An important concept of modern solid state theory is the exchange-correlation (xc) hole. On a microscopic scale the Pauli-principle and Coulomb interaction among the electrons demand that each electron is surrounded by a reduced electronic charge called the xc-hole. Our experiments demonstrate that this concept is reality [1-4]. In our experimental setup, a spin-polarized primary electron hits the sample, which may result in the emission of an electron pair. The individual electrons are registered, whereby an electronic coincidence circuit ensures that uncorrelated electrons are essentially suppressed.   The kinetic energies of the electrons is derived from their flight times to the detector and the in-plane momentum can be computed from the emission angles q and f, see panel b). As an example we display in the bottom panel data obtained with a primary electron beam of 19 eV. In this plot the data for parallel and antiparallel alignment of primary and valence electron are combined.

We selected those coincidence events, where the kinetic energies of the individual electrons are 6.75eV. This choice uniquely defines the valence state involved in the scattering process.  The rim of maximum intensity marks the boundary of a region of reduced intensity for in-plane momenta with absolute values smaller than 0.5 Å^-1. It is this depletion zone which is the manifestation of the exchange-correlation hole. The width of the depletion depends on the spin alignment of primary and valence electron. From this we conclude that the contribution due to exchange has a larger extension compared to the correlation part. [3,4]

Energy and momentum distribution of the emitted electron pairs contain important information about the electron correlation. We have discovered in a recent study that the intensity levels are very different from a metals compared to NiO. The latter is usually referred to as a “highly correlated” material. This opens the avenue to quantify the correlation strength of materials. [5,6]

Fig. 1: In panel a) a schematic view of the ToF coincidence spectrometer is presented. Emitted electron pairs can be captured on two detectors. The excitation is due to a pulsed primary spin polarized electron beam. The relative orientation of majority spin and primary electron spin can be independently reversed. We analyzed the data according to the emission geometry in b). The bottom panel displays the spin-integrated intensity from a Fe(100) surface for this geometry.