The influence of a parallel magnetic field on critical temperature and inhomogeneous current distribution of a ferromagnet/superconductor structure

Abstract

Thin two-and three-layered ferromagnetic metal (F)/superconductor (S) structures (F/S and F/S/F) in an external constant magnetic field H parallel to the F/S interface plane are investigated in the framework of the Usadel equations for the dirty limit. The thicknesses of layers F (d f ) and S (d s ) are supposed as being much less than the magnetic-penetration depth (λ H ). For the F/S and F/S/F systems the transition temperature T c is calculated as a function of d f taking into account an interaction of H with the orbital motion of the conduction electrons. It is shown that magnetic field H not only suppresses the superconductivity of the S/F and F/S/F heterostructures, but it also deepens the minima of T c (d f ) and alters significantly the form of the function T c (d f ). So the reentrant superconductivity may occur even with the magnetic field increasing, which can influence the possibility of the spin-valve regime for the F/S/F trilayer. The difference between the critical temperatures for the antiparallel (AP) and parallel (P) alignment of the F-layer magnetizations in the F/S/F trilayer essentially depends on the character of the quasi-particle motion of the F layers. This difference may strongly increase with the magnetic field growth, because superconductivity in the P alignment case may be suppressed whereas T AP c still does not equal zero. It is shown also that the screening current induced by the external magnetic field penetrates into the F layer through the S/F boundary. The screening current sharply decays and oscillates with distance from the boundary interface into the F layer.

The influence of an external magnetic field on the triplet proximity effect in ferromagnet/superconductor trilayers

“…Note that our theoretical calculations (see figure 2(a)), as in previous theoretical results [44], display the appearance of re-entrant superconductivity with increasing magnetic field (it was predicted in our works [43,52]). However, the experimental data [44] (see also symbols in figures 2(a) and (b)) do not conclusively prove the existence of re-entrant superconductivity in parallel magnetic fields.…”

“…As mentioned above, an external magnetic field can lead to a qualitative change in the phase diagrams of the FS system. Therefore, the appearance of re-entrant superconductivity with increasing magnetic field in FS bilayers and FSF trilayers was first predicted in our theoretical works [43,52] and then experimentally observed in [44]. In this regard, the influence of an external magnetic field on the phase diagrams of the FFS trilayers is an interesting point.…”

“…In this paper we consider a theory for the three-layer thin-film heterostructures FSF and FFS in the presence of an external magnetic field H applied parallel to the plane of the contact 1 . Previously the influence of the magnetic field on the properties of the symmetrical FSF system was considered in [40][41][42][43][44]. However, real FS structures are not perfectly symmetrical.…”

Experimental and theoretical analysis of the upper critical field in ferromagnet–superconductor–ferromagnet trilayers

“…A good agreement between the theory and experiment is observed for all samples. At low magnetic field, T c (d CuNi ) exhibits nonmonotonous oscillatory dependence which becomes reentrant at high enough magnetic fields (the curves from top to bottom in figure 6; see also [54]).…”

Competitive 0 and π states in S/F/S trilayers: Multimode approach

“…[48][49][50][51][52][53][54][55][56][57][58][59][60][61][62] Influence of magnetization misalignment in F layers on critical temperature in F 1 /S/F 2 /(S') structures was also investigated. 63,64 Josephson π junctions have been proposed as elements of novel superconducting nanoelectronics in many different applications.…”