Real-space Green's function approach to angle-resolved resonant photoemission: Spin polarization and circular dichroism in itinerant magnets

A first-principles approach, based on the real-space multiple scattering Green's function method, is presented for spin- and angle-resolved resonant photoemission from magnetic surfaces. It is applied to the Fe(010) valence band photoemission excited with circularly polarized x rays around the Fe $L_3$ absorption edge. When the photon energy is swept through the Fe $2p-3d$ resonance, the valence band spectra are strongly modified in terms of absolute and relative peak intensities, degree of spin polarization, and light polarization dependence. New peaks in the spin-polarized spectra are identified as spin-flip transitions induced by exchange decay of spin-mixed core holes. By comparison with single-atom and band-structure data, it is shown that both intra-atomic and multiple scattering effects strongly influence the spectra. We show how the different features linked to states of different orbital symmetry in the $d$ band are differently enhanced by the resonant effect. The appearance and origin of circular dichroism and spin polarization are analyzed for different geometries of light incidence and electron emission direction, providing guidelines for future experiments.

Figure 1

Spin- and angle-resolved direct valence band PES (ARPES) and RPES (AR-RPES) at the $L_3$ edge for one single Fe absorber in the single-atom limit, for light incidence along the magnetic moment (parallel geometry) and emission in a perpendicular direction. Left and right circular polarized light in green and blue. Direct PES process alone (“ARPES,” red) for comparison. Photon energies are 680.57 (a), 681.50 (b), 683.83 (c), 693.60 eV (d). (e) Constant initial state (CIS) spectra at peak maxima ($E=-2.2$/$-0.2$ eV for spin up/down).

Figure 2

RPES at maximum resonance ($h\nu =683.83$ eV) for a single Fe atom. Same geometry as in Fig. 1. Fundamental spectra total (tot), dichroic (dic), spin polarized (spr), and mixed (mix) for ferromagnetic (a)–(c) or Pauli paramagnetic (d) ground state.

Figure 3

(a) DOS of bulk bcc Fe from periodic LMTO calculation compared with DOS on central atom in the cluster in RSMS calculation (positive/negative DOS for spin up/down); (b) bcc Brillouin zone; (c) spin-down and (d) spin-up bands from LMTO calculation (red) and final-state free-electron dispersion (blue).

Figure 4

Spin- and angle-resolved RPES from the Fe(010) surface. Parallel geometry ($k_{\gamma }$ $\parallel$ to $M$) and normal emission. Same photon energies as in Fig. 1: 680.57 (a), 681.50 (b), 683.83 (c), 693.60 eV (d).

Figure 5

Spin-resolved ARPES and AR-RPES from the Fe(010) surface in perpendicular geometry ($k_{\gamma }$ perpendicular to $M$) at maximum resonance ($h\nu =683.83$ eV). (a) grazing incidence (along $x$), normal emission. (b) normal incidence (along $y$), off-normal emission at ($\theta ={150}^{\circ }$, $\varphi ={90}^{\circ }$) polar angles, coplanar with $M$ and $k_{\gamma }$. (c) normal incidence, off-normal emission at ($\theta ={150}^{\circ }$, $\varphi ={65}^{\circ }$) non-coplanar with $M$ and $k_{\gamma }$.