Anomalous magnetoresistance of a two-dimensional ferromagnet/ferromagnet junction on the surface of a topological insulator

We investigate charge transport in two-dimensional ferromagnet/ferromagnet junction on a topological insulator. The conductance across the interface depends sensitively on the directions of the magnetizations of the two ferromagnets, showing anomalous behaviors compared with the conventional spin valve. This stems from the way how the wave functions connect between both sides. It is found that the conductance depends strongly on the in-plane direction of the magnetization. Moreover, in sharp contrast to the conventional magnetoresistance effect, the conductance at the parallel configuration can be much smaller than that at the antiparallel configuration.

Figure 1

(Color online) Schematics of $F1/F2$ junction. The ferromagnetism is induced in the topological surface state due to the proximity effect by the ferromagnetic insulators deposited on the top. The current flows on the surface of the topological insulator.

Figure 2

(Color) tunneling conductance $\sigma$ with $Z=0$ for [(a) and (c)] $m_2=0$, and [(b) and (d)] $m_2=\sqrt{0.9}E$. $n\text{−}n$ junction at $V=0$ in (a) and (b). $p\text{−}n$ junction at $V=2E$ in (c) and (d).

Figure 3

(Color) similar plots to Fig. 2 with $Z=\pi /2$ for [(a) and (c)] $m_2=0$ and [(b) and (d)] $m_2=\sqrt{0.9}E$. n-n junction at $V=-E$ in (a) and (b). $p\text{−}n$ junction at $V=2E$ in (c) and (d).

Figure 4

(Color online) Positions of Fermi surfaces. On the $F1$, the Fermi surface moves as illustrated, as ${\mathbf{m}}_1$ rotates around $z$ axis.

Figure 5

(Color online) Connectivity of the wave function across the [(a) and (b)] $n\text{−}n$ junction and [(c) and (d)] p-n junction. The magnetizations are parallel $\left(\theta =0\right)$ in (a) and (c), while they are antiparallel $\left(\theta =\pi \right)$ in (b) and (d). The arrows represent the electron’s spin.