Field-tunable Weyl points and large anomalous Hall effect in the degenerate magnetic semiconductor ${\mathrm{EuMg}}_{2}{\mathrm{Bi}}_{2}$

Letter

Field-tunable Weyl points and large anomalous Hall effect in the degenerate magnetic semiconductor ${EuMg}_{2} {Bi}_{2}$

M. Kondo, M. Ochi, R. Kurihara, A. Miyake, Y. Yamasaki, M. Tokunaga, H. Nakao, K. Kuroki, T. Kida, M. Hagiwara, H. Murakawa, N. Hanasaki, and H. Sakai

Phys. Rev. B 107, L121112 – Published 28 March 2023

Abstract

Magnets, with topologically nontrivial Dirac/Weyl points, have recently attracted significant attention owing to their unconventional physical properties, such as a large anomalous Hall effect. However, they typically have a high carrier density and a complicated band structure near the Fermi energy. In this Letter, we report a degenerate magnetic semiconductor ${EuMg}_{2} {Bi}_{2}$ , which exhibits a single valley at the $Γ$ point, where field-tunable Weyl points form via a magnetic exchange interaction with the local Eu spins. By the high-field measurements on high-quality single crystals, we observed quantum oscillations in the resistivity, elastic constant, and surface impedance, which enabled us to determine the position of the Fermi energy $E_{F}$ . In combination with a first-principles calculation, we revealed that the Weyl points are located in the vicinity of $E_{F}$ when the Eu spins are fully polarized, leading to a peak of energy-dependent anomalous Hall conductivity due to the Berry curvature. Accordingly, in the forced ferromagnetic phase, we observed a large anomalous Hall effect (Hall angle $Θ_{AH} \sim 0.07$ ) qualitatively consistent with the calculation, which demonstrates a marked impact of the Weyl points in the simple band structure.

Received 25 July 2022
Revised 2 December 2022
Accepted 8 March 2023

DOI:https://doi.org/10.1103/PhysRevB.107.L121112

Physics Subject Headings (PhySH)

Anomalous Hall effect Electrical conductivity Fermi surface First-principles calculations Hall effect Magnetic interactions Magnetic order Magnetoresistance Magnetotransport Shubnikov-de Haas effect Spin-orbit coupling Topological Hall effect Topological materials Transport phenomena de Haas-van Alphen effect

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

M. Kondo ^1,*, M. Ochi^1,2, R. Kurihara^3,4, A. Miyake ³, Y. Yamasaki^5,6, M. Tokunaga ³, H. Nakao ⁷, K. Kuroki¹, T. Kida ⁸, M. Hagiwara⁸, H. Murakawa¹, N. Hanasaki^1,9, and H. Sakai ^1,†

¹Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan
²Forefront Research Center, Osaka University, Toyonaka, Osaka 560-0043, Japan
³The Institute for Solid State Physics, The University of Tokyo, Kashiwa, Chiba 277-8581, Japan
⁴Department of Physics, Faculty of Science and Technology, Tokyo University of Science, Noda, Chiba 278-8510, Japan
⁵Research and Services Division of Materials Data and Integrated System (MaDIS), National Institute for Materials Science(NIMS), Tsukuba, Ibaraki 305-0047, Japan
⁶Center for Emergent Matter Science (CEMS), RIKEN, Wako, Saitama 351-0198, Japan
⁷Photon Factory, Institute of Materials Structure Science, KEK, Tsukuba, Ibaraki 305-0801, Japan
⁸Center for Advanced High Magnetic Field Science (AHMF), Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
⁹Spintronics Research Network Division, Institute for Open and Transdisciplinary Reserch Initiatives, Osaka University, Suita, Osaka 565-0871, Japan

^*Corresponding author: kondo@gmr.phys.sci.osaka-u.ac.jp
^†Corresponding author: sakai@phys.sci.osaka-u.ac.jp

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Vol. 107, Iss. 12 — 15 March 2023

