Spin-dependent thermoelectric effect in polaronic Kondo transport through a Rashba quantum dot coupled with ferromagnetic leads

• We derive a new transport formula to deal with complex interactions.
• Strengthening the electron–phonon coupling can improve the charge thermopower at the Kondo temperature.
• Even small spin–orbit coupling can suppress FOM at the Kondo temperature greatly.
• The electron–phonon coupling in conjunction with the spin–orbit coupling can rebuild Fermi liquid state in the Kondo regime.

We investigate the spin-dependent thermoelectric effect of a Rashba molecular quantum dot coupled with both ferromagnetic leads and a phonon bath in the Kondo regime. A transport formula is derived to deal with the strong electron–electron and electron–phonon interaction with the spin–orbit coupling of arbitrary intensity simultaneously. The numerical results show that only strengthening the electron–phonon coupling can improve the charge thermopower, while even very small spin–orbit coupling can suppress both the thermocharge figure of merit and the thermospin one at the Kondo temperature greatly. It is also found that the electron–phonon coupling in conjunction with the spin–orbit coupling can rebuild Fermi liquid state in the Kondo regime.