Spin- and time-resolved photoelectron spectroscopy and diffraction studies using time-of-flight momentum microscopes

Momentum microscopy (MM) is a novel way of performing angular-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 and spin-resolved ARPES. This article introduces into the spin-resolved variant 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 $\rho(k,E_B)$, spin polarization $P(k,E_B)$ 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, VUV, soft- and hard-X-ray range. Spin mapping of the Heusler compounds Co$_2$MnGa and Co$_2$Fe$_{0.4}$Mn$_{0.6}$Si at $h\nu=6$~eV prove 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 $v_F(k,E_F)$, 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$_{par}$-regions so that the final-state sphere crosses many Brillouin zones in $k$-space with different $k_z$. At $h\nu=5.3$~keV this fast 4D mapping mode (at fixed $h\nu$) revealed the temperature dependence of the Fermi surface of the Kondo system YbRh$_2$Si$_2$. Probing the true bulk spin polarization of Fe$_3$O$_4$ at $h\nu=5$~keV proved its half-metallic nature. The emerging method of ToF-MM with fs X-ray pulses from a free-electron laser enables simultaneous valence, core-level and photoelectron diffraction measurements in the ultrafast regime.