Andreev spectrum and supercurrent in a multilayer ferromagnetic clean Josephson junction

In this work we consider a ballistic superconductor/multilayer–ferromagnet/superconductor junction, with interface scattering potential, which can be different in strength. We develop, for an arbitrary number of layers, compact analytic formulae for the Andreev bound state spectrum and the supercurrent. The phase dependence of the supercurrent is obtained from the Andreev amplitudes and results in an extremely simple form for any number of ferromagnetic layers. In the Matsubara summation it enters the denominator as a cos ϕ plus a ϕ-independent term. The reduced formulae are amenable to efficient numerical computation. For a few cases we also give simple equations for the numerical determination of the bound states, obtained with algebraic matrix multiplication and numerical results are discussed.