Tunneling of Dirac fermions in a magnetic-induced gapped topological insulator-based F/I/F\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F/I/F$$\end{document} junction

Klein tunneling and magnetoresistance in a ferromagnet/insulator/ferromagnet junction on the surface of a 3-dimensional topological insulator with a gate voltage applied to insulator segment are investigated in thin barrier limit. Due to creation of Dirac charged carriers in surface of a bulk topological insulator caused by spin–orbit interaction and time-reversal symmetry, its transport properties in junctions exhibit new behaviors. We suppose that vectors of magnetization in ferromagnetic regions are perpendicular to the surface of junction in two parallel and antiparallel configurations. We use Landauer–Buttiker formalism to obtain normal conductance resulted from Klein tunneling coefficient in the thin barrier limit. It is shown that transmission probability reaches one for parallel magnetization in Z=nπ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Z=n\pi $$\end{document}, while for antiparallel magnetization in Z=nπ/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Z=n\pi /2$$\end{document}, so that tunneling conductance remains constant. We focus clearly on effect of magneto-induced gap on conductivity and specifically on magnetoresistance of junction, such that an approximately step functional behavior is found for magnetoresistance in terms of magnetization and it shows a significant negative value in maximum magnetic gap of structure for Z=nπ/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Z=n\pi /2$$\end{document}. Finally, the exact period of oscillations of conductance is obtained in parallel and antiparallel magnetizations. Also, we observe Klein transmission in determined values of barrier strength for magnetic-induced gap’s greater than zero.