Unoccupied energy bands, exchange splitting, and self-energy of iron

Abstract

Unoccupied energy bands of iron are mapped by inverse photoemission from Fe(100), Fe(110), and Fe(111). The ferromagnetic exchange splitting \ensuremath{\delta}${\mathrm{E}}_{\mathrm{ex}}$ of the uppermost d band is measured for the ${\mathrm{H}}_{25}^{\ensuremath{'}}$ point, where the minority- and majority-spin subbands are both empty (\ensuremath{\delta}${\mathrm{E}}_{\mathrm{ex}}$=1.8 eV with ${\mathrm{H}}_{25\mathrm{\ensuremath{\downarrow}}}^{\ensuremath{'}}$ at 1.9 eV and ${\mathrm{H}}_{25\mathrm{\ensuremath{\uparrow}}}^{\ensuremath{'}}$ at 0.12 eV above ${\mathrm{E}}_{\mathrm{F}}$). Several other critical points are determined, such as the minority-spin ${\mathrm{\ensuremath{\Gamma}}}_{12}$ and ${\mathrm{P}}_{3}$ points, the majority-spin ${\mathrm{N}}_{3}$ point, and the higher-lying ${\mathrm{H}}_{15}$,${\mathrm{H}}_{1}$ points of s,p character. Critical points and exchange splitting are compared with first-principles, local-density calculations. The real part of the self-energy is obtained from this comparison, and the imaginary part by measuring the liftime broadening. In the d-band region, the self-energy causes a 10% compression of the bands and a linear broadening \ensuremath{\Gamma}(E)\ensuremath{\approx}0.6|E-${\mathrm{E}}_{\mathrm{F}}$|.