Fingerprints of entangled spin and orbital physics in itinerant ferromagnets via angle-resolved resonant photoemission

A method for mapping the local spin and orbital nature of the ground state of a system via corresponding flip excitations is proposed based on angle-resolved resonant photoemission and related diffraction patterns, obtained here via an ab initio modified one-step theory of photoemission. The analysis is done on the paradigmatic weak itinerant ferromagnet bcc Fe, whose magnetism, a correlation phenomenon given by the coexistence of localized moments and itinerant electrons, and the observed non-Fermi-Liquid behavior at extreme conditions both remain unclear. The combined analysis of energy spectra and diffraction patterns offers a mapping of local pure spin-flip, entangled spin-flip–orbital-flip excitations and chiral transitions with vortexlike wave fronts of photoelectrons, depending on the valence orbital symmetry and the direction of the local magnetic moment. Such effects, mediated by the hole polarization, make resonant photoemission a promising tool to perform a full tomography of the local magnetic properties even in itinerant ferromagnets or macroscopically nonmagnetic systems.

Figure 1

(a) DOS of the ferromagnetic Fe(010) cluster; (b) ARPES and AR-RPES spectra (from [47]) for parallel geometry and normal emission for excitation at the $L_3$ edge. Rest of the panel: PED, RPED for initial binding energy corresponding to the main peak and the spin-flip peak in the spin-up AR-RPES spectrum, and “source wave” patterns (the emitter is embedded in the cluster but no scattering events take place). (The plotted function is $\chi =I[\theta ,\varphi ,\epsilon ]/I_0[\theta ,\epsilon ]-1, I_0$ being the intensity averaged over all $\varphi$-dependent values. Scans are around the surface normal.)

Figure 2

Local partial DOS ($l,m$-resolved) around a Fe central ion in the cluster.

Figure 3

Spin-polarized PED and RPED patterns for parallel geometry, for excitation at the $L_3$ edge for paramagnetic Fe(010), and initial state energy corresponding to the main peak in the spin-up channel for the ferromagnetic phase.

Figure 4

PED patterns (first two rows, for left and right circular polarization) and RPED patterns (third and fourth rows, for left and right circular polarization) for two perpendicular geometries, for excitation at the $L_3$ edge for ferromagnetic Fe(010).