Phys. Rev. B 101, 081104(R) (2020) - Bulk quantum Hall effect of spin-valley coupled Dirac fermions in the polar antiferromagnet ${\mathrm{BaMnSb}}

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Bulk quantum Hall effect of spin-valley coupled Dirac fermions in the polar antiferromagnet ${BaMnSb}_{2}$

H. Sakai, H. Fujimura, S. Sakuragi, M. Ochi, R. Kurihara, A. Miyake, M. Tokunaga, T. Kojima, D. Hashizume, T. Muro, K. Kuroda, Takeshi Kondo, T. Kida, M. Hagiwara, K. Kuroki, M. Kondo, K. Tsuruda, H. Murakawa, and N. Hanasaki

Phys. Rev. B 101, 081104(R) – Published 13 February 2020

Abstract

Unconventional features of relativistic Dirac/Weyl quasiparticles in topological materials are most evidently manifested in the two-dimensional quantum Hall effect (QHE), whose variety is further enriched by their spin and/or valley polarization. Although its extension to three dimensions has been long sought and inspired theoretical proposals, material candidates have been lacking. Here, we have discovered valley-contrasting spin-polarized Dirac fermions in a multilayer form in the bulk antiferromagnet ${BaMnSb}_{2}$ , where out-of-plane Zeeman-type spin splitting is induced by in-plane inversion symmetry breaking and spin-orbit coupling in the distorted Sb square net. Furthermore, we have observed well-defined quantized Hall plateaus together with vanishing interlayer conductivity at low temperatures as a hallmark of the half-integer QHE in a bulk form. The Hall conductance of each layer is found to be nearly quantized to $2 (N + 1 / 2) e^{2} / h$ , with $N$ being the Landau index, which is consistent with two spin-polarized Dirac valleys protected by the strong spin-valley coupling.

Received 21 March 2019
Revised 20 January 2020
Accepted 22 January 2020

DOI:https://doi.org/10.1103/PhysRevB.101.081104

Physics Subject Headings (PhySH)

Landau levels Quantum Hall effect Topological phases of matter

Antiferromagnets Dirac semimetal Mott insulators

Resistivity measurements Shubnikov-de Haas effect

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

H. Sakai^1,2,*, H. Fujimura¹, S. Sakuragi³, M. Ochi¹, R. Kurihara³, A. Miyake³, M. Tokunaga³, T. Kojima⁴, D. Hashizume⁵, T. Muro⁶, K. Kuroda³, Takeshi Kondo³, T. Kida⁷, M. Hagiwara⁷, K. Kuroki¹, M. Kondo¹, K. Tsuruda¹, H. Murakawa¹, and N. Hanasaki¹

¹Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan
²PRESTO, Japan Science and Technology Agency, Kawaguchi, Saitama 332-0012, Japan
³The Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan
⁴Department of Chemistry, Osaka University, Toyonaka, Osaka 560-0043, Japan
⁵RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
⁶JASRI, Sayo, Hyogo 679-5198, Japan
⁷Center for Advanced High Magnetic Field Science (AHMF), Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan

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

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Vol. 101, Iss. 8 — 15 February 2020

