The effects of δ-doping on GMR in 2DEG modulated with two ferromagnetic stripes of center misalignment

Using high precision numerical calculations with an improved transfer matrix method, we calculated the transmission probabilities, the conductance, as well as the modified giant magnetoresistance ratio with δ-doping in several GMR model devices. We also obtained the spectrum of the giant magnetoresistance ratio as a function of the Fermi energy, the dependence of the peak magnetoresistance ratio value, and its Fermi energy position on the weight and the position of the δ-doping. The results are then compared with the previous theoretical calculations and experimental data. The results shows that our results are better than previous theoretical calculations results, and pointed out that some mistakes must be made during the previous theoretical calculation for physical quantities of GMR devices in anti-parallel alignment. Graphical Abstract In this work, using high precision numerical calculations and the improved transfer matrix method, we calculated the transmission probability, conductance and magnetoresistance ratio(MRR) with δ-doping in 2DEG modulated with two ferromagnetic stripes of center misalignment, and then obtain the dependence of the peak MRR value and its Fermi energy position on the δ-doping weight and position. Furthermore, the results are then compared with the previous theoretical calculations and experimental data. Our results are better than previous theoretical calculations results, and are completely consistent with the experimental results by comparison. This improved method is general, and it is demonstrated very fast for evaluating various spin-dependent transport properties and magnetoresistance ratio in complex hybrid magnetic-electric structures.