Research ArticleMATERIAL PROPERTIES

Quantum Hall effect in a bulk antiferromagnet EuMnBi2 with magnetically confined two-dimensional Dirac fermions

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Science Advances  29 Jan 2016:
Vol. 2, no. 1, e1501117
DOI: 10.1126/sciadv.1501117
  • Fig. 1 Transport coupled with the magnetic order of Eu sublattice.

    (A to D) Temperature dependence of magnetic and transport properties near the AFM transition temperature (TN) for EuMnBi2. (A) Magnetic susceptibility M/H for the field parallel to the c axis (H||c) at 0.1 T (blue) and 7 T (red). Open symbols are the data for the field perpendicular to the c axis (Hc) at 0.1 T. (B) Intensity of resonant magnetic reflection (0 0 11) at 6.975 keV at 0 T. The inset shows the profile of the (0 0 11) reflection along [001] at 6.975 keV (resonant) and 7.00 keV (nonresonant). In-plane resistivity ρxx (C) and interlayer resistivity ρzz (D) at 0 and 9 T (H||c). Schematic sample configuration for the resistivity measurement is shown in each panel. emu/mol, electromagnetic unit per mole; a.u., arbitrary unit. (E) Schematic illustration of the plausible magnetic structure for EuMnBi2 at zero field, together with the formal valence of each ion. The arrangement of the Mn sublattice is assumed to be the same as in SrMnBi2 (45). (F) Magnetic phase diagram for the Eu sublattice as functions of field (H||c) and temperature. PM and AFM denote the paramagnetic and antiferromagnetic states, respectively. Hf and Hc correspond to the transition fields to the spin-flop AFM and PM (forced ferromagnetic) phases, respectively. Black arrows are schematic illustration of the Eu moments sandwiching the Bi layer. Note the Mn sublattice orders at ~315 K (>TN).

  • Fig. 2 Magnetic field dependence of magnetic and transport properties at high fields.

    (A to D) M (A), ρzz (sample #3) (B), ρxx (C), and Hall resistivity ρyx (sample #1) (D) for EuMnBi2 at selected temperatures for the field parallel to the c axis up to ~55 T. Schematic illustration of the Eu2+ moments adjacent to the Bi layer for H < Hf, Hf < H < Hc, and Hc < H is presented in (A). The inset in (B) shows the field profile of ρzz (below 9 T) for EuMnBi2, EuZnBi2, and SrMnBi2. f.u., formula unit.

  • Fig. 3 Quantized Hall plateaus and SdH oscillations.

    (A) Normalized inverse Hall resistivity Embedded Image versus BF/B measured at 1.4 K for samples #1 and #2, where BF is the frequency of SdH oscillation and B = μ0(H + M) is the magnetic induction. Embedded Image is the step size between the consecutive plateaus in 1/ρyx (see fig. S7B). (B and C) ρxx, second field derivative −d2ρxx/dB2 for sample #1 (B) and ρzz for sample #3 (C) versus BF/B measured at 1.4 K. Vertical dotted lines denote half-integer multiples shifted by −γ, where γ ~ −0.1 is a phase factor estimated from the fan plot. (Inset) Landau fan plot (1/B versus N) for #1, #2, and #3. The slope and intercept with the N axis give BF and γ − δ, respectively (Table 1). A phase shift δ should be negligibly small for a quasi-2D Fermi surface, as discussed in the main text.

  • Fig. 4 Hysteresis and split of the Landau level.

    ρxx as a function of 1/B at 50 mK and 1.4 K. The curve at 50 mK is shifted downward for clarity. The arrow denotes the ρxx valley noticeable at 50 mK. Long solid and dashed lines indicate the integer and half-integer multiple of BF/B − γ, respectively. Short solid line denotes the position corresponding to the field H = Hc.

  • Table 1 Parameters related to the SdH oscillations and quantized Hall plateaus in the spin-flop phase (at 1.4 K and 5.3 to 22 T).

    BF and γ are the results of linear fit to the Landau fan plot.

    Sample no.ρijBF (T)γ (phase factor)Sample thickness (μm)Embedded Image (μΩcm)s (degeneracy factor)
    1ρxx, ρyx26.1(2)−0.12(4)1305255.5
    2ρxx, ρyx23.1(2)−0.12(2)785785.0
    3ρzz19.5(1)−0.08(2)

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/2/1/e1501117/DC1

    Detailed analyses on resonant x-ray magnetic scattering for EuMnBi2

    Detailed magnetic properties for EuMnBi2

    Magnetic properties for EuZnBi2

    Magnetization and transport features around 20 T for EuMnBi2

    Hall angle and step size between the consecutive 1/ρyx plateaus for EuMnBi2

    Powder x-ray diffraction profile for each compound and typical geometry of the samples and electrodes

    Fig. S1. Resonant x-ray magnetic scattering for EuMnBi2 near the Eu L3 absorption edge.

    Fig. S2. Extinction rules and candidates of magnetic structure of Eu sublattice.

    Fig. S3. Determination of magnetic structure of Eu sublattice.

    Fig. S4. Detailed magnetic properties for EuMnBi2.

    Fig. S5. Magnetic properties for EuZnBi2.

    Fig. S6. Magnetization and transport features around 20 T.

    Fig. S7. Hall angle and step size between the consecutive 1/ρyx plateaus.

    Fig. S8. Powder x-ray diffraction profile for each compound and geometry of the samples and electrodes.

    References (46, 47)

  • Supplementary Materials

    This PDF file includes:

    • Detailed analyses on resonant x-ray magnetic scattering for EuMnBi2
    • Detailed magnetic properties for EuMnBi2
    • Magnetic properties for EuZnBi2
    • Magnetization and transport features around 20 T for EuMnBi2
    • Hall angle and step size between the consecutive 1/ρyx plateaus for EuMnBi2
    • Powder x-ray diffraction profile for each compound and typical geometry of the samples and electrodes
    • Fig. S1. Resonant x-ray magnetic scattering for EuMnBi2 near the Eu L3 absorption edge.
    • Fig. S2. Extinction rules and candidates of magnetic structure of Eu sublattice.
    • Fig. S3. Determination of magnetic structure of Eu sublattice.
    • Fig. S4. Detailed magnetic properties for EuMnBi2.
    • Fig. S5. Magnetic properties for EuZnBi2.
    • Fig. S6. Magnetization and transport features around 20 T.
    • Fig. S7. Hall angle and step size between the consecutive 1/ρyx plateaus.
    • Fig. S8. Powder x-ray diffraction profile for each compound and geometry of the samples and electrodes.
    • References (46, 47)

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