Kondo effect in a deformed molecule coupled asymmetrically to ferromagnetic electrodes

The nonequilibrium Kondo effect is studied in a moleculequantum dot coupled asymmetrically to two ferromagnetic electrodesby employing the nonequilibrium Green function technique. Thecurrent-induced deformation of the molecule is taken into account,modeled as interactions with a phonon system, andphonon-assisted Kondo satellites arise on both sides of the usual mainKondo peak. In the antiparallel electrode configuration, theKondo satellites can be split only for the asymmetric dot-leadcouplings, distinguished from the parallel configuration wheresplitting also exists, even though it is for symmetric case. We alsoanalyze how to compensate the splitting and restore the suppressedzero-bias Kondo resonance. It is shown that one can change the TMRratio significantly from a negative dip to a positive peak only byslightly modulating a local external magnetic field, whose value isgreatly dependent on the electron--phonon coupling strength.