Fermi surface of Co(0001) and initial-state linewidths determined by soft x-ray angle-resolved photoemission spectroscopy

Soft x-ray angle-resolved photoemission spectroscopy (SX-ARPES) reveals the band dispersion and Fermi surface of bulk ferromagnetic Co(0001). The spectral peak widths are narrower than previously observed in low-energy ARPES experiments. From very general considerations and in contrast to low-energy experiments, we show that the final-state broadening is significantly reduced in the experimentally measured linewidth. SX-ARPES yields the intrinsic initial-state lifetime ${\Gamma }_i=1/2{\Sigma }_i\left(\vec{k},E\right)$, the latter being the initial state self-energy, quantifying the correlations and indicating an energy and momentum dependence. Our results open a way to a direct measurement of the many-particle effects in solid-state physics, which does not require a modeling of the final state and provides a genuine description of the initial state.

Figure 1

(Color online) SX-ARPES maps measured as a function of the binding energy and $k_{\parallel }$ for two different values of $k_{\perp }$: (a) along the $\Gamma M$ (with $h\nu =570\text{eV}$), (b) $AL$ (with $h\nu =654\text{eV}$). (c) shows an ARPES map along the $A\Gamma A$ direction $\left(k_{\perp }\right)$ obtained by changing the photon energy. The color scale is shown between the panel (b) and (c). In (b) and (c) the intensities at $E_B>3\text{eV}$ are plotted in a different color scale to enhance the weak sp band. In all the three panels GGA calculations (spin-up bands in black continuous and spin-down bands in dashed green lines) are overlapped for comparison.

Figure 2

(Color online) Cobalt Fermi-surface mappings measured in the $\Gamma MK$ plane with $h\nu =570\text{eV}$ (top) and in the $\Gamma ALM$ plane as a function of the photon energy (bottom) by stacking MDCs obtained by integrating over $\pm 50\text{meV}$ about the Fermi level. The Brillouin-zone high-symmetry directions are indicated by yellow lines, while the spin-up (up black triangles) and spin-down (down green triangles) mark the theoretical Fermi-surface contours derived from our GGA calculations (indicated in only one irreducible wedge of the Brillouin zone, to avoid redundancy). The color scale is indicated at the bottom right.

Figure 3

(Color online) Experimental EDCs (black open circles) taken at the $\Gamma$, $A$, and $M$ points plotted together with the convolved (light green or gray thick continuous line) and bare spectrum (blue or dark gray dashed line), composed of a sum of Lorentzian peaks (thin red or light gray lines). In the bottom right panel the DMFT calculations (Ref. 24) (black continuous line for spin-up and red or gray dashed line for spin-down) and the experimental widths for both spin-up (up triangles) and spin-down (down triangles) are compared. The error bar on the peak widths is as large as the symbols and is given by the experimental energy resolution, not by the (smaller) error on the parameter determined by the fit.