Large Unidirectional Magnetoresistance in a Magnetic Topological Insulator

We report current-direction dependent or unidirectional magnetoresistance (UMR) in magnetic or nonmagnetic topological insulator (TI) heterostructures, ${\mathrm{Cr}}_x({\mathrm{Bi}}_{1-y}{\mathrm{Sb}}_y{)}_{2-x}{\mathrm{Te}}_3/({\mathrm{Bi}}_{1-y}{\mathrm{Sb}}_y{)}_2{\mathrm{Te}}_3$, that is several orders of magnitude larger than in other reported systems. From the magnetic field and temperature dependence, the UMR is identified to originate from the asymmetric scattering of electrons by magnons. In particular, the large magnitude of UMR is an outcome of spin-momentum locking and a small Fermi wave number at the surface of TI. In fact, the UMR is maximized around the Dirac point with the minimal Fermi wave number.

Figure 1

(a) Schematic diagram of spin-momentum locking of the surface Dirac state in TI. (b),(c)  Schematic illustration of the concept for UMR in TI heterostructures ${\mathrm{Cr}}_x({\mathrm{Bi}}_{1-y}{\mathrm{Sb}}_y{)}_{2-x}{\mathrm{Te}}_3/({\mathrm{Bi}}_{1-y}{\mathrm{Sb}}_y{)}_2{\mathrm{Te}}_3$ ($\mathrm{CBST}/\mathrm{BST}$) on InP substrate under $+J$ (b) and $-J$ (c) dc current. Here, magnetic field, magnetization, and dc current are along the in-plane direction, where dc current is applied perpendicular to the magnetization direction. (d) Schematic illustration of a “normal” $\mathrm{CBST}/\mathrm{BST}$ heterostructure. (e) Magnetic field dependence of resistance $R_{\mathrm{xx}}$ for the sample depicted in (d), measured under $J=+1\mu \mathrm{A}$ (red) and $J=-1\mu \mathrm{A}$ (blue) at 2 K. (f) Difference of the resistance $\mathrm{\Delta }{R}_{\mathrm{xx}}$ of plus and minus current shown in (e). (g)–(i) The same as (d)–(f) for the “inverted” $\mathrm{BST}/\mathrm{CBST}$ heterostructure. (j) $\mathrm{\Delta }{R}_{\mathrm{xx}}$ measured under various current for the normal $\mathrm{CBST}/\mathrm{BST}$ heterostructure. (k) Current $J$ dependence of $\mathrm{\Delta }{R}_{\mathrm{xx}}$ at 2 K under $B=0.7\mathrm{T}$ for the normal $\mathrm{CBST}/\mathrm{BST}$. The black dotted line shows a slope in the low-$J$ region.

Figure 2

(a) Schematic sample configuration for the measurement of in-plane magnetic field $\phi$ dependence of $\mathrm{\Delta }{R}_{\mathrm{xx}}$. $\phi$ is measured from the $y$ axis. (b),(c) Magnetic field and $\phi$ dependence (by 30° step) of normalized $\mathrm{\Delta }{R}_{\mathrm{xx}}$, $\mathrm{\Delta }{R}_{\mathrm{xx}}/\mathrm{\Delta }{R}_{\mathrm{xx}}^0$. Here, $\mathrm{\Delta }{R}_{\mathrm{xx}}^0$ is $\mathrm{\Delta }{R}_{\mathrm{xx}}$ at $\phi =0°$ and 1.0 T. (d)–(f) The same as (a)–(c) for the out-of-plane magnetic field $\theta$ dependence. $\theta$ is measured from the $z$ axis. Here, $\mathrm{\Delta }{R}_{\mathrm{xx}}^0$ is $\mathrm{\Delta }{R}_{\mathrm{xx}}$ at $\theta =90°$ and 1.0 T.

Figure 3

(a) Magnetic field dependence of $\mathrm{\Delta }{R}_{\mathrm{xx}}$ at various temperatures. (b) Schematic concepts of asymmetric scattering of spin-polarized surface Dirac electrons by magnons. (c) Temperature dependence of $\mathrm{\Delta }{R}_{\mathrm{xx}}$ under various magnetic fields. (d) Numerical calculation results of temperature dependent $\mathrm{\Delta }{R}_{\mathrm{xx}}$ under various magnetic fields.

Figure 4

(a),(b) Gate voltage $V_G$ dependence of Hall resistance ($R_{\mathrm{yx}}$) and longitudinal resistance ($R_{\mathrm{xx}}$) under magnetic field $B(||z)$ of 0.01 and 14 T at 2 K. (c),(d) Magnetic field and $V_G$ dependence of $\mathrm{\Delta }{R}_{\mathrm{xx}}$. The $\mathrm{\Delta }{R}_{\mathrm{xx}}$ is taken at $B(||y)=0.7\mathrm{T}$.