Transport and Magnetoresistance in Topological Insulator-Based Ferromagnetic/Insulator/Ferromagnetic Junction in the Presence of External Electric Field

Using Landauer-Buttiker formalism, thin barrier approximation, and Klein tunneling theory, the effects of external electric field and induced exchange magnetic gap on the conductance and specifically magnetoresistance (MR) of a topological insulator-based ferromagnet/insulator/ferromagnet (TI-based F/I/F) junction have investigated. Conductance and MR for parallel (P) and antiparallel (AP) magnetic gap configurations are obtained and discussed. The results of MR reveal a significant negative value for maximum magnetic gap at z = (n + 3/4)pi (n = 0, 1...), i.e., in smaller insulator barrier strengths in the presence of an external electric field, while it appears at z = n pi (n = 1, 2...) without electric field in Ref. Linder et al., Phys. Rev. Lett., 104:067001, 2010 (z is the barrier strength). Also, we have found that maximum transmission probability (TP) increases with magnetic gap in the presence of electric field which is one for P case in z = (n + 1/6)pi and approaches to one for induced magnetic gap near the Fermi energy for AP case in the absence of electric field and z = (n + 1/2)pi. Finally, the conductance and MR oscillate with the magnetic gap and barrier strength.