Tunnel magneto-Seebeck effect in magnetic tunnel junctions with a single-crystal barrier

We have studied the tunnel magneto-Seebeck (TMS) effect in magnetic tunnel junctions with a single-crystal barrier using an extending spintronic theory developed previously by us. The theory is founded on optical methods, and thus, compared to the conventional theories, it can better take into account the periodicity of the single-crystal barrier and the coherence of the tunneling process. The results show that, the Seebeck coefficients can oscillate with the barrier thickness. Physically, the oscillations come from the diffraction of the tunneling electrons by the periodic potential of the single-crystal barrier. Owing to the oscillations, there appear a series of peaks of the TMS ratio for some barrier thicknesses which correspond to the zero points of the Seebeck coefficients. In particular, the magnitudes of the calculated Seebeck coefficients are in accordance with the experimental values of the intrinsic Joule heating. Furthermore, the influences of the ferromagnetic electrodes and barrier on the oscillations are investigated. It is found that, the ferromagnetic electrodes only have a remarkable influence on the amplitudes of the oscillations, whereas the barrier has significant influences on both the amplitudes and periods.