Unconventional planar Hall effect in exchange-coupled topological insulator--ferromagnetic insulator heterostructures

Unconventional planar Hall effect in exchange-coupled topological insulator–ferromagnetic insulator heterostructures

David Rakhmilevich, Fei Wang, Weiwei Zhao, Moses H. W. Chan, Jagadeesh S. Moodera, Chaoxing Liu, and Cui-Zu Chang

Phys. Rev. B 98, 094404 – Published 6 September 2018

Abstract

The Dirac electrons occupying the surface states (SSs) of topological insulators (TIs) have been predicted to exhibit many exciting magnetotransport phenomena. Here we report the experimental observation of an unconventional planar Hall effect (PHE) and a gate-tunable hysteretic planar magnetoresistance in EuS/TI heterostructures, in which EuS is a ferromagnetic insulator (FMI) with an in-plane magnetization. In such exchange-coupled FMI/TI heterostructures, we find a significant (suppressed) PHE when the in-plane magnetic field is parallel (perpendicular) to the electric current. This behavior differs from previous observations of the PHE in ferromagnets and semiconductors. Furthermore, as the thickness of the 3D TI films is reduced into the 2D limit, in which the Dirac SSs develop a hybridization gap, we find a suppression of the PHE around the charge-neutral point indicating the vital role of Dirac SSs in this phenomenon. To explain our findings, we outline a symmetry argument that excludes linear Hall mechanisms and suggest two possible nonlinear Hall mechanisms that can account for all the essential qualitative features in our observations.

Received 13 September 2017
Revised 20 August 2018

DOI:https://doi.org/10.1103/PhysRevB.98.094404

Physics Subject Headings (PhySH)

Exchange interaction Hall effect

Heterostructures Topological insulators

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

David Rakhmilevich^1,2, Fei Wang³, Weiwei Zhao³, Moses H. W. Chan³, Jagadeesh S. Moodera^1,4, Chaoxing Liu³, and Cui-Zu Chang^1,3,*

¹Francis Bitter Magnet Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
²School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02139, USA
³Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
⁴Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

^*Corresponding author: cxc955@psu.edu

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Issue

Vol. 98, Iss. 9 — 1 September 2018

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Images

Figure 1
The EuS/ ${(B i_{0.22} S b_{0.78})}_{2} T e_{3}$ heterostructures. (a) X-ray diffraction spectrum of a 5-nm EuS/4-QL ${(B i_{0.22} S b_{0.78})}_{2} T e_{3}$ heterostructure, with the peaks of the epitaxial ${(B i_{0.22} S b_{0.78})}_{2} T e_{3}$ film and EuS film identified by blue and red arrows, respectively. (b) Schematic drawing of the sample structure and the Hall bar configuration. An image of the real Hall bar is shown in Ref. [22]. (c) Schematic diagrams showing the shift of the Dirac SSs in the presence of the in-plane magnetization. The linear surface bands are a bit tilted due to the quadratic term $D k^{2}$ included in the Hamiltonian of the Dirac surface states. The green arrows denote the spin of the Dirac electrons.
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Figure 2
Gate-dependent measurements on EuS/ ${(B i_{0.22} S b_{0.78})}_{2} T e_{3}$ heterostructures measured at $T = 1 K$ . The gate ( $V_{g}$ ) dependence of the sheet longitudinal sheet resistance ( $R_{x x}$ ) of 4-QL (with Dirac SSs) and 3-QL (with a hybridization gap) heterostructures is shown in (a) and (c), respectively. The corresponding $I_{s d} − V_{s d}$ curves for several $V_{g} s$ are shown in (b) and (d).
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Figure 3
In-plane magnetotransport in EuS/ ${(B i_{0.22} S b_{0.78})}_{2} T e_{3}$ heterostructures. (a), (c) Representative PHE and PMR measurements for several $V_{g} s$ taken on 5-nm EuS/4-QL ${(B i_{0.22} S b_{0.78})}_{2} T e_{3}$ (with Dirac SSs) (a) and 5-nm EuS/3-QL ${(B i_{0.22} S b_{0.78})}_{2} T e_{3}$ (with a hybridization gap) (c) heterostructures, respectively. (b), (d) Summary of the $V_{g}$ dependence of PHR and PMR for 5-nm EuS/4-QL ${(B i_{0.22} S b_{0.78})}_{2} T e_{3}$ (b) and 5-nm EuS/3-QL ${(B i_{0.22} S b_{0.78})}_{2} T e_{3}$ (d) heterostructures, respectively. The error bars for the PHR quantify the deviations in the signal around the limits of the transition, while the error bars in PMR quantify the deviations around 600 Oe. The zero PMR value in (d) was assigned due to the inability to observe a clear MR dependence while the error bar quantifies the fluctuations in the signal.
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Figure 4
Angle-dependent PHE and PMR measurements in another 5-nm EuS/4-QL ${(B i_{0.22} S b_{0.78})}_{2} T e_{3}$ heterostructure. (a)–(c) PHE (top panels) and PMR (bottom panels) taken on another 5-nm EuS/4-QL ${(B i_{0.22} S b_{0.78})}_{2} T e_{3}$ (with Dirac SSs) heterostructure with $Φ = 0^{\circ}$ (a), $Φ = 30^{\circ}$ (b), and $Φ = 90^{\circ}$ (c), respectively. $Φ$ is the angle between the current I and the in-plane magnetic field B. (d) Summary of the PHR as a function of $Φ$ . The dashed line is a fit to $A \cdot \cos Φ$ (A is the amplitude).
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Figure 5
Out-of-plane magnetotransport in a 5-nm EuS/4-QL ${(B i_{0.22} S b_{0.78})}_{2} T e_{3}$ heterostructure. (a) Out-of-plane Hall resistance $R_{y x}$ at different $V_{g} s$ and $T = 2 K$ . (b) MR curves at different $V_{g} s$ and $T = 2 K$ .
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