Two transient time in the charge and spin current

Using magnetic tunnel junction formed by two leads made of ferromagnetic metals and a thin insulating barrier, we study its time depedent charge and spin current following a square voltage pulse. Magnetic fluctuations in the tunnel junction is modeled as magnons, and its influence on the tunneling is treated as a local bosonic mode described by the spinful Anderson-Holstein model. We compute the time dependent spin and charge current perturbatively with Lang-Frisov transformation to handle the strong local electron-magnon or electron phonon interaction at finite temperature. Two transient behaviors are seen in the charge and spin currents. Those two time scales due to different spin and charge responses within one junction could be useful for parallel computing within a single unit.