Length dependence of magnetoresistance in organic spin valves

With the Su-Schrieffer-Heeger model and Green's function method, the length dependence of magnetoresistance in organic spin valves is calculated in the frame of tunneling transport. Based on different energy level alignments between the molecule and the electrodes, the length effect on the magnetoresistance is investigated in three transport schemes, barrier tunneling, resonant tunneling, and transition between them. In the first scheme, a length-induced exponential or linear decline of the magnetoresistance is obtained. An oscillation and nonlinear dependence are observed in the second and third schemes. The mechanism is explained by investigating the transmission spectra at different lengths, where the evolution of the efficient transmission in the bias window with length differs in different schemes. The results agree with many experimental measurements qualitatively.