Injection of spin current at the superconductor/ferromagnetic insulator interface

•We studied the spintronic of superconducting/ferromagnetic interfaces.•We detemined the spin current and spin conductance at the interface.•Temperature and chemical potential imbalance effects were analysed.•A discontinuous jump in the spin current was found. We used the Linear Response Theory to determine the injection of spin current at the interface between a ferromagnetic insulator (FMI) and a superconductor (SC). As quasi-particles (the excited states on the superconductor ground state) cannot penetrate the FMI, there is no electric current across the interface. However, a spin-flip scattering allows quasi-particles to exchange spin with localized electrons in the FMI via magnons. Assuming an imbalance δμ=μ↑-μ↓ between the up and down-spin in the SC, quasi-particles in the most populated state are reflected with spin inversion while magnons are absorbing or emitting at the interface. Depending on the value of δμ, we obtained two different behaviors of the spin current in the phase transition from a superconducting to a normal metal phase. For δμ1.20Δ(0) the spin current presents a discontinuous jump at Tc. The dependence on δμ is also determined as well as the spin conductance.