Renormalization of Bulk Magnetic Electron States at High Binding Energies

The quasiparticle dynamics of electrons in a magnetically ordered state is investigated by high-resolution angle-resolved photoemission of Ni(110) at 10 K. The self-energy is extracted for high binding energies reaching up to 500 meV, using a Gutzwiller calculation as a reference frame for correlated quasiparticles. Significant deviations exist in the 300 meV range, as identified on magnetic bulk bands for the first time. The discrepancy is strikingly well described by a self-energy model assuming interactions with spin excitations. Implications relating to different electron-electron correlation regimes are discussed.

Figure 1

(a) Symmetry plane along $k_{\parallel }$ in Ni(110) with schematic Fermi surface, showing ARPES scan at $K$ point in 2nd BZ (blue). (b) ARPES band map of ${\Sigma }_{2\downarrow }$ band along $\Gamma \mathrm{\text{−}}K$, taken $h\nu =100\mathrm{eV}$. Black line indicates MDC peak positions. (c) Gutzwiller Fermi surface cut in $k_{\perp }$ plane, highlighting curvature perpendicular to the surface.

Figure 2

Effect of $k_{\perp }$ broadening: (a) $\Gamma \mathrm{\text{−}}K$ symmetry line in Gutzwiller Fermi surface, with weighted MDCs (FWHM $0.05{\AA }^{-1}$) as intensity plot (for $w=4\AA$). (b)  Modeled effective MDC from the weighted sum of MDCs (red circles). Compared to a symmetric Lorentzian (black dots), the asymmetric Lorentzian is a good analytical fit (blue line). (c) ARPES data along $\Gamma \mathrm{\text{−}}K$ (red circles). The deviation from symmetric behavior (black dots) is well fitted by the asymmetric Lorentzian (blue line).

Figure 3

(a) ARPES band data at the Ni(110) $K$ point, represented by fitted MDC peak positions (red), and calculated Gutzwiller dispersion (black). Two energy ranges with deviations are apparent. (b) Extracted real part of the self-energy (black circles). It can be described by adding contributions from electron-phonon (blue) and electron-magnon interaction (green), leading to the red sum curve.

Figure 4

(a) Raw MDC data (red) corresponding to Fig. 3a, and fitted curves employing the asymmetric peak model (black). (b) Imaginary part of self-energy (black). It shows two shoulders that can be described by electron-phonon (blue) and electron-magnon coupling (green), Kramers-Kronig consistent with $\mathrm{Re}\Sigma$ of Fig. 3b. The sum curve (red) including a small electron-electron contribution (yellow) is a good description of the ARPES data.