Disentangling electron-boson interactions on the surface of a familiar ferromagnet

Håkon I. Røst, Federico Mazzola, Johannes Bakkelund, Anna Cecilie Åsland, Jinbang Hu, Simon P. Cooil, Craig M. Polley, and Justin W. Wells

Phys. Rev. B 109, 035137 – Published 17 January 2024

Abstract

We report energy renormalizations from electron-phonon and electron-magnon interactions in spin minority surface resonances on Ni(111). The different interactions are identified, disentangled, and quantified from the characteristic signatures they provide to the complex self-energy and the largely different binding energies at which they occur. The observed electron-magnon interactions exhibit a strong dependence on momentum and the electron energy band position in the bulk Brillouin zone. In contrast, electron-phonon interactions observed from the same bands appear to be relatively momentum and symmetry independent. Additionally, a moderately strong $(λ > 0.5)$ electron-phonon interaction is distinguished from a near-parabolic spin majority band not crossing the Fermi level.

Received 4 November 2022
Revised 6 December 2023
Accepted 20 December 2023

DOI:https://doi.org/10.1103/PhysRevB.109.035137

Physics Subject Headings (PhySH)

Electronic structure Magnetic coupling Magnons Phonons Surface states

Ferromagnets

Angle-resolved photoemission spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Håkon I. Røst ^1,2, Federico Mazzola^3,4, Johannes Bakkelund ¹, Anna Cecilie Åsland ¹, Jinbang Hu ¹, Simon P. Cooil ⁵, Craig M. Polley ⁶, and Justin W. Wells ^1,5,*

¹Department of Physics, Norwegian University of Science and Technology (NTNU), NO-7491 Trondheim, Norway
²Department of Physics and Technology, University of Bergen, 5007 Bergen, Norway
³Department of Molecular Sciences and Nanosystems, Ca' Foscari University of Venice, 30172 Venice, Italy
⁴Istituto Officina dei Materiali, Consiglio Nazionale delle Ricerche, Trieste I-34149, Italy
⁵Department of Physics and Centre for Materials Science and Nanotechnology, University of Oslo, 0318 Oslo, Norway
⁶MAX IV Laboratory, Lund University, Lund, 22484 Sweden

^*Corresponding author: j.w.wells@fys.uio.no

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Issue

Vol. 109, Iss. 3 — 15 January 2024

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Images

Figure 1
The electronic structure of Ni(111). (a) Sketch showing the projection of the bulk Brillouin zone of Ni onto the (111) plane. (b) Measured constant energy surface of Ni(111) at $E_{F}$ (left) and the calculated band structure with free-electron final states (right), both using $h ν = 21.2 eV$ . (c) Volumetric representation of the measured Ni(111) band structure. The energy cut has been performed from $\bar{Γ}$ and along the $\pm b_{s}$ directions as shown in (b). (d) Measured band structure ( $E$ vs $k_{| |}$ ) along the $+ b_{s}$ direction. A clear spin splitting of the states can be seen close to $E_{F}$ . The assignment of minority and majority states is based on the density functional theory calculation in (b). (e) Photoemission intensity as a function of final-state wave number $k_{z}$ . (f) The calculated, unrenormalized spin minority surface states (red) of Ni(111) along the $+ b_{s}$ direction. The shaded background (gray) represents the surface-projected, spin majority bulk bands. Surface resonance states can be observed near $(E_{B}, k_{| |}) = (0.0 eV, 0.82 Å^{- 1})$ .
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Figure 2
EBC in the spin minority band along $- b_{s}$ near the high-symmetry points $\bar{M}$ and ${\bar{K}}^{'}$ . (a) The measured energy band structure, overlaid with the unrenormalized (green) band and the experimentally determined, renormalized spin band position (red triangles). (b) The real self-energy $Re Σ$ of the fitted band in (a). The $Re Σ$ (gray) found from Eq. (2) is shown to satisfy causality with $Im Σ$ through the Kramers-Kronig transformation (blue). A three-boson model (purple line) consisting of two distinct EPCs with energies $ℏ ω_{ph} = 18 meV$ and $ℏ ω_{ph} = 36 meV$ , respectively, and one EMC with energy $ℏ ω_{mag} = 154 meV$ , best describes the measured line shape. The individual EPC (dashed orange) and EMC (dashed black) models are highlighted.
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Figure 3
EBC in the spin-minority band along $+ b_{s}$ near the high-symmetry points ${\bar{M}}^{'}$ and $\bar{K}$ . (a) The measured energy dispersion of the spin bands overlaid with the unrenormalized band (green) and the experimentally determined, renormalized spin minority band position (red triangles). (b) The real self-energy $Re Σ$ (gray) of the fitted band in (a), shown to be consistent with the imaginary part $Im Σ$ through the K-K transformation (blue). A two-boson model (purple line) consisting of one EPC at $ℏ ω_{ph} = 23 meV$ , and one EMC at $ℏ ω_{mag} = 340 meV$ , best describes the measured line shape. The individual EPC (dashed orange) and EMC (dashed black) models have been highlighted.
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Figure 4
EBC in the spin majority energy band along $- b_{s}$ near the high-symmetry points $\bar{M}$ and ${\bar{K}}^{'}$ . (a) The measured electron energy dispersion along $- b_{s}$ , overlaid with the experimentally determined, renormalized position of the spin majority band (red triangles), and suggested one-particle “bare” bands for both spin configurations (in green). (b) The real and imaginary self-energies of the fitted spin majority band in (a). Each component is shown to be consistent through the K-K transformation. The EBC appears at $50 m eV$ below the spin majority energy band maximum $E_{BM}$ . The interaction is best described by EPC from $E_{BM}$ with $λ_{ph} = 0.55$ (purple) instead of EMC from $E_{F}$ (dashed gray). The added energy broadening from electron-impurity scattering and the finite instrumental resolution (dashed horizontal black line) is also shown. (c) ARPES simulations of the spin bands in (a), implementing either EMC at $ℏ ω_{mag} = 235 meV$ below $E_{F}$ (right) or EPC at $ℏ ω_{ph} = 50 meV$ below $E_{BM}$ (left) in the spin majority band. Both models have an additional EPC contribution in the spin minority band at $ℏ ω_{ph} = 35 meV$ below $E_{F}$ , as suggested from the self-energy analysis summarized in Table 1.
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