The Total 3s Emission Yield as Bulk-Sensitive Probe for a True Soft X-ray Absorption Spectrum?

– The detection of the true soft X-ray absorption typically needs specially prepared sub-µm thin samples for transmission measurements. Bulk experiments instead have to rely on yield methods, e.g. electron yield with limitations for insulating samples, sensitivity to applied fields and with limited bulk sensitivity. Fluorescence yield methods instead do not have those limitations but have been found to deviate in general from the absorption spectrum. Here, we demonstrate that restricting the detection to the 3s -fluorescence channel (with the detector at a special angle where all polarizations contribute equally) restores the true X-ray absorption spectrum for all 3d Metal L 2,3 -edges. These theoretically-derived results are rationalized by the lack of 3s-3d interaction in the core-excited state. Comparing X-ray absorption versus 3s -PFY for arbitrary detection geometries for both linear and circular polarized light, deviations appear that can become as large as 15%.

X-ray absorption spectroscopy has become a standard tool for electronic structure analysis of materials 1 , whereas the small line widths in the soft X-ray range combine element specificity with the best potential energy resolution for all elements 2 . The 3d-transition metal L 2,3 -edges (where a 2p electron is mainly excited into unoccupied 3d states: 2p 6 3d n 2p 5 3d n+1 ) provide direct information on the 3d electronic structure in those materials, relevant e.g. for catalysis 3 , magnetism and magnetic storage 4 as well as battery applications 5 . Soft X-rays tuned to energies at specific absorption edges do not penetrate deep into matter, restricting transmission measurements of the sample absorption to specially prepared sub-µm thin specimen in vacuum.
For studies on thick samples, indirect yield methods provide an alternative. The drain current from the sample after X-ray excitation is often used: the soft X-ray excitation leads to the emission of electrons. The now charged sample neutralizes by attracting electrons. This current is measured and largely proportional to the original soft X-ray excitation, i.e. the true x-ray absorption. Due to the limited electron escape depth from the sample, drain current measurements are a surface-sensitive probe of X-ray absorption with limitations for insulating samples and problems in electric and magnetic fields. Detecting the fluorescence yield instead provides a more bulk-like probe of X-ray absorption.
With these alternative indirect methods one assumes that there is no variation in the respective yield of emission over the studied energy range. However it is known that this assumption is incorrect for fluorescence yield on systems with strong local correlations 6 . Optical effects like saturation due to similar penetration and escape depths of the x-ray photons can influence fluorescence yield spectra and depend particularly on the experimental geometry. In addition, the measurement of the total fluorescence yield (TFY) can be affected by strong resonances at energies lower than the investigated absorption edge. In liquid solutions 7-10 , but also in solid Fe 2 O 3 7 , measurements of the TFY-x-ray absorption spectrum (XAS) display intensity dips. They are explained with the dominant oxygen 2p emission being decreased by the onset of absorption at the transition metal. This decrease is only partially compensated by emission from the metal. It was emphasized before that measuring the fluorescence yield-XAS via the total 3d to 2p emission, referred to as the 3d-partial fluorescence yield (PFY), provides all X-ray absorption features, but that there are intensity differences which directly relate to the on-site electronic correlations 8,11 . Especially the intensity of the L 3 edge in 3d-PFY-XAS is lower than expected 11 .
This hinders for example using the branching ratio between the L 2 and L 3 6 and Co 2+ (H 2 O) 6 ) appears to provide an "undistorted" or true XAS or at least it provides the correct L 3 /L 2 branching ratio.
In this letter we show theoretically that 3s-PFY can indeed restore the true XAS, albeit only when a special experimental geometry is used. First we rationalize the absence of intensity differences with the absence of the influence of on-site electronic correlations in the XAS excited state due to the closed 3s shell in case isotropic x-ray absorption and 3s emission of 3d-metal ions in an octahedral (O h ) crystal field is considered. Thereafter, simulations of more experimentally relevant situations, such as in the experiments of Golnak 13 and Soldatov et al. 10 5 are discussed, in which the detection geometry suppresses certain fluorescence polarizations. We show that differences between true XAS and 3s-PFY may then actually occur.
First, we will start with discussing calculations in the isotropic approximation, e.g., all polarizations of the incoming and outgoing photons are equally added. We have done calculations for the 3d fillings 3d 1 to 3d 8 . Considering a 3d 9 system (for example Cu 2+ ) is unnecessary, since the filled d-shell in the X-ray absorption final state (2p 5 3d 10 ) does not have 3d-3d correlations and therefore no differences between XAS and any PFY-XAS are expected.
All the simulated spectra with isotropic x-ray absorption and 3s fluorescence revealed that 3s-

