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Helical magnetic order and Fermi surface nesting in noncentrosymmetric ScFeGe

Sunil K. Karna et al.
Phys. Rev. B 103, 014443 – Published 27 January 2021
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  • INTRODUCTION
  • EXPERIMENTAL DETAILS
  • EXPERIMENTAL RESULTS
  • RESULTS OF FIRST-PRINCIPLES CALCULATIONS
  • DISCUSSION AND CONCLUSIONS
  • ACKNOWLEDGMENTS
    • Supplemental Material
    References

    Abstract

    An investigation of the structural, magnetic, thermodynamic, and charge transport properties of noncentrosymmetric hexagonal ScFeGe reveals it to be an anisotropic metal with a transition to a weak itinerant incommensurate helimagnetic state below TN=36 K. Neutron diffraction measurements discovered a temperature and field independent helical wave vector k = (0 0 0.193) with magnetic moments of 0.53 μB per Fe confined to the ab plane. Density functional theory calculations are consistent with these measurements and find several bands that cross the Fermi level along the c axis with a nearly degenerate set of flat bands just above the Fermi energy. The anisotropy found in the electrical transport is reflected in the calculated Fermi surface, which consists of several warped flat sheets along the c axis with two regions of significant nesting, one of which has a wave vector that closely matches that found in the neutron diffraction. The electronic structure calculations, along with a strong anomaly in the c -axis conductivity at TN, signal a Fermi surface driven magnetic transition, similar to that found in spin density wave materials. Magnetic fields applied in the ab plane result in a metamagnetic transition with a threshold field of ≈6.7 T along with a sharp, strongly temperature dependent discontinuity and a change in sign of the magnetoresistance for in-plane currents. Thus, ScFeGe is an ideal system to investigate the effect of in-plane magnetic fields on a helimagnet with a c -axis propagation vector, where the relative strength of the magnetic interactions and anisotropies determine the topology and magnetic structure.

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    • Received 18 September 2020
    • Revised 9 December 2020
    • Accepted 11 January 2021

    DOI:https://doi.org/10.1103/PhysRevB.103.014443

    ©2021 American Physical Society

    Physics Subject Headings (PhySH)

    1. Physical Systems
    Noncentrosymmetric materialsNoncollinear magnets
    1. Techniques
    Density functional calculationsMagnetization measurementsNeutron diffractionResistivity measurements
    Condensed Matter, Materials & Applied Physics

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    Vol. 103, Iss. 1 — 1 January 2021

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    • Figure 1
      Figure 1

      Crystal structure. (a) Crystal structure of ScFeGe, highlighting the triangular network of Fe located at the 3f site. (b) Two-dimensional view of the crystal structure along the c axis displaying the distorted kagome lattice of Sc.

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    • Figure 2
      Figure 2

      Neutron powder diffraction. High-resolution neutron powder-diffraction data (red crosses) taken at (a) 285 K and (b) 2 K. The green line is the result of a structural refinement which indicated an Fe2P hexagonal crystal structure having the P6¯2m space group with peak positions indicated by the blue vertical lines. Several low intensity peaks were identified as originating from a small Sc4Fe4Ge6.6 impurity phase and from the Al sample holder. The refinement includes these contributions with peak positions indicated by the orange and black vertical lines. The remaining difference between the data and the fit is included as a purple line at the bottom of the figure. The asterisk marked in (b) is a magnetic peak. Data were collected at the HB-2A beam line at ORNL.

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    • Figure 3
      Figure 3

      Magnetic susceptibility, magnetization, and specific heat capacity. (a) Temperature T, dependence of the magnetic susceptibility χ, with magnetic field H, oriented parallel to the a and c crystallographic axes. (b) H dependence of the magnetization M for the same field orientations. (c) Specific heat capacity divided by T, Cp(T)/T, vs T2 at zero field. Inset: Low temperature region shown on an expanded scale. The solid line is the best fit of a linear form to the data. (d) Proposed magnetic phase diagram of ScFeGe as a function of temperature T and magnetic field H applied parallel to the crystallographic a axis. The metamagnetic transition observed in M(H) [Fig. 3] is plotted in the phase diagram as solid blue spheres, and the magnetic ordering temperature is represented by a green triangle and magenta circle obtained, respectively, from the neutron diffraction and specific heat measurements. The orange rectangles indicate the transition from negative to positive MR for T>10K observed in Δρa/ρa(0) [Figs. 4 and 4] whereas the hatched region in the phase diagram indicates a positive magnetoresistance.

