Superconducting magnetoresistance in Co/Nb/Co trilayers optimized through matching the involved length scales of the ferromagnet and superconductor

Magnetoresistance effects observed in superconductor/ferromagnet (SC/FM) hybrids, SC/FM bilayers and FM/SC/FM trilayers, have attracted much interest in recent years. Here we focus on the stray-fields-based superconducting magnetoresistance effect (sMRE) observed in Co(dCo)/Nb(dNb)/Co(dCo) trilayers with sufficiently thick Co outer layers so that out-of-plane magnetic domains (MDs) and MDs walls (MDWs) emerge all over their surface when subjected to a parallel external magnetic field, Hex equal to the coercive field, Hc. Asking for the optimum conditions to maximize the sMRE, we explore the interference between three basic length scales of the SC and FM structural units: the thickness of the SC interlayer (dSC), the zero-temperature coherence length (ξ(0)) and the width of out-of-plane MDs (DMDs). To this effect, simulations-based modeling of the transverse stray dipolar fields, Hz,dip that emerge at the interior of the out-of-plane MDs is performed. Both cases of homogeneous and inhomogeneous micromagnetic characteristics (saturation magnetization, Msat and width, DMDs) of the out-of-plane MDs are investigated. Furthermore, the influence of the microstructure of the bottom and top Co layers on the macroscopic coercive field of the TLs is addressed. The obtained modeling results respond well when tested against experimental data. The generic criteria reported here on the optimum matching of dSC, ξ(0) and DMDs aiming to maximize the sMRE magnitude in relevant FM/SC/FM trilayers, can assist the design of relevant cryogenic devices.