abstract: Attaining a sufficiently large critical current density (Jc) in magnetic-barrier Josephson junctions has been one of the greatest challenges to the development of dense low-power superconductor memories. Many experimentalists have used various combinations of superconductor (S) and ferromagnetic (F) materials, with limited success towards the goal of attaining a useful Jc. This trial-and-error process is expensive and time consuming. An improvement in the fundamental understanding of transport through the ferromagnetic layers and across the superconductor-ferromagnetic interface could potentially give fast, accurate predictions of the transport properties in devices and help guide the experimental studies. In this thesis, parameters calculated using density functional methods are used to model transport across Nb/0.8 nm Fe/Nb/Nb and Nb/3.8 nm Ni /Nb/Nb Josephson junctions. The model simulates the following transport processes using realistic parameters from density functional theory within the generalized gradient approximation: (a) For the first electron of the Cooper pair in the superconductor to cross the interface- conservation of energy and crystal momentum parallel to the interface (kll). (b) For the second electron to be transmitted coherently- satisfying the Andreev reflection interfacial boundary conditions and crossing within a coherence time, (c) For transmission of the coherent pair through the ferromagnetic layer- the influence of the exchange field on the electrons’ wavefunction and (d) For transport through the bulk and across the interfaces- the role of pair-breaking from spin-flip scattering of the electrons. Our model shows the utility of using realistic electronic-structure band properties of the materials used, rather the mean-field exchange energy and empirical bulk and interfacial material parameters used by earlier workers. [Kontos et al. Phys. Rev Lett, 93(13), 137001. (2004); Demler et al. Phys. Rev. B, 55(22), 15174. (1997)]. The critical current densities obtained from out model for Nb/0.8 nm Fe/Nb is 104 A/cm2 and for Nb/3.8 nm Ni/Nb is 7.1*104 A/cm2. These values fall very close to those observed experimentally- i.e. for Nb/0.8 nm Fe/Nb is 8*103 A/cm2 [Robinson et al" Phys. Rev. B 76, no. 9, 094522. (2007)] and for Nb/3.8 nm of Ni/Nb is 3*104 A/cm2 [Blum et al Physical review letters 89, no. 18, 187004. (2002). This indicates that our approach could potentially be useful in optimizing the properties of ferromagnetic-barrier structures for use in low-energy superconducting memories. / Dissertation/Thesis / Masters Thesis Materials Science and Engineering 2018