Optimizing the magnitude of the magnetoresistance observed in ferromagnet/superconductor/ferromagnet trilayers: A formula to combine all involved parameters

Abstract

The competitive nature of ferromagnetism and superconductivity in Ferromagnet/Superconductor (FM/SC) hybrids has attracted much interest in the last decades. In particular, the superconducting magnetoresistance (SMR) observed in FM/SC/FM trilayers (TLs) is related to the manipulation of the transport properties of the SC interlayer by the magnetic domain structure of the FM outer layers with out-of-plane anisotropy. In our recent work [Sci. Rep. 5, 13420 (2015)], a phenomenological model was proposed that describes successfully the scaling of the SMR magnitude with the relevant macroscopic parameters and microscopic length scales of the SC and FM structural units. Based on this model, here we investigate the contribution of the parameters that affect indirectly the SMR magnitude and do not appear in the original model. To this end, the parameters of both the SC interlayer (i.e., the thickness, dSC, the mean free path, l, the coherence length, ξ(0), etc.) and the FM outer layers (i.e., the thickness, dFM) are examined. The theoretical simulations presented here and experimental data unveil the indirect contribution of these parameters on the magnitude of the SMR and confirm the predictive power of the original phenomenological model. Accordingly, this model can be employed as a generic formula to combine successfully all involved parameters in every kind of FM/SC/FM TLs, ultimately optimizing the magnitude of the SMR.