## 2 Experimental Design  
A simplified schematic of the setup is shown in Figure 1. Measurements were performed with the MUSIX experimental end station [17] at the FL24 beam line of the free-electron laser in Hamburg (FLASH). The FEL was tuned to generate third harmonic radiation around the oxygen \(K\)- and nickel \(L_{2,3}\)-edges (from 506 eV to 566 eV and 842 eV to 887 eV, respectively), producing bursts of 40 pulses with 10 \(\upmu\)s spacing within the burst and 10 bursts per second. Before the beam line, the beam is defined by two apertures: 5 mm apertures are used at the O \(K\)-edge and 2 mm apertures at the Ni \(L\)-edges. Then, the average FEL pulse energy was monitored using the signal from an X-ray gas monitor detector (XGMD) [18], after which the fundamental radiation was suppressed by a 13 meter long gas attenuator unit containing \(9.7\times 10^{-2}\) mbar of neon (O \(K\)-edge) or \(1.7\times 10^{-2}\) mbar of krypton (Ni \(L\)-edges) in addition to two Si membrane filters of 401 nm and 200 nm thickness. Figure 1: Schematic setup Experimental setup at the FL24 beam line of the free electron laser in Hamburg (FLASH) (left) and exemplary detector images (right). The free electron laser (FEL) beam is initially transmitted through a beam splitting grating, optimized for high intensity in the first diffraction orders. The zeroth and one of the first diffraction orders are then focused onto the sample with a vertical focal size of about 35 \(\upmu\)m at a grazing incidence of 11.5 \({}^{\circ}\). The specular reflection of both beams is directed onto the variable line spacing diffraction grating of the spectrometer and dispersed onto a charge-coupled device (CCD). Since the spectrometer disperses both beams orthogonally to the beam separation, the two beams yield separate spectra on the detector. The green and red lines mark the regions of interest in which spectral intensity is integrated and correspond to the spectra in Figure 2a. 1208 single images are averaged while the undulators are scanned across the O \(K\)-edge with both beams on the NiO sample. The average image shows the spectral structure within the scanned spectral interval. The beam is then split horizontally by a transmission grating of 3.8 mm height and 0.9 mm width, optimized to produce similar intensity in the zeroth and first diffraction orders: It is made from a Si-membrane of 1.1 um thickness with rectangular grooves of 960 nm depth and 7.9 um period at 50% aspect ratio. The zeroth and first diffraction orders are each directed onto the sample, focused by bendable mirrors to a spot of about 35 um height and 80 um width, at a grazing angle \(\theta\) of 11.5\({}^{\circ}\). The specular reflections of both beams are analyzed by the spectrometer of the MUSIX endstation [17], consisting of a variable line spacing grating and an in-vacuum charge-coupled device (CCD) (GreatEyes Model GE-VAC 2048 2048). The 13.5 um square pixels of the CCD were read out with an ADC clocked with 3 MHz in high gain mode and 16 pixel binning orthogonal to the spectral axis to increase the frame rate and decrease noise while preserving the spectral resolution. This resulted in a framerate of 5 Hz. The FEL, producing bursts of 10 Hz, was chopped accordingly, so that each detector image represented an average over one burst of 40 pulses. The photon energy dispersion on the CCD was measured as 10.73 pixel/eV at the O \(K\)-edge and 7.8 pixel/eV at the Ni \(L\)-edges. Samples consisted of epitaxial NiO films of 40 nm thickness, grown on MgO(001) substrates. A 2 nm thick MgO underlayer was deposited by radio frequency magnetron sputtering in 3 mTorr argon at a temperature below 100 \({}^{\circ}\)C followed by a NiO layer that was deposited at 700 \({}^{\circ}\)C in an Ar (90%)/O\({}_{2}\) (10%) gas mixture at a pressure of 3 mTorr and was then annealed in-situ at the same temperature (700 \({}^{\circ}\)C) for 15 min in the same Ar-O\({}_{2}\) gas mixture.