EN
Phonon-assisted electronic tunneling is studied through a double quantum dot coupled in parallel to ferromagnetic electrodes. The current-voltage characteristics for the system are derived within the nonequilibrium Green function technique based on equation of motion. It is found that additional phonon-induced resonance peaks appear in the spectral function on both sides of the main resonances corresponding to the quantum dot energy levels. It is shown that the "molecular-like" resonances are reproduced in the phonon side bands in the differential conductance. A significant phonon-induced enhancement of tunnel magnetoresistance as well as tunnel magnetoresistance oscillations are also predicted.