PFY-XAS and XAS are completely identical after normalization (See Supporting Information).
This result is substantiated as follows: 3d-PFY deviates from true XAS, because of an additional 2p-3d exchange correlation effect entering in the 3d2p core-hole fluorescent decay 11 . For 3s-PFY instead, the exchange correlations do not appear in the 3s2p fluorescent decay step because the completely filled 3s shell in the core-excited state is not influenced by those correlations. Nevertheless, after 3s to 2p fluorescent decay, correlations between 3s and 3d occur, but only result in a redistribution of spectral weight inside the 3s decay channel, while not influencing the total 3s emission as measured in 3s-PFY. This argument is valid as long as the 3s sub-valence states are completely filled in the ground and core excited states, which is the case when they are at sufficiently lower energy than the 3d valence states. For the main group elements in the third period, the 3s level contributes to the valence states and will thus show deviations between 3s-PFY and XAS. For the 3d transition metals and even heavier elements, the 3s levels are separated by more than 20 eV from the Fermi level and no differences between 3s-PFY and true XAS are expected.
Since for all the 3d-metal L 2,3 absorption edges 3s emission is present, 3s-PFY can become a more universal yield measure of 3d-metal materials for obtaining the true XAS 13 , also when compared to the commonly used inverted oxygen 2p emission 5,9,10 , since the latter is only possible if oxygen is present in the sample and when the 3d-metal edge of interest is above the oxygen K-edge. We note though that compared to 3d-PFY, 3s emission is weaker than 3d emission because of the smaller number of electrons and smaller transition matrix elements.
In experiments, the outgoing fluorescence may get partially absorbed inside the sample. This effect is termed self-absorption (also sometimes mentioned as part of saturation effects) and is especially strong when the 3d emission is energetically close to the resonant L 2,3 -edge absorption edge. The strong variations in the absorption of the fluorescence while penetrating through the sample to the detector, effectively distorts the measured yield (but can be corrected for with known spectral distributions 9 ). For 3s-PFY this effect can be largely neglected, since the emission energy is sufficiently separated in energy from the actual absorption resonance.
In perfect O h symmetry, there is no difference between the different spatial dimensions, thus for the X-ray absorption, isotropic XAS is the same as the horizontally (X-) polarized XAS and vertically (Z-) polarized XAS. For our simulations, we have chosen the Y-direction as the incoming beam direction. Calculating 3s-PFY with one of these incoming polarizations, while using isotropic 3s-fluorescence (adding the X-, Y-and Z-polarized fluorescence), the 3s-PFY spectrum still matches the true XAS (in Supporting information Figure 1) for the different polarizations.
In our theoretical treatment we can extract the different geometry components X, Y and Z independently for both the incoming (absorbed) and outgoing (fluorescent) X-rays.  Figure 1. We note here that for these simulations the rule of thumb of 10Dq=0.6*oxidation state 14 was used, which agrees often very well to experimental data with particular formal oxidation states, especially for oxides 1,15 .

Fe 2+ (middle) and Ni 2+ (right) in O h symmetry with 10Dq=0.6*(oxidation state).
At a first glance, these symmetry-selected simulated 3s-PFY spectra (green dotted lines) largely overlap with the simulated XAS spectra (black lines) for Ti 3+ , Fe 2+ and Ni 2+ in O h symmetry shown in Figure 1. Again, this proves that 3s-PFY with a detector at any angle might 9 indeed be useful in branching ratio determination for spin state analysis 12 . However, there are deviations in both the horizontally (X-) polarized (up to 15%) and vertically (Z-) polarized 3s-PFY absorption spectra compared to the true XAS as can be seen in the difference plots (red lines in top and middle of Figure 1). In addition, the differences for both incoming polarizations are not compensated and are larger when only crossed polarizations contribute (X-polarized in, measured X in Y out +X in Z out =2B, red lines, middle) as opposed to the Z-polarized spectra with respect to the incoming beam (in the direction of the horizontal polarization X).
In order to re-create a situation where the detector angle allows for a correct measurement of the true XAS in O h symmetry, the detector has to be specially placed: the angle has to be chosen such that the differently polarized outgoing 3s-fluorescence channels (the X, Y and Z-polarized components) are detected with equal contribution. In general, with α and θ being the spherical angles (α, the angle within the XY-plane, and θ the angle to the Z-axis), the detected fluorescence intensity is I=X out *sin 2 (α)*sin 2 (θ) + Y out *cos 2 (α)*sin 2 (θ) + Z out *cos 2 (θ). In order to guarantee that all components are registered with equal intensity, the angular pre-factors have to be the same. This is fulfilled for sin(α)=cos(α), i.e. α =45° and sin 2 (θ)=2/3, i.e. θ at the magic 10 angle to the Z-axis ~54,7°. When the detector is located at this specific position, one can recover the 3s-PFY in a "pseudo-isotropic fluorescence situation" and, as a consequence, 3s-PFY spectra are representing the true XAS for linear dichroism studies. We point out that this solution not only holds for O h symmetry but may be considered valid for any symmetry.
It is also interesting to analyze how the X-ray Magnetic Circular Dichroism (XMCD) signal behaves for 3s-PFY versus true XAS, since a recent paper has shown that there are problems with the sum rules from XMCD with 3d-PFY/TFY detection 16 . XMCD simulations of true XAS and 3s-PFY for Ti 3+ , Fe 2+ and Ni 2+ in O h symmetry with a magnetic field of B=10T are shown in Figure 2. The XMCD signal and shape for 3s-PFY with isotropic or "pseudo-isotropic" 3sfluorescence conditions (green dotted lines, Figure 2) is observed to be the same as the true XAS (black lines). For 3s-PFY with only the 3s-fluorescence from the Y-and Z-polarization components (with a fluorescence yield detector at 90° to the incoming beam, red lines in Figure 2) the signal is not only enhanced but it also seems to contain features that are not present in the standard XMCD (black lines). Especially for Ni 2+ this is very apparent, since the red line even moves out of the window and there is a non-zero XMCD at -7 eV, below the Ni L 2 shown that 3s-PFY may then lead to substantial differences as compared to the true XAS. We discussed that these differences can be overcome by selecting the right angle for the detector in order to create a "pseudo-isotropic fluorescence situation". In addition, the 3s-PFY probe gives the correct branching ratio (e.g., same as true XAS) in contrast to 3d-PFY 11 .
With recent developments in PFY detection with transition-edge sensors 17 8,11 . The integrated emission as function of excitation energy in the CTM4RIXS interface then yields the simulated 3s-PFY-XAS. In this report only simulations performed with Quanty are shown, but the CTM4XAS simulations lead to the same results.

Notes
The authors declare no competing financial interests.