Momentum microscopy (MM) is a novel way of performing angle-resolved photoelectron spectroscopy (ARPES). Combined with time-of-flight (ToF) energy recording, its high degree of parallelization is advantageous for photon-hungry experiments like ARPES at x-ray energies, spin-resolved and time-resolved ARPES. This article introduces the technique of ToF-MM and illustrates its performance by selected examples obtained in different spectral ranges. In a multidimensional view of the photoemission process, spectral density function ρ(k,EB), spin polarization P(k,EB), and related quantities of circular dichroism in the angular distribution (CDAD) are part of the “complete experiment,” a concept adopted from atomic photoemission. We show examples of spin-resolved valence-band mapping in the UV and VUV, and the soft- and hard-x-ray range. Spin mapping of the Heusler compounds such as Co2MnGa and Co2Fe0.4Mn0.6Si at hν = 6 eV proves that the second compound is a half-metallic ferromagnet. Analysis of the Tamm state on Re(0001) using VUV-excitation reveals a Rashba-type spin texture. Bulk band structure including Fermi surface, Fermi-velocity distribution vF(k,EF), full CDAD texture, and spin signature of W(110) have been derived via tomographic mapping with soft x-rays. Hard x rays enable accessing large k||-regions so that the final-state sphere crosses many Brillouin zones in k-space with different kz’s. At hν = 5.3 keV, this fast 4D mapping mode (at a fixed hν) revealed the temperature dependence of the Fermi surface of the Kondo system YbRh2Si2. Probing the true bulk spin polarization of Fe3O4 at hν = 5 keV proved its half-metallic nature. The emerging method of ToF-MM with fs x-ray pulses from free-electron lasers enables simultaneous valence, core-level, and photoelectron diffraction measurements in the ultrafast regime.

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