A Peculiar Solitary Re-entrant Superconductivity Induced by an External Magnetic Field in Ferromagnet-Superconductor Heterostructures

Abstract

We solve the boundary value problem for the Usadel-like equations in the dirty limit case for thin-film three-layered ferromagnet (F) -superconductor (S) structures. Our theoretical approach taking into account of the asymmetry and triplet superconducting correlations is valid in the external magnetic field presence as in the real experimental setup for the FS spin valve explorations. Based on the recent experimental data obtained for the symmetrical (FSF) trilayer in an external magnetic field, we expand the theoretical description to the asymmetrical FSF and FFS trilayers. We also consider the peculiar re-entrant superconductivity and solitary superconductivity induced by the external magnetic field for the FFS trilayer.

How experimentally to detect a solitary superconductivity in dirty ferromagnet-superconductor trilayers?

“…As was mentioned above, such an extraordinary nonmonotonic dependence T c (d f 2 ) is called solitary superconductivity. Note again that for the parallel state, the system is always in the resistive state [7,8,9] and hence, the difference ∆T = T AP c − T P c ≡ T AP c is a maximal. The physical reason for this phenomenon is simple: the exchange field of the intermediate F 2 layer, which is a strong depairing factor for the superconducting state, is partially compensated at AP state, herewith the "effective" exchange field becomes smaller and superconductivity appears.…”

“…The deviation of the magnetic alignment from the AP state results in the fast vanishing of this compensation and, as a result, in the reduction of the critical temperature [7,8,9]. This important feature of the system with solitary superconductivity makes them the most promising for superconducting spin valve applications, because the high values of difference ∆T are necessary for stable operation of spin valve.…”

“…We also discuss its of the spin valve applications. As was mentioned above the solitary superconductivity in FFS system may be observed only in the AP state [7,8,9]. In order to prepare state with a well-defined solitary superconductivity experimentalists should adhere to the following algorithm.…”

“…Earlier we theoretically investigate a solitary superconductivity for F 1 F 2 S system [7,8,9]. The solitary superconductivity corresponds to a localized region on the phase diagram of…”

“…For strong ferromagnets such as Fe, Ni or Co the decay depth is approximately few nanometers. The peculiarity of the FS proximity effect and interplay between the S and F parameter orders give rise to a number of interesting phenomena and effects (see reviews [2,3,4] and the references therein), for example, the reentrant [5,6,7] and solitary superconductivity [8,9], nonmonotonic behaviors of the critical temperature T c as function of the mutual alignment of the magnetizations of the F layers [10,11] and so on.…”