Fig. 2: Element-resolved electronic spectra of the CrMnFeCoNi HEA.

a Calculated partial density of states (pDOS) for Cr, Mn, Fe, Co, and Ni in the CrMnFeCoNi alloy using LDA and LDA + DMFT, shown as yellow and blue solid lines, respectively. Measured energy distribution curves (EDCs) at the XAS L₃ absorption maximum as black solid lines. The self-convolutions of the pDOS (Cini-Sawatzky Theory, CST) are given by dashed lines in corresponding colors. For Fe and Ni, additional pDOS calculations using LDA + DMFT with modified Hubbard U values are shown as green lines. In the pDOS the LDA + DMFT approach introduces satellite features not present in the pure LDA results for all elements. For Cr, the EDCs align well with the pDOS, being valence band like, while Mn shows good overlap between the EDCs and CST maxima. In contrast, Fe, Co, and Ni exhibit increasing distance between EDCs and self-convolution peaks. Lager U values for Fe and Ni shift the satellites towards higher binding energies without significantly altering the overall pDOS. b Comparison of experimental valence band photoemission spectroscopy (PES) data (black line) with one-step model calculations for LDA (yellow dashed line) and LDA + DMFT (blue line). For LDA + DMFT a shoulder at 8 eV (Ni marker), which is absent in the LDA results is found, and the LDA + DMFT spectrum is more smeared overall. The offset between PES and calculations at high binding energies is due to the experimental background not mimicked in the calculations. d Calculated Bloch spectral function (BSF) for CrMnFeCoNi using LDA (c) and LDA + DMFT (d). The color maps represent the spectral intensity. For LDA, the states near the Fermi energy are already smeared through disorder, whereas for LDA + DMFT, bands at higher binding energies also exhibit significant smearing due to reduced quasiparticle lifetimes, to the extent that subbands may not be resolved, as seen between the Γ and L points.