Theory of spin-polarized electron-capture spectroscopy in ferromagnetic nickel

A detailed time-dependent many-body theory is developed for the study of spin-polarized electron-capture spectroscopy. The head-on collisions of ${\mathrm{H}}^{+}$, ${\mathrm{D}}^{+}$, and ${\mathrm{He}}^{++}$ ions with a nickel atom are chosen as models. Ionic trajectories are calculated classically taking fully into account the distance-dependent repulsive potential of the nickel 3d electrons. For the electronic part of the Hamiltonian the most general on-site interaction terms allowed by atomic symmetry are used. The total electronic many-body states are classified by group-theoretical methods with respect to the orbital and spin ‘‘good’’ quantum numbers, L, ${\mathit{L}}_{\mathit{z}}$, and ${\mathit{S}}_{\mathit{z}}$; the latter two are conserved during the collision process. The nickel configurations 3${\mathit{d}}^9$, 3${\mathit{d}}^8$, and 3${\mathit{d}}^7$ are taken into account. They correspond to the treatment of elastic scattering, one-electron capture, and two-electron capture on the same footing. The time-dependent Schrödinger equation for this system is solved exactly. Experimentally accessible quantities such as the occupation numbers of all the states as well as the zero-, one-, and two-electron-capture probabilities are monitored along the trajectories of the scattering species on the femtosecond time scale. Probabilities of 21% and 0.35% for one- and two-electron capture, respectively are found, in good agreement with experiments on surfaces. Similarly, a spin polarization between -60% and -100% is calculated. It turns out that this predominant capture of minority electrons is a consequence of angular-momentum conservation and is strongly enhanced by electron correlations. The result implies that the probing of magnetism by electron capture occurs on a significantly longer time scale than the probing of single-electron properties.