Topological electronic structure evolution with symmetry-breaking spin reorientation in $({\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Co}}_{x})\mathrm{Sn}$

Topological electronic structure evolution with symmetry-breaking spin reorientation in $({Fe}_{1 - x} {Co}_{x}) Sn$

Robert G. Moore, Satoshi Okamoto, Haoxiang Li, William R. Meier, Hu Miao, Ho Nyung Lee, Makoto Hashimoto, Donghui Lu, Elbio Dagotto, Michael A. McGuire, and Brian C. Sales

Phys. Rev. B 106, 115141 – Published 23 September 2022

Abstract

Topological materials hosting kagome lattices have drawn considerable attention due to the interplay between topology, magnetism, and electronic correlations. The $({Fe}_{1 - x} {Co}_{x}) Sn$ system not only hosts a kagome lattice but has a tunable symmetry-breaking magnetic moment with temperature and doping. In this study, angle-resolved photoemission spectroscopy and first-principles calculations are used to investigate the interplay between the topological electronic structure and varying magnetic moment from the planar to axial antiferromagnetic phases. Evidence for a theoretically predicted gap at the Dirac point is revealed in the low-temperature axial phase, but no gap opening is observed across a temperature-dependent magnetic phase transition. However, topological surface bands are observed to shift in energy as the surface magnetic moment is reduced or becomes disordered over time during experimental measurements. The shifting surface bands may preclude the determination of a temperature-dependent bulk gap, but this highlights the intricate connections between magnetism and topology with a surface/bulk dichotomy that can affect material properties and their interrogation.

Received 28 April 2022
Revised 28 July 2022
Accepted 15 September 2022

DOI:https://doi.org/10.1103/PhysRevB.106.115141

Physics Subject Headings (PhySH)

Electronic structure Magnetic interactions Magnetic phase transitions Topological phase transition Topological phases of matter

Angle-resolved photoemission spectroscopy Density functional theory

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Robert G. Moore ^1,*, Satoshi Okamoto¹, Haoxiang Li¹, William R. Meier ¹, Hu Miao¹, Ho Nyung Lee¹, Makoto Hashimoto², Donghui Lu ², Elbio Dagotto^1,3, Michael A. McGuire¹, and Brian C. Sales¹

¹Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
²Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
³Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA

^*moorerg@ornl.gov

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Vol. 106, Iss. 11 — 15 September 2022

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Figure 1
Magnetic and electronic structure of ( ${Fe}_{1 - x} {Co}_{x}$ )Sn. (a) Schematic of atomic and magnetic structure for the planar, tilted, and axial magnetic phases. The kagome lattice is highlighted in purple. (b) Brillouin zone (BZ) with surface projection and high-symmetry points identified. (c) Fermi surface map for $x = 0.06$ with (BZ) overlay. Red arrow indicates ARPES energy-momentum cut for subsequent data. (d) ARPES data for $x = 0.06$ at $h ν = 92 eV$ , chosen to maximize the Dirac and Weyl-like band intensities. (e) ARPES data for $x = 0.17$ at $h ν = 130 eV$ , which corresponds to the H and $H^{'}$ points where a maximum gap at the Dirac point is predicted. (f), (g) Curvature method plot for ARPES data in (d) and (e), respectively. Surface WP for $x = 0.06$ is outlined in yellow, and bulk DPs are outlined in red.
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Figure 2
Comparison of ARPES data for $x = 0.17$ in the low-temperature axial phase with simulations. (a–c) Image plots for region around the bulk DP outlined in Fig. 1 for binned ARPES data, $2 Δ = 80$ -meV simulation, and $2 Δ = 0$ -meV simulation, respectively. (d–f) EDC curves for binned ARPES data, $2 Δ = 80 meV$ and $2 Δ = 0 meV$ simulations, respectively. For the ARPES EDCs, the red, blue, and green curves highlight regions with different intensities and widths (see main text). (g–i) Fitted dispersion results for ARPES data, $2 Δ = 80 meV$ , and $2 Δ = 0 meV$ simulations, respectively. The blue markers are for free fit parameters, while the red markers are for constrained fits. (j–l) Curvature method analysis for ARPES data, $2 Δ = 80 meV$ and $2 Δ = 0 meV$ simulations, respectively.
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Figure 3
Temperature-dependent ARPES data and EDC fits for $x = 0.06$ . (a) ARPES data for $x = 0.06$ taken at different temperatures with the rightmost panel taken after cooling back down to $T = 20 K$ . (b) EDCs at the $\bar{K}$ point showing the surface WP, bulk DP, and bulk bands for the different temperatures. Model fits of the data are shown for $T = 20 K$ and 240 K. (c) Model fit results vs temperature for the position and width of the surface WP and bulk DP. (d) Model fit results vs data collection time for the position and width of the surface WP and bulk DP. The planar (green), tilted (blue), and axial (orange) phases are shaded in (c) and (d). (e) Comparison of EDCs at $T = 20 K$ before the temperature cycle and after the temperature cycle, highlighting the degradation of the surface WP spectral intensity. (f) Comparison of EDCs at $T = 20 K$ before the temperature cycle for two different probed locations on the sample highlighting the sample surface inhomogeneities. (g) Curvature method plot of $x = 0.06$ ARPES data with temperature-dependent model fit results overlay for surface and bulk dispersive features away from the $\bar{K}$ high-symmetry point.
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Figure 4
Comparison of ARPES with DFT calculations. (a) DFT bulk bands with $M = 1.94 μ_{B}$ for planar (green) and axial (red) AFM phases overlaid on ARPES data for $x = 0.06$ . In the zoomed region outlined in blue, the contrast for the ARPES data is adjusted to highlight the Dirac dispersion. (b) DFT bulk bands with $M = 1.80 μ_{B}$ for planar (green) and axial (red) AFM phases overlaid on ARPES data for $x = 0.06$ . In the zoomed region outlined in orange, the contrast for the ARPES data is adjusted to highlight the Dirac dispersion. (c) DFT slab calculations with ${Sn}_{2}$ termination for different $M$ . (d) DFT slab calculations with ${Fe}_{3} Sn$ termination for different $M$ . For (c) and (d) the surface WP and the bulk DP are highlighted for clarity.
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Physical Review B

covering condensed matter and materials physics

Topological electronic structure evolution with symmetry-breaking spin reorientation in $({Fe}_{1 - x} {Co}_{x}) Sn$

Robert G. Moore, Satoshi Okamoto, Haoxiang Li, William R. Meier, Hu Miao, Ho Nyung Lee, Makoto Hashimoto, Donghui Lu, Elbio Dagotto, Michael A. McGuire, and Brian C. Sales

Phys. Rev. B 106, 115141 – Published 23 September 2022

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Physical Review B

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Topological electronic structure evolution with symmetry-breaking spin reorientation in (Fe1−xCox)Sn

Robert G. Moore, Satoshi Okamoto, Haoxiang Li, William R. Meier, Hu Miao, Ho Nyung Lee, Makoto Hashimoto, Donghui Lu, Elbio Dagotto, Michael A. McGuire, and Brian C. Sales

Phys. Rev. B 106, 115141 – Published 23 September 2022

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Topological electronic structure evolution with symmetry-breaking spin reorientation in $({Fe}_{1 - x} {Co}_{x}) Sn$