Spin Hall effect in a spin-1 chiral semimetal

Open Access

Spin Hall effect in a spin-1 chiral semimetal

Ke Tang, Yong-Chang Lau, Kenji Nawa, Zhenchao Wen, Qingyi Xiang, Hiroaki Sukegawa, Takeshi Seki, Yoshio Miura, Koki Takanashi, and Seiji Mitani

Phys. Rev. Research 3, 033101 – Published 29 July 2021

Abstract

The spin-1 chiral semimetal is a state of quantum matter hosting unconventional chiral fermions that extend beyond the common Dirac and Weyl fermions. B20-type CoSi is a prototypal material that accommodates such an exotic quasiparticle. To date, the spin-transport properties in the spin-1 chiral semimetals have not been thoroughly explored. In this work, we fabricated B20-CoSi thin films on sapphire $c$ -plane substrates by magnetron sputtering and studied the spin Hall effect (SHE) by combining experiments and first-principles calculations. The SHE of CoSi was investigated using CoSi/CoFeB/MgO heterostructures via spin Hall magnetoresistance and harmonic Hall measurements. First-principles calculations yield an intrinsic spin Hall conductivity (SHC) at the Fermi level that is consistent with the experiments and reveal its unique Fermi-energy dependence. Unlike the Dirac and Weyl fermion-mediated Hall conductivities that exhibit a peaklike structure centering around the topological node, SHC of B20-CoSi is odd and crosses zero at the node with two antisymmetric local extrema of opposite sign situated below and above in energy. Hybridization between Co $d$ -Si $p$ orbitals and spin-orbit coupling are essential for the SHC, despite the small (∼1%) weight of the Si $p$ orbital near the Fermi level. This work expands the horizon of topological spintronics and highlights the importance of Fermi-level tuning in order to fully exploit the topology of spin-1 chiral fermions for spin-current generation.

Received 7 April 2021
Revised 24 June 2021
Accepted 28 June 2021

DOI:https://doi.org/10.1103/PhysRevResearch.3.033101

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Spin Hall effect Spintronics

Multilayer thin films Semimetals

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Ke Tang ^1,2, Yong-Chang Lau ^3,4, Kenji Nawa ^1,5, Zhenchao Wen ^1,*, Qingyi Xiang¹, Hiroaki Sukegawa ¹, Takeshi Seki^3,4, Yoshio Miura¹, Koki Takanashi^3,4,6, and Seiji Mitani^1,2

¹National Institute for Materials Science (NIMS), Tsukuba 305-0047, Japan
²Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba 305-8577, Japan
³Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan
⁴Center for Spintronics Research Network, Tohoku University, Sendai 980-8577, Japan
⁵Graduate School of Engineering, Mie University, Tsu 514-8507, Japan
⁶Center for Science and Innovation in Spintronics, Core Research Cluster, Tohoku University, Sendai 980-8577, Japan

^*wen.zhenchao@nims.go.jp

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Vol. 3, Iss. 3 — July - September 2021

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Figure 1
Structural properties of CoSi films and heterostructure for SOT devices. (a) Unit cell of the cubic B20 crystal structure of CoSi and schematic of the band structures of a spin-1 fermion. (b) RHEED pattern of CoSi (47 nm) film surface deposited on a sapphire $c$ -plane substrate. (c) The out-of-plane XRD spectrum of substrate $/ CoSi (47) / {Mg}_{2} Al O_{x}$ (2 nm). (d) The surface morphology of multilayer stacks with the structure of CoSi/CoFeB/MgO for SOT devices.
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Figure 2
The measurement of SMR in CoSi. (a) Illustration of a Hall bar device with the measurement setup and coordinate system, and an optical microscope image of a Hall bar device. (b) Plots of the dependence of resistance on the angle between M and σ for two Hall bar devices with $t_{CoSi} = 4.4$ and 9.0 nm. (c) Inverse of the sheet resistance as a function of CoSi thickness. The red solid line represents the linear fitting curve in a proper range shown by the black solid squares. (d) Extracted SMR ratio as a function of CoSi thickness. Red solid line is the fitting curve using Eq. (1).
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Figure 3
Harmonic Hall measurement at room temperature for quantifying the SOTs generated from CoSi films. (a) Schematic of the setup for the harmonic Hall measurement. (b) Hall resistance measured under an out-of-plane magnetic field for Hall bar devices with $t_{CoSi} = 4.5$ , 5.8, 7.2, and 8.5 nm. (c) First-harmonic Hall resistance $R_{ω}$ as a function of φ. Solid line is the fitted curve by Eq. (2). (d) Second-harmonic Hall resistance $R_{2 ω}$ as a function of φ. Solid curves are the decomposed components of $R_{2 ω}$ based on Eq. (3). $R_{ω}$ and $R_{2 ω}$ shown in (c,d) were measured at $H_{ext} = 2 kOe$ for the device with $t_{CoSi} = 7.2 nm$ . (e) Parameters A and (f) B as a function of $H_{ext}$ and the inverse of $H_{ext}$ , respectively. (g) CoSi thickness dependence of $ξ_{DL}$ and $ξ_{FL}$ . (h) $σ_{SH}$ and $σ_{FL}$ as a function of CoSi thickness. The solid lines are the fitting curves by Eq. (5).
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Figure 4
Temperature dependence of transport properties and SOTs for CoSi films and CoSi/CoFeB heterostructures. (a) The dependence of carrier concentration, mobility, and normalized resistivity on temperature. (b) Parameters A and (c) B as a function of $H_{ext}$ and the inverse of $H_{ext}$ , respectively, at different temperatures. (d) Temperature dependences of $ξ_{DL}$ ( $ξ_{FL}$ ) and (e) $σ_{DL}$ $(σ_{FL})$ . (f) $σ_{DL} / n$ as a function of the carrier mobility for the CoSi/CoFeB heterostructures.
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Figure 5
Band structure and spin Hall conductivity of CoSi. (a) Relativistic band structure of B20-CoSi along high-symmetry $k$ points in the first BZ. Weights of the Co $d$ (blue) and Si $p$ (yellow) orbitals are represented by the size of the symbol. The Fermi level is at $E = 0 eV$ . Horizontal lines indicate the energy positions relative to the Fermi energy. The inset focuses on the crossing bands of the spin-1 chiral fermion around $Γ$ . (b) Spin Berry curvature ( $Ω_{x y}^{z}$ ) contributions along the high-symmetry $k$ -point paths on the Fermi level. The results from the full SOC (black) and the SOC on only Co (cyan) or Si (magenta) are shown. (c) Energy dependence of calculated spin Hall conductivity, $σ_{x y}$ , in the rigid band model. The region of experimental results is also indicated. (d) Illustration of the first BZ showing the $k$ paths. Note that X is at (0.5, 0, 0) and X′ is at (0, 0.5, 0), respectively.
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Figure 6
Spin Berry curvature contributions projected onto the $k_{x} k_{y}$ plane at $k_{z} = 0$ in the BZ. (a) Energy slice at 0.24, (b) 0.12, (c) 0.06, (d) 0.03, (e) 0.00 (Fermi level), and (f) −0.03 eV, respectively [see also Fig. 5 and 5]. The color bar indicates positive (red) and negative (blue) contributions of $Ω_{x y}^{z}$ . The $k_{x} k_{y}$ plane corresponds to filled area (blue) in Fig. 5.
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