Splitting and Restoration of Kondo Peak in a Deformed Molecule Quantum Dot Coupled to Ferromagnetic Electrodes

We adopt the nonequilibrium Green's function method to theoretically study the Kondo effect in a deformed molecule, which is treated as an electron-phonon interaction (EPI) system. The self-energy for phonon part is calculated in the standard many-body diagrammatic expansion up to the second order in EPI strength. We find that the multiple phonon-assisted Kondo satellites arise besides the usual Kondo resonance. In the antiparallel magnetic configuration the splitting of main Kondo peak and phonon-assisted satellites only happen for asymmetrical dot-lead couplings, but it is free from the symmetry for the parallel magnetic configuration. The EPI strength and vibrational frequency can enhance the spin splitting of both main Kondo and satellites. It is shown that the suppressed zero-bias Kondo resonance can be restored by applying an external magnetic field, whose magnitude is dependent on the phonoic effect remarkably. Although the asymmetry in tunnel coupling has no contribution to the restoration of spin splitting of Kondo peak, it can shrink the external field needed to switch tunneling magnetoresistance ratio between large negative dip and large positive peak.