Superconducting magnetoresistance effect observed in Co/Nb/Co trilayers under a parallel magnetic field: The importance of matching the width of magnetic domain walls of the Co layers with the thickness of the Nb interlayer

Abstract

Magnetoresistance effects observed in ferromagnet/superconductor (FM/SC) hybrids, FM/SC bilayers (BLs) and FM/SC/FM trilayers (TLs), have attracted much interest. Here, we focus on the stray-fields-based superconducting magnetoresistance effect (sMRE) observed in Co(dCo)/Nb(dNb)/Co(dCo) TLs 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. To explore the conditions necessary for maximization of the sMRE, we focus on the different kinds of the stray dipolar fields, Hdip, that emerge at the interior of the out-of-plane MDs and at the boundaries of MDWs; these have a different inherent tendency to create straight and semi-loop vortices, respectively. In the recent literature, the creation of straight and semi-loop vortices has been addressed at some extent both theoretically [Laiho et al., Phys. Rev. B 67, 144522 (2003)] and experimentally [Bobba et al., Phys. Rev. B 89, 214502 (2014)] for the case of FM/SC BLs. Here, we address these issues in FM/SC/FM TLs in connection to the sMRE. Specifically, we focus on an experimental finding reported recently [D. Stamopoulos and E. Aristomenopoulou, J. Appl. Phys. 116, 233908 (2014)]; strong magnetostatic coupling of the FM outer layers is accompanied by an intense sMRE in TLs in which the thickness of the SC interlayer, dSC, matches the width of MDWs, DMDWs. To investigate this finding, we employ simulations-modeling and energy-considerations and propose two quantitative criteria that facilitate the creation of straight vortices over semi-loop ones. The first focuses on the maximization of the stray Hdip that occur at the interior of the out-of-plane MDs. The second enables the estimation of a crossover between the preferable creation of one kind of vortices over the other. Both criteria respond well, when tested against experimental results. These generic criteria on the interference between dSC and DMDWs can assist the design of cryogenic devices based on FM/SC/FM TLs.