In a magnetic multilayer, magnetizations can be manipulated by spin transfer torque. Both spin transfer torque and its reciprocal effect, spin pumping, are governed by spin mixing conductance. The magnitude of spin mixing conductance at the interface of nearly magnetic metal has been theoretically shown to be enhanced by electron-electron interaction. However, experiments show both increasing and decreasing values of spin mixing conductance for metals with larger electron-electron interaction. Here we take into account the effect of electron-electron interaction on the screening of the Coulomb interaction at the magnetic interface to correctly describe the experiment.