Nonequilibrium Spin-transfer Torque in SFNFS Junctions

Abstract

Abstract. We report theoretical results for the nonequilibrium spin current and spin-transfer torque in voltage-biased SFNFS Josephson structures. The subharmonic gap structures and high voltage asymptotic behaviors of the dc and ac components of the spin current are analyzed and related to the spin-dependent inelastic scattering of quasiparticles at both F layers. Spin-polarized current passing through a ferromagnet can transfer spin angular momentum to the ferromagnet and exert a torque on the magnetic moment [1,2]. This mechanism offers unique opportunities to manipulate the magnetic state of nanomagnets. Experimentally spin-transfer torque driven magnetization precession and magnetization reversal have been observed in magnetic multilayers [3,4]. A well studied multilayer system is the magnetic nanopillar which consists of a ferromagnetnormal metal-ferromagnet (FNF) trilayer connected to normal metal electrodes. The typical thickness of each layer is several nm, and the diameter of the pillar is of the order of 50 nm [4]. When sandwiched between superconducting electrodes, the FNF trilayer can mediate finite Josephson coupling to form a SFNFS Josephson junction [5]. In such junctions, scattering of quasiparticle at the magnetic interfaces is sensitive to the phase shift in each F layer as well as the condensate phase difference φ across the junction. This indicates the spin momentum transfer between the quasiparticles and ferromagnets can be tuned by varying φ . Waintal and Brouwer calculated the phase-sensitive equilibrium torque in SFNFS junctions [6]. They also showed the nonequilibrium torque in NFNFS junctions acquires novel features, e.g. it can favor perpendicular configuration of the two moments [7].Here we investigate the nonequilibrium spin-transfer torque in SFNFS point contacts under bias voltage V . The setup and the coordinate system are shown in We use the quasiclassical theory of superconductivity [9] and solve numerically the transport equations for the Green's functions in each region which obey proper boundary conditions at interface F a and F b [8]. The spin currents are then determined from the local Keldysh Green's functions. Within this approach the proximity effect and the multiple Andreev reflection (MAR) at both interfaces are fully taken into account.The spin current in the N layer, measured in unit of N f v f ∆Ah/2 where A is the contact cross sectional area and ∆ is the superconducting gap, is shown in Fig. 2 for ψ = π/2 and zero temperature. As in the case of nanopillars with normal metal electrodes, the dc spin current flow is a consequence of spin filtering at the F layers. Its voltage dependence, however, is nonlinear and possesses subharmonic gap structures due to the onset and resonances of MAR processes. At V = 0, the dc spin current vector is along x direction, which tends to cause the moments to precess around each other [6]. As V is increased, the magnitude of dc currents along y and z direction, which tend to bring the moments towards or away from each other, grow with...

Transfer-matrix approach to multiband Josephson junctions

“…Due to the importance of Josephson junctions in numerous applications the Josephson effect has been subject of intense theoretical study. The current-phase relation as well as the oscillation of the electron transport in a voltage biased point contact known as the ac-Josephson effect has been theoretically investigated for different situations 9,10,11 including unconventional superconductivity 12 , spin active magnetic barriers 13,14,15 and the effect of pair breaking due to disorder 16 . It has been shown that within the quasiclassical theory interfaces can be described by effective boundary conditions 17 that can be included by mainly two different approaches: the scattering-matrix approach and the transfer-matrix approach 12 .…”

Nonequilibrium transport in superconductor/ferromagnet/superconductor diffusive junctions: Interplay between proximity effect and ferromagnetism

“…Equilibrium density of states was also studied 4,5 . On the other hand, to the best of our knowledge, the nonequilibrium transport in SFS mesoscopic junctions has not been studied yet neither from theoretical nor from experimental point of view except for theoretical investigations of magnetic quantum point contacts 6,7,8,9 . We address our theoretical paper to the part of this problem and study the phase-coherent transport in diffusive voltage-biased SFS plane junctions.…”