Giant Edelstein effect in topological-insulator–graphene heterostructures

The control of a ferromagnet's magnetization via only electric currents requires the efficient generation of current-driven spin torques. In magnetic structures based on topological insulators (TIs) current-induced spin-orbit torques can be generated. Here we show that the addition of graphene, or bilayer graphene, to a TI-based magnetic structure greatly enhances the current-induced spin-density accumulation and significantly reduces the amount of power dissipated. We find that this enhancement can be as high as a factor of 100, giving rise to a giant Edelstein effect. Such a large enhancement is due to the high mobility of graphene (bilayer graphene) and to the fact that the graphene (bilayer graphene) sheet very effectively screens charge impurities, the dominant source of disorder in topological insulators. Our results show that the integration of graphene in spintronics devices can greatly enhance their performance and functionalities.

Figure 1

Sketch of (a) a TI-graphene-FM and (b) a magnetically doped TI-graphene heterostructure. In (a) the random charges are shown. In (b) the spheres represent the magnetic dopant; the random charges are not shown explicitly. (c) Atom arrangement for the commensurate stacking considered. (d) Bands for TI-SLG for $\mathrm{\Delta }=0,\delta \mu =0$. (e) Bands for TI-BLG for $\mathrm{\Delta }=20$ meV and $\delta \mu =0$. (f) Spin texture on the Fermi surface formed by the bands shown in (d) for ${\epsilon }_F=100$ meV.

Figure 2

Diagrams used to calculate the charge conductivity and the spin-current response.

Figure 3

(a) $\langle {\tau }_0\left({\epsilon }_F\right)\rangle$ and (b) $\langle {\tau }_t\left({\epsilon }_F\right)\rangle$ for $\mathrm{\Delta }=0$ meV, $\delta \mu =0$ meV, and $n_{\mathrm{imp}}={10}^{12}{\mathrm{cm}}^{-2}$. The solid lines correspond to $t=45$ meV, while dashed lines correspond to the limit $t=0$ meV.

Figure 4

(a) ${\chi }^{s_x{J}_y}$ as a function of ${\epsilon }_F$ for $\delta \mu =0,t=45$ meV, and $\mathrm{\Delta }=20$ meV $\left(\mathrm{\Delta }=0\right)$ with out-of-plane magnetization $\widehat{m}=\widehat{z}(\perp )$, shown by solid (dashed) lines. Inset: sketch showing the spin-density accumulation on the top and bottom surfaces of a TI induced by a current in the $y$ direction. (b) ${\chi }^{s_x{J}_y}$ as a function of ${\epsilon }_F$ for in-plane $\widehat{m}=\widehat{x}(\parallel )$ [out-of-plane $\widehat{m}=\widehat{z}(\perp )]$ magnetization and $\mathrm{\Delta }=20$ meV, shown by dashed (solid) lines. The other parameters are the same as in (a). (c) Enhancement of ${\chi }^{s_x{J}_y}$ in a TI-BLG system compared to TI alone as a function of ${\epsilon }_F$ and $\delta \mu$ for $\mathrm{\Delta }=0$. (d) ${\chi }^{s_x{J}_y}$ for TI-BLG when $t=0$. In all the panels, the disorder parameters are $n_{\mathrm{imp}}={10}^{12}{\mathrm{cm}}^{-2}$ and $d=1$ nm.

Figure 5

(a) ${\chi }^{s_x{J}_y}$ as a function of the exchange interaction $\mathrm{\Delta }$ for a TI-FM heterostructure at ${\epsilon }_F=60$ meV. (b) Ratio ${\chi }^{s_x{J}_y}/{\chi }_{TI}^{s_x{J}_y}$ of the TI-BLG-FM (red circles) and TI-SLG-FM (blue squares) responses to the TI-FM response. The magnetization direction is out of plane, $\widehat{m}=\widehat{z}(\perp )$.

Figure 6

(a) ${\chi }^{s_x{J}_y}/{\chi }_{TI}^{s_x{J}_y}$ as a function of the tunneling amplitude $t$ for TI-SLG and TI-BLG heterostructures at ${\epsilon }_F=60$ meV and $\delta \mu =0$. (b) ${\chi }^{s_x{J}_y}$ as a function of the effective distance to the impurities $d$ for TI-SLG and TI-BLG heterostructures at ${\epsilon }_F=60$ meV and $\delta \mu =0$.

Figure 7

${\sigma }^{yy}\left({\epsilon }_F\right)$ for TI (dashed line), TI-SLG (dotted line), and TI-BLG (solid line) for (a) $\mathrm{\Delta }=0$ and (b) $\mathrm{\Delta }=20$ meV with out-of-plane magnetization, $\widehat{m}=\widehat{z}(\perp )$. $t=45$ meV, $\delta \mu =0$, and $n_{\mathrm{imp}}={10}^{12}{\mathrm{cm}}^{-2}$.

Figure 8

TI-BLG band structure for $\delta \mu =125$ meV and tunneling amplitude $t=45$ meV.

Figure 9

(a) ${\chi }^{s_x{J}_y}$ as a function of twist angle $\theta$ for TI-SLG. (b) Same as (a) for TI-BLG.