Large Anomalous Hall Effect in Topological Insulators with Proximitized Ferromagnetic Insulators

Masataka Mogi, Taro Nakajima, Victor Ukleev, Atsushi Tsukazaki, Ryutaro Yoshimi, Minoru Kawamura, Kei S. Takahashi, Takayasu Hanashima, Kazuhisa Kakurai, Taka-hisa Arima, Masashi Kawasaki, and Yoshinori Tokura

Phys. Rev. Lett. 123, 016804 – Published 2 July 2019

Abstract

We report a proximity-driven large anomalous Hall effect in all-telluride heterostructures consisting of the ferromagnetic insulator ${Cr}_{2} {Ge}_{2} {Te}_{6}$ and topological insulator ${(Bi, Sb)}_{2} {Te}_{3}$ . Despite small magnetization in the ${(Bi, Sb)}_{2} {Te}_{3}$ layer, the anomalous Hall conductivity reaches a large value of $0.2 e^{2} / h$ in accord with a ferromagnetic response of the ${Cr}_{2} {Ge}_{2} {Te}_{6}$ . The results show that the exchange coupling between the surface state of the topological insulator and the proximitized ${Cr}_{2} {Ge}_{2} {Te}_{6}$ layer is effective and strong enough to open the sizable exchange gap in the surface state.

Received 30 November 2018
Revised 24 March 2019

DOI:https://doi.org/10.1103/PhysRevLett.123.016804

Physics Subject Headings (PhySH)

Anomalous Hall effect Chern insulators Electrical conductivity Exchange interaction Ferromagnetism Magnetotransport Surface states Topological insulators Topological materials

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Masataka Mogi ^1,*, Taro Nakajima², Victor Ukleev^2,3, Atsushi Tsukazaki⁴, Ryutaro Yoshimi², Minoru Kawamura², Kei S. Takahashi^2,5, Takayasu Hanashima⁵, Kazuhisa Kakurai^2,6, Taka-hisa Arima^2,7, Masashi Kawasaki^1,2, and Yoshinori Tokura^2,2,8,†

¹Department of Applied Physics and Quantum Phase Electronics Center (QPEC), University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan
²RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
³Laboratory for Neutron Scattering and Imaging (LNS), Paul Scherrer Institute (PSI), CH-5232, Villigen, Switzerland
⁴Institute for Materials Research, Tohoku University, Sendai, Miyagi 980-8577, Japan
⁵PRESTO, Japan Science and Technology Agency (JST), Chiyoda-ku, Tokyo 102-0075, Japan
⁶Comprehensive Research Organization for Science and Society (CROSS), Tokai, Ibaraki 319-1106, Japan
⁷Department of Advanced Materials Science, University of Tokyo, Kashiwa, Chiba 277-8561, Japan
⁸Tokyo College, University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan

^*mogi@cmr.t.u-tokyo.ac.jp
^†tokura@riken.jp

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Vol. 123, Iss. 1 — 3 July 2019

