Effects of spin-dependent quasiparticle renormalization in Fe, Co, and Ni photoemission spectra:An experimental and theoretical study

We have investigated the spin-dependent quasiparticle lifetimes and the strength of electron correlation effects in the ferromagnetic 3$d$ transition metals Fe, Co, and Ni by means of spin- and angle-resolved photoemission spectroscopy. The experimental data are accompanied by state-of-the-art many-body calculations within the dynamical mean-field theory and the three-body scattering approximation, including fully relativistic calculations of the photoemission process within the one-step model. Our quantitative analysis reveals that inclusion of local many-body Coulomb interactions are of ultimate importance for a realistic description of correlation effects in ferromagnetic 3$d$ transition metals. However, we found that more sophisticated many-body calculations with larger modifications in the case of Fe and Co are still needed to improve the quantitative agreement between experiment and theory. In general, it turned out that not only the dispersion behavior of energetic structures should be affected by nonlocal correlations but also the line widths of most of the photoemission peaks are underestimated by the current theoretical approaches. The increasing values of the on-site Coulomb interaction parameter $U$ and the band narrowing of majority spin states obtained when moving from Fe to Ni indicate that the effect of nonlocal correlations becomes weaker with increasing atomic number, whereas correlation effects tend to be stronger.

Figure 1

(a) Geometry of the ARPES experiment. (b) LEED pattern of the bcc Fe(011) surface. (c) Sixfold symmetry observed in the LEED pattern of the hcp Co(0001) surface. (d) LEED pattern of the fcc Ni(111) surface. (e) and (f) Sketch of the SBZs of the three surfaces. The hcp lattice is rotated by 90${}^{\circ }$ with respect to the corresponding LEED pattern in (c). The magnetization orientation is also indicated in (e), (f), and (g).

Figure 2

(Upper panel) Series of experimental spin-integrated photoemission spectra of (a) bcc Fe(110), (b) hcp Co(0001), and (c) fcc Ni(111) measured with $p$ polarization in normal emission along the $\Gamma$N, $\Gamma$A, and $\Gamma$L directions of the corresponding BBZ at different excitation energies in steps of 2 eV. On the left, several photon energies are given. On the right, the curves are labeled by the wave vectors in units of Å${}^{-1}$. (Lower panel) (d) and (e) Corresponding calculations obtained by the LSDA + DMFT + 1SM method for an in-plane magnetization according to the experimental situation.

Figure 3

Analogous data as in Figs. 1a, 1b, 1c, 1d, 1e, 1f but now spin resolved. (Upper panel) Experiment [upward black (dark) triangles, majority spin states; downward red (light) triangles, minority spin states). (Lower panel) (d)–(f) LSDA + DMFT + 1SM theory [black (dark) and red (light) lines for majority and minority spin electrons, respectively]. Additional labels on top of the spectra indicate majority [black (dark) triangles] and minority [red (light) triangles] bulk states, while vertical black (dark) [red (light)] bars majority [minority] spin surface-related features. The curves are labeled by the photon energies (right) and the wave vectors (left) for all lattices in units of Å${}^{-1}$ for comparison.

Figure 4

Bloch spectral functions of bcc Fe(110), hcp Co(0001), and fcc Ni(111). The photoemission peak positions are obtained from spin-resolved measurements for different polarizations (diamond for $p$ and circle for $s$ polarization). The spin-projected Bloch spectral functions are obtained by the LSDA + DMFT method for majority (upper panel) and minority (lower panel) spin states. The symmetries of the different states are also indicated.

