Magnetization-orientation dependence of the superconducting transition temperature calculated forF∕S∕Ftrilayer structures

Abstract

We theoretically investigate the superconducting critical temperature T c dependence on the relative orientation of the magnetizations in F/S/F trilayer structures, where F is a ferromagnet and S is a superconductor. The values of T c are obtained from the linearized Usadel equations. We discuss the usual approximations employed to solve those equations and show that they are invalid in the parameter range of interest. We also compare approximate results of several authors. Adapting the numeric method used previously for F / S bilayers to the case of F/S/F trilayers, we find critical temperatures for parallel and antiparallel magnetic configurations with no approximations involved. Our results qualitatively explain experimental data and provide guidelines for optimizing the experimental systems.

Superconducting spin-valve effect and triplet superconductivity inCoOx/Fe1/Cu/Fe2/Cu/Pbmultilayer

“…A large number of works confirmed the predicted influence of the mutual orientation of the magnetizations in the F1/S/F2 structure on T c (see, e.g., [16][17][18][19][20][21]). However, the magnitude of the spin valve effect ∆T c = T AP c − T P c turns out to be smaller than the width of the superconducting transition δT c itself.…”

Ferromagnet-superconductor proximity effect: The clean limit

“…The dependence of the critical temperatures on the mutual orientations of ferromagnetic moments is also hardly observable in dirty FISIF hybrids with finite interface transparency. 16,18 However, for such structures with higher transparency the inverse proximity effect is significant.…”

“…2,3,4,5,6,7,8 and 9, 10,11,12,13,14,15,16,17,18,19,20 ). The interplay of ferromagnetism and superconductivity results in characteristic proximity effects near the contacts between two metals: the Andreev reflection is suppressed in the presence of a ferromagnet; 21 conversely, the superconducting correlations, described via the pair amplitude, extend in the ferromagnetic material in an oscillatory way.…”

Phase diagrams of ferromagnet-superconductor multilayers with misaligned exchange fields

“…For a strong enough exchange field, the oscillation is so strong that superconductivity is suppressed at a critical thickness but can reappear at a larger thickness. This kind of non-monotonic dependence of T c was thoroughly studied 4,5,6,8,10,11,23 for F-S bilayers and symmetric F-S-F trilayers. The crossing of the two T c curves in Fig.…”

“…The superconducting critical temperature T c in diffusive hybrid S-F structures has been studied both theoretically 1,2, 3,4,5,6,7,8,9,10,11 and experimentally 12,13,14,15,16,17,18,19,20,21 in several recent publications. It has been shown 1,2 that T c has a non-monotonic dependence on the thickness d f of the ferromagnetic layers that provide information about the strength of the ferromagnetic exchange field and about the transparencies of the S-F interfaces.…”