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Figure 1
(a) Temperature dependence of out-of-plane (red) and in-plane (blue) magnetic susceptibilities measured at 0.01 T in a cooling run. The vertical dotted line denotes the Néel temperature $T_{N}$ ( $= 6.7$ K) for the Eu sublattice. The inset shows a photograph of a typical crystal. (b) Temperature dependence of intensity of resonant magnetic reflection (0 0 1.5) at $E = 6.975$ keV at 0 T. The inset shows the intensities of (0 0 1.5) magnetic reflection below and above $T_{N}$ (3 and 8 K, respectively). (c) The temperature dependence of in-plane resistivity $ρ_{x x}$ below 20 K. The inset shows the overall temperature dependence of $ρ_{x x}$ . (d) Calculated band structure of ${EuMg}_{2} {Bi}_{2}$ for the A-type antiferromagnetic order of Eu spins. The inset shows the first Brillouin zone. (e) The magnetic phase diagram of ${EuMg}_{2} {Bi}_{2}$ as functions of the field ( $B ∥ c$ ) and temperature ( $T$ ). PM, A-AFM, and f-FM denote the paramagnetic, A-type antiferromagnetic, and forced-ferromagnetic phases, respectively. $B_{c}$ corresponds to the transition field to the f-FM phase. The inset exhibits the crystal and magnetic structure of ${EuMg}_{2} {Bi}_{2}$ . The easy-axis direction is here assumed to be parallel to the $b$ axis because the in-plane spin direction cannot be determined from the present experiment on a sample with magnetic domains [35] (see Fig. S2 for details). (f)–(h) The field dependence of (f) magnetization $M$ , (g) $ρ_{x x}$ , and (h) Hall resistivity $ρ_{y x}$ (up to 9 T). Triangles in (f) and (g) denote $B_{c}$ at various temperatures below $T_{N}$ . All $ρ_{x x}$ data in (g) are shifted vertically by 20 or 40 $µ Ω cm$ for clarity. The insets show a schematic illustration of measurements of $ρ_{x x} (V_{x x})$ and $ρ_{y x} (V_{y x})$ .
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Figure 2
Field dependence of anomalous Hall angle $Θ_{AH} = ρ_{y x}^{AH} / ρ_{x x}$ at various temperatures. The oscillatory structure above 6 T is due to SdH oscillation for $ρ_{y x}$ . The inset shows the field dependence of $ρ_{y x}$ and its anomalous part $ρ_{y x}^{A}$ at 2 K. The black dotted line corresponds to the ordinary part $ρ_{y x}^{N}$ of $ρ_{y x}$ at 2 K, which is obtained from the liner fit to the experimental data above $B_{c}$ . Note here that the $ρ_{y x}^{N}$ is vertically shifted to demonstrate the fitted result at the high-field region. The red curve represents the field dependence of the magnetization $M$ at 2 K.
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Figure 3
(a)–(c)Valence band structures around the $Γ$ point near $E_{F}$ (lower panels) for various magnetic states (upper panels). Red and blue colors of band dispersions represent spin up and spin down, respectively. The dotted lines denote the Fermi energy $E_{F}$ determined from the SdH frequency $B_{F}$ at $T = 1.4$ K. The vertical arrows in (b) and (c) denote the size of spin splitting. The insets of (a) and (c) show the schematic illustration of Fermi surfaces within the $k_{x} k_{y}$ plane, where the color denotes the $〈 S_{z} 〉$ value. (d) Anomalous Hall conductivity $σ_{x y}^{A}$ as a function of $E_{F}$ . The solid black curve represents the calculated result for the f-FM phase. The solid red circle denotes the experimental data (2 K, 9 T) for pristine ${EuMg}_{2} {Bi}_{2}$ , while the open blue squares and open green triangle denote those for the Mg-annealed crystals and In-doped crystal (see Fig. S9 for details), respectively.
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Figure 4
(a)–(c) Field dependence of (a) $ρ_{x x}$ , (b) resonance frequency of tunnel diode oscillator $Δ f$ , and (c) the relative change of longitudinal elastic constant $Δ C_{33} / C_{33}$ at $T = 1.4$ K up to $\sim 50$ T. Triangles denote the oscillatory component. The inset shows the fast Fourier transform (FFT) spectrum of $- d^{2} ρ_{x x} / d {(1 / B)}^{2}$ for a field of 5–15 T. $q$ and $ξ$ in (c) indicate the propagation and polarization direction of ultrasonic waves, respectively. (d) $- d^{2} ρ_{x x} / d {(1 / B)}^{2}$ vs $1 / B$ at various field tilt angles ( $θ$ ), where $θ$ is the angle between the $c$ axis and magnetic field (see inset). (e) The $θ$ dependence of oscillation frequency $B_{F}$ , which is determined from the FFT spectra of $- d^{2} ρ_{x x} / d {(1 / B)}^{2}$ shown in the inset.
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Physical Review B

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Field-tunable Weyl points and large anomalous Hall effect in the degenerate magnetic semiconductor ${EuMg}_{2} {Bi}_{2}$

M. Kondo, M. Ochi, R. Kurihara, A. Miyake, Y. Yamasaki, M. Tokunaga, H. Nakao, K. Kuroki, T. Kida, M. Hagiwara, H. Murakawa, N. Hanasaki, and H. Sakai

Phys. Rev. B 107, L121112 – Published 28 March 2023

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Physical Review B

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Field-tunable Weyl points and large anomalous Hall effect in the degenerate magnetic semiconductor EuMg2Bi2

M. Kondo, M. Ochi, R. Kurihara, A. Miyake, Y. Yamasaki, M. Tokunaga, H. Nakao, K. Kuroki, T. Kida, M. Hagiwara, H. Murakawa, N. Hanasaki, and H. Sakai

Phys. Rev. B 107, L121112 – Published 28 March 2023

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Field-tunable Weyl points and large anomalous Hall effect in the degenerate magnetic semiconductor ${EuMg}_{2} {Bi}_{2}$