Figure 5

Comparison between experimental and theoretical spectra at the $A$ point of Co(0001) [(a) and (b) ($h$$\nu =48$ eV)] and at the L point of Ni(111) [(c) and (d) ($h$$\nu =72$ eV)] for $p$ polarization. (a and c) Spin-integrated experimental spectra [thick black (dark) dots], single-particle LSDA-based calculation including surface effects [thick dotted red (light) line] and LSDA + DMFT + 1SM spectra [thick solid red (light) line]. (b and d) Spin-integrated LSDA + DMFT + 1SM calculations for different $U$ values. Thin red (light) dotted, dashed, thick, and thin solid lines for $U=1.5$, 2, 2.5, and 3 (2.8) eV, respectively. In (a) and (c), symmetry labels in the two corresponding BBZ are also indicated.

Figure 6

(a) Experimental Ni angle-integrated photoemission spectrum taken at $h$$\nu =150$ eV. The Ni 6-eV satellite structure appears at about 6.3-eV binding energy. (b) LSDA + DMFT calculation of the spin-integrated DOS for a $U$ value of 2.8 eV. The satellite feature appears at about 7.2-eV binding energy. (c) Spin- and angle-resolved photoemission spectra taken in normal emission at $h$$\nu =66$ eV with $s$-polarized light. Open black (dark) squares, majority spin states; open red (light) squares, minority spin states; solid black (dark) and red (light) lines serve as guides for the eyes. Spin-integrated intensity, green (gray) thick dotted line. (d) LSDA + DMFT + 1SM spin-resolved photoemission calculation in normal emission at $h$$\nu =66$ eV for a $U$ value of 2.8 eV; solid black (dark) and red (light) lines indicate majority and minority spin states; green line shows the spin-integrated intensity.

Figure 7

(a) Comparison of spin-resolved experimental spectra near the $\Gamma$ point (top) obtained for $s$-polarized light with corresponding photoemission calculations using a $U$ value of 1.5 eV (bottom). Blue (gray) thin dotted line, experimental spin-integrated spectrum obtained for $p$ polarization; black (dark) upward triangles and solid lines, majority spin states; red (light) downward triangles and solid lines, minority spin states; green (gray) thick dotted line, spin-integrated intensity. (b) Comparison between the spin-integrated experimental spectra of Fe(110) at the $\Gamma$ point for $p$ polarization with the single-particle LSDA-based calculation, the LSDA + DMFT spectra, and the LSDA + DMFT + 1SM spectra. (c) LSDA + DMFT + 1SM calculations for $U=1.5$–3 eV. The inset shows the energy dependence of Im${\Sigma }_{\mathrm{DMFT}}$ for $U$ values from 1.5 to 3 eV.

Figure 8

(Left panels) Fits to spin-resolved valence band spectra at 0.21$\Gamma$N ($h$$\nu =35$ eV) of the Fe(110) BBZ for $p$ polarization [(a) and (b)] and $s$ polarization [(c) and (d)]. (Middle panels) Same for Co(0001) at $x=0.62\Gamma$A ($h$$\nu =56$ eV) of the BBZ, but for $p$ polarization [(e) and (f)] and for $s$ polarization [(g) and (h)]. (Right panels) Same for Ni(111) at $x=0.01\Gamma$L ($h$$\nu =28$ eV) of the BBZ, but for $p$ polarization [(i) and (j)] and for $s$ polarization [(k) and (l)]. Upward black (dark) and downward red (light) triangles and arrows for majority and minority spin spectra, respectively. Black (dark) and red (light) solid lines represent the corresponding fit results. Symmetry labels, surface resonance (SR), and surface state (SS) features are indicated.

Figure 9

Comparison between the experimental (symbols) and theoretical (lines) imaginary parts of the self-energies of (a) Fe(110), (b) Co(0001), and (c) Ni(111) for majority [black (dark) color] and minority [red (light) color] spin electrons. The experimental data points only contain the electronic and impurity scattering contributions to the linewidth. The theoretical calculations correspond to Im${\Sigma }_{\mathrm{DMFT}}$ (thick solid lines) and to Im${\Sigma }_{3BS}$ (thin dotted lines) for $U$(Fe) $=$ 1.5 eV, $U$(Co) $=$ 2.5 eV, and $U$(Ni) $=$ 2.8 eV