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    • Figure 4
      Figure 4

      Charge transport. (a) Temperature, T, dependence of the resistivity with the current, I, parallel to the a axis, ρa, and current parallel to the c axis, ρc, at zero field. Inset: dρa/dT vs T. (b) MR for current parallel to the a axis, Δρa/ρa(0)=(ρa(H)−ρa(0))/ρa(0), at the indicated temperatures. Data shown for H parallel to the a axis. (c) Magnetoresistance (MR) for current parallel to the c axis, Δρc/ρc(0)=(ρc(H)−ρc(0))/ρc(0), at the indicated temperatures. Data are shown for field, H, parallel and perpendicular to the c axis, as indicated in the figure. Inset: ρc on an expanded scale at low T. (d) MR for current parallel to the a axis, Δρ/ρ0=(ρa(H)−ρa(0))/ρa(0), at the indicated temperatures. Data shown for H applied along the [1 2¯ 0] direction.

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    • Figure 5
      Figure 5

      Mössbauer spectroscopy. (a) Mössbauer spectra of ScFeGe collected above and below the magnetic ordering at 36 K. (b) T dependence of the isomer shift (left) and hyperfine field (right).

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    • Figure 6
      Figure 6

      X-ray absorption spectroscopy near edge structure (XANES). (a) Room temperature (RT) and low temperature (LT) (20 K) K-edge of Fe from ScFeGe (blue and red, respectively) and iron foil (Fe metal, green); inset shows the first-derivative edge positions. (b) RT and LT K-edge of Sc from ScFeGe (purple and red, respectively), scandium foil (Sc metal, blue), and in scandia (Sc2O3, green); inset shows the first-derivative edge positions. (c) RT and LT K-edge of Ge from ScFeGe (purple and red, respectively), germanium powder (Ge, blue), and germania (GeO2, green); inset shows the first-derivative edge positions.

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    • Figure 7
      Figure 7

      Neutron powder diffraction data collected at zero field above (70 K) and below (2 K) TN. Asterisk indicates the single magnetic diffraction peak. Inset shows the magnetic peak of neutron powder diffraction at 2 K in magnetic fields (H) of 0 and 4 T.

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    • Figure 8
      Figure 8

      Temperature T dependence of the lattice parameters a and c at magnetic fields H of 0 and 4 T for ScFeGe.

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    • Figure 9
      Figure 9

      Single-crystal neutron diffraction and magnetic structure. (a) Comparison of the calculated and observed values of the squared structure factors at T=285 K. The model for the hexagonal crystal structure with the P6¯2m space group and structural parameters determined from the PXRD at room temperature, and listed in Table S1 in the Supplemental Material [27], were used to calculate the expected intensity. (b) Comparison of the calculated and observed values of the squared structure factors for the incommensurate magnetic phase established at T=4.0 K at zero field. A helical magnetic structure model was employed in the calculation. (c) L scans near the (001) Bragg peak at several representative temperatures collected using the four-circle diffractometer HB-3A. (d) T dependence of the peak intensity of (0 0 0.193) and (0 0 0.807) incommensurate magnetic peaks measured using triple-axis spectrometer HB-1A, indicating a magnetic ordering at TN∼36 K. The solid line is a fit of a standard critical behavior model to the intensity (see text). (e) Schematic demonstrating the incommensurate helical magnetic structure at zero field. (f) View of the magnetic structure along the c axis.

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    • Figure 10
      Figure 10

      Band structure. (a) Calculated electronic band structure of nonmagnetic ScFeGe for energies E within 1 eV of the Fermi energy EF. Spin-orbit coupling is included. EF is at zero energy. Highlighted in red are the nearly degenerate flat bands near EF. (b) The first Brillouin zone of a hexagonal lattice [51].

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    • Figure 11
      Figure 11

      Calculated electronic band structure of nonmagnetic ScFeGe showing orbitals of (a) Fe, (b) Sc, and (c) Ge in which d-type orbitals of the Fe atoms are the dominant feature for these bands. The size of the filled circles are proportional to the weight projected onto the orbitals. (d) Calculated electronic band structure of nonmagnetic ScFeGe, using first-principles calculations (blue line) and Wannier functions (red dashed line), where Kohn-Sham states are projected onto Fe-d, Sc-d, and Ge-p localized orbitals. The spin-orbit coupling is included. The Fermi level is at zero energy.

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    • Figure 12
      Figure 12

      Fermi surface. (a) Side and (b) top views of the calculated three-dimensional Fermi surface (FS) sheets in the first Brillouin zone for nonmagnetic bulk ScFeGe. (c) Calculated bulk FSs on a cleaved [1 0 1¯ 0] surface. The coordinates of kz1 and kz2 are (0 0 0.262) and (0 0 0.191), respectively. (d) Bulk FSs at kz=−0.136, −0.265, and −0.456 and labeled as ➀, ➁, and ➂, respectively. The spin-orbit coupling is included.

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    • Figure 13
      Figure 13

      Schematics of the supercells used in the (a) helical 90∘ (1×1×4) supercell and (b) helical-72∘ (1×1×5) supercell calculations. For clarity, only the iron atoms are shown with the spin orientations represented by red arrows.

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