Research ArticleAPPLIED PHYSICS

Emergence of a real-space symmetry axis in the magnetoresistance of the one-dimensional conductor Li0.9Mo6O17

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Science Advances  05 Jul 2019:
Vol. 5, no. 7, eaar8027
DOI: 10.1126/sciadv.aar8027
  • Fig. 1 Crystal structure, band structure, and metal-insulator transition of LMO.

    (A) Projection of four unit cells onto the ac plane, where the MoO6 octahedra hosting the conducting zigzag chains (oriented out of this plane along the b axis) are highlighted in purple. Blue sphere, Mo; red/pink, O; green, Li. (B) In each unit cell, there are double zigzag chains made of corner-sharing octahedra. The octahedra at the top of the figure have had all nonessential oxygen atoms removed. The corner oxygen shared by adjacent in-chain octahedra is denoted in red, while interchain oxygen is denoted in pink. (C) Simplified Fermi surface of LMO showing the weakly dispersive, quasi-1D bands along the a axis due to the weak interchain hopping energy (top panel), which, nevertheless, causes an energy gap around the Fermi surface (schematic green curves in the lower panel). The small energy gap easily allows excitation of electron-hole pairs, i.e., excitons. (D) In-chain resistivity versus temperature showing a metal-insulator transition around Tmin ~ 25 K, below which the insulating form of the resistivity can be well fitted by a power law (see section S4C and fig. S11). Crystallographic drawings were produced using VESTA (44).

  • Fig. 2 Asymmetric MR of LMO within the ac plane.

    (A) Notation of angles for magnetic fields rotated within the three principal planes of the coordinate system specified in Fig. 1A. (B) Normalized ADMR curves obtained at various temperatures as a constant magnetic field of 13 T is rotated within the ac plane. The ADMR evolves from symmetric (about the a or the c axis) at high temperatures to asymmetric at low temperatures. Data are shifted vertically for clarity. Here, current is injected along the a axis. (C) Left panel: Mirror reflection of the ADMR curves at T = 37 K [in (A)] about the c axis. Right panel: Corresponding reflection plot at T = 4.2 K. The shaded region indicates the degree of asymmetry between these two curves. (D) Evolution of the asymmetric MR with temperature. The solid circles represent the degree of asymmetry in the ADMR, quantified by taking the normalized integrated area inside the red and blue curves in (B) defined as σ ≡ (ALHSARHS)/(ALHS + ARHS). Inset: Blowup of the same figure between 10 and 40 K, to highlight the growth of the asymmetry below Tmin. The dashed line is a fit to a simple parabolic temperature dependence. (E) Similar ADMR sweeps as in Fig. 2B, but for the current along the b axis, showing a similar asymmetry at low temperatures. (F) At a fixed temperature (T = 1.2 K), the asymmetry in the ADMR grows with increasing field.

  • Fig. 3 Origin of the asymmetry and determination of the critical angle.

    (A) Field sweeps of the MR at 1.2 K are measured at various angles within the ac plane, showing the evolution of the peak field with angle. The angle of the dashed thick curve is ~6° from the c axis. The maximal MR at B = 2, 5, 10, 15, 20, 25, and 30 T are denoted by empty symbols and correspond to the peaks in (B). Inset: Expanded plot of the region of the MR curves contained below the dashed line in the main panel. (B) Same data as in (A), replotted for fixed field strengths. Each is vertically shifted for better visibility. Comparison with Fig. 2F shows almost identical behavior. (C) Same data as in (A) with the field values scaled by |cosθ|. The actual scaling factor, i.e., the ratio between Bscaled and B, is depicted in fig. S7. Inset: Expanded plot of the dashed rectangle in the main panel. (D) The resultant peak field values obtained from Fig. 3C plotted as a function of angle within the ac plane. At the critical angle θCR, the negative MR is maximally suppressed.

  • Fig. 4 Identification of the critical angle.

    (A) Blowup of the unit cell of LMO showing the alignment of the critical angle θCR (purple arrow) with the polar axis of the MoO6 octahedra. (B) Rotation of the unit cell’s frame of reference to the polar axis. (C) A pair of MoO6 octahedra showing the orientation of the dyz orbitals along this polar axis. A dark exciton, composed of dyz (in green) and dxz (not shown) orbitals, is formed in adjacent octahedra residing in two zigzag chains within a unit cell. Both orbitals have the same quantization axis (again indicated by the purple arrow). Crystallographic drawings were produced using VESTA (44).

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/7/eaar8027/DC1

    Section S1. Similar observation in a superconducting sample (fig. S6)

    Section S2. Scaling factor used in Fig. 3C and fig. S6C

    Section S3. Canted angle between adjacent MoO6 octahedra

    Section S4. Theory of dark excitons and its contribution to resistivity and MR along the a axis

    Section S5. Deconvolution of the anisotropic MR in LMO

    Table S1. Location of the maxima and minima in the angular MR in LMO above Tmin.

    Fig. S1. Mirror reflection of the ADMR curves at various temperatures about the c axis.

    Fig. S2. The magnitude of asymmetry as a function of temperature for MR curves of current along the b axis.

    Fig. S3. Contrast in the asymmetric MR response upon rotation within the three crystallographic planes.

    Fig. S4. Normalized ADMR curves obtained at various temperatures as a constant magnetic field of 13 T, rotated within the bc plane.

    Fig. S5. Absence of asymmetric MR (I//b) with increasing field strength for B rotated within the bc plane.

    Fig. S6. Origin of the asymmetric MR and determination of the critical angle for a second, superconducting LMO crystal.

    Fig. S7. Scaling factor used in Fig. 3C and fig. S6C, respectively.

    Fig. S8. A close view of the canted MoO6 octahedra in LMO.

    Fig. S9. Configurations of electric contacts applied to our LMO crystals.

    Fig. S10. Schematic of crystallization of dark excitons.

    Fig. S11. Power-law behavior of resistivity along the b axis in both insulating and superconducting LMO crystals.

    References (4551)

  • Supplementary Materials

    This PDF file includes:

    • Section S1. Similar observation in a superconducting sample (fig. S6)
    • Section S2. Scaling factor used in Fig. 3C and fig. S6C
    • Section S3. Canted angle between adjacent MoO6 octahedra
    • Section S4. Theory of dark excitons and its contribution to resistivity and MR along the a axis
    • Section S5. Deconvolution of the anisotropic MR in LMO
    • Table S1. Location of the maxima and minima in the angular MR in LMO above Tmin.
    • Fig. S1. Mirror reflection of the ADMR curves at various temperatures about the c axis.
    • Fig. S2. The magnitude of asymmetry as a function of temperature for MR curves of current along the b axis.
    • Fig. S3. Contrast in the asymmetric MR response upon rotation within the three crystallographic planes.
    • Fig. S4. Normalized ADMR curves obtained at various temperatures as a constant magnetic field of 13 T, rotated within the bc plane.
    • Fig. S5. Absence of asymmetric MR (I//b) with increasing field strength for B rotated within the bc plane.
    • Fig. S6. Origin of the asymmetric MR and determination of the critical angle for a second, superconducting LMO crystal.
    • Fig. S7. Scaling factor used in Fig. 3C and fig. S6C, respectively.
    • Fig. S8. A close view of the canted MoO6 octahedra in LMO.
    • Fig. S9. Configurations of electric contacts applied to our LMO crystals.
    • Fig. S10. Schematic of crystallization of dark excitons.
    • Fig. S11. Power-law behavior of resistivity along the b axis in both insulating and superconducting LMO crystals.
    • References (4551)

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