable as the periodic switching of the relative orientation of the magnetic moments of the ferromagnetic layers in the ac Josephson effect.
“…Eq. (21). With this model for the scattering matrices S a and S b , a typical plot of the supercurrent at φ = π/2 as a function of θ is shown in Fig.…”
Section: Numerical Resultsmentioning
confidence: 99%
“…This is a very suggestive result, as it was recently predicted that the Josephson current should be very sensitive to the angle θ between the two magnetic moments. 20,21 In what follows, we refrain from calculating the full equilibrium torque but concentrate on it φ-dependent part, the rationale being that it is precisely the φ-dependent part that can be viewed as the supercurrent induced torque. As we shall see, the φ-dependent part of the torque only has contributions from energies within ∆ 0 of the Fermi energy and can, therefore, be calculated from the scattering properties of the junction at and near the Fermi level.…”
Section: Spin Current and Spin Torquementioning
confidence: 99%
“…14,19 Josephson junctions with two magnetic layers were studied in Refs. 20,21, where it was shown that the supercurrent for antiparallel alignment of the magnetic moments can be larger than for parallel alignment.…”
We show that a Josephson current flowing through a ferromagnet-normal-metal-ferromagnet trilayer connected to two superconducting electrodes induces an equilibrium exchange interaction between the magnetic moments of the ferromagnetic layers. The sign and magnitude of the interaction can be controlled by the phase difference between the order parameters of the two superconductors. We present a general framework to calculate the Josephson current induced magnetic exchange interaction in terms of the scattering matrices of the different layers. The effect should be observable as the periodic switching of the relative orientation of the magnetic moments of the ferromagnetic layers in the ac Josephson effect.
“…The possibility for forming the π-junction owing to interfaces containing magnetic impurities, was indicated for the first time in [1]. Since then the supercurrent across magnetically active interfaces has been studying theoretically both in S-FM-S junctions with a ferromagnetic metal separating superconductors [2,3,4,5,6,7], and in S-FI-S junctions with interfaces made of a ferromagnetic insulator or semiconductor [8,9,10]. The 0-π transition in S-F-S junctions was predicted under certain conditions in both cases [2,3,9].…”
The Josephson current in S-F-S junctions is described by taking into account different reflection (transmission) amplitudes for quasiparticles with spin up and down. We show that the 0-π transition in the junctions can take place at some temperature only for sufficiently strong spin-activity of the interface. In particular, Andreev interface bound state energies in one spin channel have to be all negative, while in the other one positive. Only one spin channel contributes then to the zero-temperature Josephson current. At the temperature of the 0-π transition two spin channels substantially compensate each other and can result in a pronounced minimum in the critical current in tunnel junctions. The minimal critical current is quadratic in small transparency and contains first and second harmonics of one and the same order.Growing interest at the time being to spin-dependent transport in superconductor-ferromagnet systems concerns, in particular, the dc Josephson effect. The possibility for forming the π-junction owing to interfaces containing magnetic impurities, was indicated for the first time in [1]. Since then the supercurrent across magnetically active interfaces has been studying theoretically both in S-FM-S junctions with a ferromagnetic metal separating superconductors [2,3,4,5,6,7], and in S-FI-S junctions with interfaces made of a ferromagnetic insulator or semiconductor [8,9,10]. The 0-π transition in S-F-S junctions was predicted under certain conditions in both cases [2,3,9]. Recently the effect has been observed experimentally in S-FM-S junctions [11].0-π transition in S-FM-S highly transparent junctions is mostly discussed with respect to the proximity effect in a ferromagnetic metal [2]. An exchange field in a ferromagnetic metal between two superconductors induces specific oscillations in the exponentially decaying Cooper pair density. For this reason an exchange field dependent oscillations in the critical current can arise in S-FM-S sandwiches. In S-FI-S junctions the proximity effect in a ferromagnetic insulator or semiconductor usually is much weaker, as compared with the case of a ferromagnetic metal, and can be disregarded. It has been found experimentally that a ferromagnetic semiconductor represents a ferromagnetic barrier in tunnel junctions, providing different transmission probabilities for up and down spins [12,13]. In S-FM-S tunnel junctions the proximity in a ferromagnetic metal does not manifest itself in the critical current in the dominating, linear in small transparency term. In all these cases spin-discrimination by the interface is especially important, as it results in proximity effects induced by a ferromagnetic layer in adjacent superconducting regions. If the interface thickness is less than the superconducting coherence length, the interface effects on the junction properties are conveniently described by the S-matrix approach. As this was demonstrated in [9], a quasiparticle scattering on magnetically active interfaces can themselves lead to a formation of a π-junction,...
“…5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21 ) and the physics of 0-π oscillations (see e.g. 22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38 ) in S|F heterostructures. The concept of odd-frequency pairing dates back to Refs.…”
We present a study of the proximity effect and the inverse proximity effect in a superconductor|ferromagnet bilayer, taking into account several important factors which mostly have been ignored in the literature so far. These include spin-dependent interfacial phase shifts (spin-DIPS) and inhomogeneous textures of the magnetization in the ferromagnetic layer, both of which are expected to be present in real experimental samples. Our approach is numerical, allowing us to access the full proximity effect regime. In Part I of this work, we study the superconducting proximity effect and the resulting local density of states in an inhomogeneous ferromagnet with a non-trivial magnetic texture. Our two main results in Part I are a study of how Bloch and Néel domain walls affect the proximity-induced superconducting correlations and a study of the superconducting proximity effect in a conical ferromagnet. The latter topic should be relevant for the ferromagnet Ho, which was recently used in an experiment to demonstrate the possibility to generate and sustain long-range triplet superconducting correlations. In Part II of this work, we investigate the inverse proximity effect with emphasis on the induced magnetization in the superconducting region as a result of the "leakage" from the ferromagnetic region. It is shown that the presence of spin-DIPS modify conclusions obtained previously in the literature with regard to the induced magnetization in the superconducting region. In particular, we find that the spin-DIPS can trigger an anti-screening effect of the magnetization, leading to an induced magnetization in the superconducting region with the same sign as in the proximity ferromagnet.
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