Current switches based on asymmetric ferromagnet-superconductor nanostructures with allowance for a triplet channel in a
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ONIC PROPERTIES OF SOLID
Current Switches Based on Asymmetric Ferromagnet–Superconductor Nanostructures with Allowance for a Triplet Channel in an External Magnetic Field M. V. Avdeev and Yu. N. Proshin* Kazan Federal University, Kazan, 420008 Tatarstan, Russia *email: [email protected] Received September 30, 2012; in final form, May 31, 2013
Abstract—We analyze the properties of asymmetric threelayer (FSF and FFS) heterostructures consisting of a ferromagnet (F) and a superconductor (S) in an external magnetic field. The asymmetry of FS systems can be due to the difference in the parameters characterizing the F layers (in particular, noncollinearity of the magnetizations of the ferromagnets, leading to the generation of the longrange triplet component of the superconducting condensate). We consider the case of strong scattering of conduction electrons from non magnetic impurities (the socalled dirty limit), for which we derive the equations for the pair amplitude and corresponding boundary conditions to these equations, which are valid in the presence of an external mag netic field. We discuss possible applications of these FS heterostructures as spin switches on the basis of anal ysis of their phase diagrams, and we give recommendations for determining the optimal parameters required for their stable operation. The occurrence of peculiar reentrant superconductivity in the FFS systems on an increase of the external magnetic field is predicted. DOI: 10.1134/S1063776113140082
1. INTRODUCTION The study of physical phenomena occurring due to the proximity effect [1] in artificially prepared hetero structures consisting of ferromagnetic (F) and super conducting (S) layers has attracted considerable atten tion of researchers in recent years. The essence of the proximity effect is that superconducting correlations in such thinfilm systems can penetrate from the S layer to a small depth of the F layer due to transparency of the SF interface. It should be recalled, that in tradi tional superconductors with the stype pairing the Cooper pairs are formed by electrons with opposite spins [2], while a strong exchange field I in a ferromag net strives to align the electron spins in parallel, which leads to suppression of superconductivity because the condition I Ⰷ Δ is observed in nearly all cases, where Δ is the characteristic scale energy of the binding energy in a Cooper pair (see, for example, review [3]). For this reason, the coexistence of superconductivity and ferromagnetism in homogeneous materials requires the fulfillment of awkward conditions. How ever, such coexistence of superconductivity and ferro magnetism can easily be attained in artificially pre pared FS systems, in which the ferromagnetic and superconducting order parameters are spatially sepa rated. One of the features of the proximity effect in FS systems is the manifestation of a nonuniform gapless state of the FFLO type in layered FS systems, which was predicted by Larkin and Ovchinnikov [4] and by
Fulde and Ferrel [5] for a homogen
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