A new spin- and angle-resolved inverse photoemission setup with a low-energy electron source is presented. The spin-polarized electron source, with a compact design, can decouple the spin polarization vector from the electron beam propagation vector, allowing one to explore any spin orientation at any wavevector in angle-resolved inverse photoemission. The beam polarization can be tuned to any preferred direction with a shielded electron optical system, preserving the parallel beam condition. We demonstrate the performances of the setup by measurements on Cu(001) and Au(111). We estimate the energy resolution of the overall system at room temperature to be ∼170 meV from k B T eff of a Cu(001) Fermi level, allowing a direct comparison to photoemission. The spin-resolved operation of the setup has been demonstrated by measuring the Rashba splitting of the Au(111) Shockley surface state. The effective polarization of the electron beam is P = 30% ± 3%, and the wavevector resolution is Δ k F ≲ 0.06 Å−1. Measurements on the Au(111) surface state demonstrate how the electron beam polarization direction can be tuned in the three spatial dimensions. The maximum of the spin asymmetry is reached when the electron beam polarization is aligned with the in-plane spin polarization of the Au(111) surface state.

We reply to the Comment by Donath et al. on our setup, which allows a total 3D control of the polarization direction of the electron beam in an inverse photoemission spectroscopy (IPES) experiment, a significant advance with respect to previous setups with partial polarization control. Donath et al. claim an incorrect operation of our setup after comparing their results, treated to enhance the spin asymmetry, with our spectra without the same treatment. They also equal spectra backgrounds instead of equaling peak intensities above the background. Thus, we compare our Cu(001) and Au(111) results with the literature. We reproduce previous results, including spin-up/spin-down spectral differences observed for Au and not observed for Cu. Also, spin-up/spin-down spectral differences appear at the expected reciprocal space regions. In the Comment, it is also stated that our tuning of the spin polarization misses the target because the spectra background changes when tuning the spin. We argue that the background change is irrelevant to IPES since the information is contained in peaks produced by primary electrons, those having conserved their energy in the inverse photoemission process. Second, our experiments agree with previous results from Donath et al. [Wissing et al., New J. Phys. 15, 105001 (2013)] and with a zero-order quantum-mechanical model of spins in vacuum. Deviations are explained by more realistic descriptions including the spin transmission through an interface. Consequently, the operation of our original setup is fully demonstrated. Our development corresponds to “the promising and rewarding angle-resolved IPES setup with the three-dimensional spin resolution,” as indicated in the Comment, after our work.