Response to "Comment on 'Spin- and angle-resolved inverse photoemission setup with spin orientation independent from electron incidence angle'" [Rev. Sci. Instrum. 93, 093904 (2022)].

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.