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In-Plane Magnetoresistance on the Surface of Topological Insulator

We study the tunneling magneto-transport properties of the Ferromagnetic Insulator-Normal Insulator-Ferromagnetic Insulator(F$\mid$N$\mid$F) and Ferromagnetic Insulator-Barrier Insulator-Ferromagnetic Insulator (F$\mid$B$\mid$F) junctions on the surface of topological insulator in which in-plane magnetization directions of both ferromagnetic sides can be parallel and antiparallel. We derive analytical expressions for electronic conductances of the two mentioned junctions with both parallel and antiparallel directions of magnetization and using them calculate magnetoresistance of the two junctions. We use thin barrier approximation for investigating the F$\mid$B$\mid$F junction. We find that although magnetoresistance of the F$\mid$N$\mid$F and F$\mid$B$\mid$F junctions are tunable by changing the strength of magnetization texture, they show different behaviors with variation of magnetization. In contrast to the magnetoresistance of F$\mid$N$\mid$F, magnetoresistance of F$\mid$B$\mid$F junctions shows very smooth enhance by increasing the strength of magnetization. We suggest an experimental set up to detect our predicted effects.