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Images

Figure 1
(a) Schematic drawing of the interfacial exchange coupling in a 3D TI sandwiched by FMIs. (b) Schematic of crystal structures of TI ${(Bi, Sb)}_{2} {Te}_{3}$ and FMI ${Cr}_{2} {Ge}_{2} {Te}_{6}$ with the relationship of stacking orientation expected from their Te arrangements in the respective layer planes. (c) Cross-sectional high-angle annular dark-field STEM image of the $CGT (12 nm) / BST (9 nm) / CGT (12 nm)$ heterostructure grown on an InP substrate with a BST buffer layer (left). The lateral atomic distance of each layer obtained by the Fourier transformation of the left image plotted along the growth direction (right).
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Figure 2
(a) Schematic of the PNR experimental setup for the $CGT / BST / CGT$ structure. (b) Magnetization hysteresis loops under out-of-plane ( $H_{⊥}$ ) and in-plane ( $H_{∥}$ ) magnetic fields for the identical $CGT (12 nm) / BST (9 nm) / CGT (12 nm)$ sample used in the PNR experiments. The black arrow represents the saturation field for the in-plane direction. (c) Measured (dots) and fitted (solid lines) reflectivity curves for the x-ray (black) and neutron of spin-up ( $R^{+}$ ) (red) and spin-down ( $R^{-}$ ) (blue) as a function of momentum transfer ( $Q_{z}$ ) on a logarithmic scale. The error bars represent one standard deviation. (d) PNR spin-asymmetry ratio $(R^{+} - R^{-}) / (R^{+} + R^{-})$ obtained from experimental and fitted reflectivity curves in (c). The error bars represent one standard deviation. (e) X-ray SLD (black) and neutron SLD divided into the nuclear (blue) and the magnetic (red) SLDs as a function of the distance from the InP substrate surface ( $z$ ). The $r_{e}$ in the unit of the x-ray SLD denotes the classical electron radius of $2.8179 \dots \times 10^{- 15} m$ . For the magnetic SLD, the value of $M$ corresponding to the neutron SLD is shown in the right ordinate.
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Figure 3
(a) Schematic layout of $CGT (12 nm) / {({Bi}_{1 - x} {Sb}_{x})}_{2} {Te}_{3} (2 nm) / {Bi}_{2} {Te}_{3} (2 nm) / {({Bi}_{1 - x} {Sb}_{x})}_{2} {Te}_{3} (2 nm) / CGT (12 nm)$ heterostructure. (b), (c), Temperature ( $T$ ) [out-of-plane magnetic field ( $μ_{0} H_{⊥}$ )] dependence of the longitudinal sheet resistivity ( $ρ_{x x}$ ) in zero-field (b) [the Hall resistivity ( $ρ_{y x}$ ) at 2 K (c)] of $CGT / {({Bi}_{1 - x} {Sb}_{x})}_{2} {Te}_{3} / {Bi}_{2} {Te}_{3} / {({Bi}_{1 - x} {Sb}_{x})}_{2} {Te}_{3} / CGT$ ( $x = 0.3$ , 0.6, 0.64) heterostructures. (d) Sb fraction ( $x$ ) dependence of the sheet carrier density ( $| n_{2 D} |$ ) (top), the longitudinal sheet conductivity ( $σ_{x x}$ ) (middle), and the Hall conductivity ( $σ_{x y}$ ) (bottom) at 2 K. (Insets) Simplified schematics of band structures representing the different Fermi energies; the blue lines represent the dispersion of the surface state. (e) The anomalous Hall conductivity ${σ_{x y}}^{A}$ is plotted against the $σ_{x x}$ plot, with the use of the data for the present heterostructures shown in (d) in comparison with other various FMI-TI heterostructures [17, 21, 22, 23, 24, 25]. The values of ${σ_{x y}}^{A}$ and $σ_{x x}$ are taken from the data obtained at the lowest temperature in the measurements (2–5 K) for the magnetized state where the out-of-plane magnetization saturates.
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Figure 4
(a) $M − T$ and (b) $σ_{x y} − T$ curves measured under field cooling with $μ_{0} H_{⊥} = 0.05 T$ in $BST / CGT$ ( $t = 1.4$ , 2.2, 2.9, and 8.1 nm) bilayer structures. Black arrows indicate the Curie temperature $T_{C}$ for highlighting the changes against $t$ . (c) CGT thickness $t$ dependence of $σ_{x y}$ (red closed circles, left red ordinate) and the spontaneous magnetization $M_{s}$ (black closed squares, right black ordinate) at 2 K under zero magnetic field (top) and $σ_{x x}$ at 2 K (blued closed circles, left blue ordinate) and $T_{C}$ (black closed squares, right black ordinate) (bottom). (Inset) Schematic layout of ${({Bi}_{0.5} {Sb}_{0.5})}_{2} {Te}_{3} (6 nm) / CGT (t nm)$ bilayer structure.
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