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Figure 1
(a) Crystal structure for ${BaMnSb}_{2}$ deduced from the single-crystal x-ray diffraction at $\sim 100$ K. The formal valence of each ion is also described. (b) Planar view of the distorted ${Sb}^{-}$ square net (with 1D zigzag chains) coordinated with Ba ions. (c) Calculated band structure for ${BaMnSb}_{2}$ with the SOC. Fermi surfaces for ${BaMnSb}_{2}$ , deduced from (d) the ARPES intensity map at $\sim 60 K$ (integrated over 100 meV at the Fermi level) and (e) first-principles calculation. The $k$ component along the crystallographic $a$ ( $c$ ) axis corresponds to $k_{x}$ ( $k_{y}$ ) [see (b)]. In (e), the Fermi energy is set at $- 130 meV$ measured from the valence band top so that the valley size matches the result of the quantum oscillation [39]. The color of the Fermi surfaces represents the spin polarization $〈 s_{z} 〉$ . (f) Cut of the ARPES intensity taken along the white dashed line in (d), with the calculation results overlaid on the right side (white dotted curve). The ARPES data are symmetrized with respect to $k_{y} = 0$ . (g) Calculated Dirac-like band dispersion near the $Y$ point along the $M - Y - M$ line, where the $〈 s_{z} 〉$ value of each band is represented by red (up) and blue (down) colors. The dashed curve denotes the band dispersion calculated without the SOC.
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Figure 2
Field ( $B$ ) dependence of (a) Hall resistivity $ρ_{y x}$ and (b) interlayer conductivity $σ_{z z}$ ( $= 1 / ρ_{z z}$ ) for ${BaMnSb}_{2}$ at selected temperatures for $B | | b$ up to $\sim 55 T$ . The measurement setup is schematically shown in each panel. The inset shows $σ_{z z}$ vs $1 / B$ at low fields ( $< 9 T$ ), where the SdH frquency $B_{F}$ is defined [ $B_{F} = 21.3 (2) T$ for the sample No. 2] [39].
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Figure 3
(a) Normalized inverse Hall resistivity ( $ρ_{y x}^{0} / ρ_{y x}$ ) and (b) $σ_{z z}$ vs $B_{F} / B$ at 1.4 K for $B | | b$ , where $B_{F}$ is the SdH frequency estimated separately for each sample [39]. $1 / ρ_{y x}^{0}$ (=650 ${S cm}^{- 1}$ ) is obtained from the step size of the $1 / ρ_{y x}$ plateaus between $B_{F} / B = 0.5$ and $B_{F} / B = 1.5$ , where $σ_{z z}$ is almost vanishing.
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Figure 4
(a) Angular ( $θ$ ) dependence of $σ_{z z}$ vs $B_{F} (θ) / B$ at 1.4 K, where $B_{F} (θ)$ is the SdH frequency at each $θ$ . $θ$ is the angle between the field and the $b$ axis shown in (c). Each curve at $θ \geq 7^{\circ}$ is shifted vertically (by 1 or 2 ${S cm}^{- 1}$ ) for clarity. Each origin is denoted by a solid circle on the left axis. (b) Angular dependence of $B_{F}$ and the corresponding cross-sectional area of the Fermi surface $S_{F}$ . The solid curve expresses $B_{F} (0) / cos θ$ . (c) Geometry of the interlayer resistivity measurement in tilted fields.
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Physical Review B

covering condensed matter and materials physics

Bulk quantum Hall effect of spin-valley coupled Dirac fermions in the polar antiferromagnet ${BaMnSb}_{2}$

H. Sakai, H. Fujimura, S. Sakuragi, M. Ochi, R. Kurihara, A. Miyake, M. Tokunaga, T. Kojima, D. Hashizume, T. Muro, K. Kuroda, Takeshi Kondo, T. Kida, M. Hagiwara, K. Kuroki, M. Kondo, K. Tsuruda, H. Murakawa, and N. Hanasaki

Phys. Rev. B 101, 081104(R) – Published 13 February 2020

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Physical Review B

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Bulk quantum Hall effect of spin-valley coupled Dirac fermions in the polar antiferromagnet BaMnSb2

H. Sakai, H. Fujimura, S. Sakuragi, M. Ochi, R. Kurihara, A. Miyake, M. Tokunaga, T. Kojima, D. Hashizume, T. Muro, K. Kuroda, Takeshi Kondo, T. Kida, M. Hagiwara, K. Kuroki, M. Kondo, K. Tsuruda, H. Murakawa, and N. Hanasaki

Phys. Rev. B 101, 081104(R) – Published 13 February 2020

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Bulk quantum Hall effect of spin-valley coupled Dirac fermions in the polar antiferromagnet ${BaMnSb}_{2}$