Strain analysis from M-edge resonant inelastic X-ray scattering of nickel oxide films

a Electronic structure modifications due to strain are an eﬀective method for tailoring nano-scale functional materials. Demonstrated on nickel oxide (NiO) thin films, Resonant Inelastic X-ray Scattering (RIXS) at the transition-metal M 2,3 -edge is shown to be a powerful tool for measuring the electronic structure modification due to strain in the near-surface region. Analyses from the M 2,3 -edge RIXS in comparison with dedicated crystal field multiplet calculations show distortions in 40 nm NiO grown on a magnesium oxide (MgO) substrate (NiO/MgO) similar to those caused by surface relaxation of bulk NiO. The films of 20 and 10 nm NiO/MgO show slightly larger diﬀerences from bulk NiO. Quantitatively, the NiO/MgO samples all are distorted from perfect octahedral ( O h ) symmetry with a tetragonal parameter Ds of about (cid:2) 0.1 eV, very close to the Ds distortion from octahedral ( O h ) symmetry parameter of (cid:2) 0.11 eV obtained for the surface-near region from a bulk NiO crystal. Comparing the spectra of a 20 nm film of NiO grown on a 20 nm magnetite (Fe 3 O 4 ) film on a MgO substrate (NiO/Fe 3 O 4 /MgO) with the calculated multiplet analyses, the distortion parameter Ds appears to be closer to zero, showing that the surface-near region of this templated film is less distorted from O h symmetry than the surface-near region in bulk NiO. Finally, the potential of M 2,3 -edge RIXS for other investigations of strain on electronic structure is discussed.


Introduction
The electronic structure of nano-sized layers on surfaces of functional solid materials may be different to that of bulk samples. In particular, epitaxial strain between the nano-layers and substrate surfaces provides a powerful strategy to manipulate (atomic-scale) physical properties by shortening or extending their chemical bonds via lattice-mismatch, commonly referred to as strain engineering. This strain engineering has become a key tactic for improving material properties of graphene and similar materials, 1,2 high-T c superconductors, 3 energy storage materials, 4 quantum materials 5 and solid heterogeneous (electro-)catalysts. [6][7][8][9][10] Lattice strain is typically measured through the analysis of lattice peak positions measured with hard X-ray diffraction. On nano-sized materials the low amount of material together with small interaction cross sections for the hard X-ray radiation only provides small signals, averaged over the whole film thickness. Especially for the analysis of strain in surface-near regions, signals are largely shielded by the stronger bulk diffraction. In addition, it is not the lattice changes due to strain themselves that are important in strain engineering, but it is the associated change in electronic structure, e.g., the band gap and valence and conduction band properties, that ultimately leads to enhanced properties of the material. Already for simple binary correlated oxides, e.g., cobalt(II) oxide (CoO) 8,11 and nickel oxide (NiO), 12,13 the strain of the system has been shown to have an influence on properties such as the orbital polarization or the spin and corresponding relative magnetization, or on catalytic activity. For more complex materials strain engineering provides an attractive alternative method for tailoring materials' properties beyond what is possible through doping or chemical substitution. 10,14 As combination of X-ray absorption and emission spectroscopy, Resonant Inelastic X-ray Scattering (RIXS), is specific for determining electronic structure properties such as the band gap, 15 covalent interactions, 16 potential energy surfaces 17 and excited states 18 with element-and oxidation-state specificity. In this report it will be shown that RIXS is also sensitive to changes in electronic structure due to induced strain. Usually for 3d-transition metal materials, Metal L 2,3 -edge RIXS (schematically 2p 6 3d n -2p 5 3d n+1 -2p 6 3d n ) is performed for bulk electronic structure studies, partially because it turns out to provide the best possible energy resolution due to sharpest core levels and thus highest chemical and functional information. 19 However, to provide information on the electronic structure near surfaces, M 2,3 -edge RIXS (3p 6 3d n -3p 5 3d n+1 -3p 6 3d n ) is a viable alternative. In particular, for heterogeneous solid catalyst systems, the (near-) surface region provides the chemical activity and a detailed understanding of the changes of the electronic structure in this region is crucial. The X-ray attenuation length in (bulk) NiO is much shorter when addressing the M 2,3 resonances instead of the L 2,3 levels: across the full L 2,3 -edge resonances an average attenuation length of about 50 nm is observed for NiO, with detuning from the L 3 -edge maximum yielding probing depths of around 300 nm. For the M 2,3 -edge the probing depth is roughly 16 nm 20 and thus provides much higher sensitivity to the near-surface region, while L 2,3 -edge RIXS probes a more significant part of the bulk of the sample. Therefore the M 2,3edge RIXS of 3d-transition metal materials is particularly wellsuited to study the electronic structure changes in thin films induced by strain from the substrate.
In this research, we will provide theoretical Ni M-edge RIXS multiplet calculations with tetragonal distortions from octahedral (O h ) symmetry. We will show that as a function of distortion, certain signals in the RIXS spectra are changing and in particular that ratios between particular peak areas can be used to quantify the distortion from O h symmetry. As such, the theoretically obtained ratios can be matched onto ratios obtained for experimental spectra of different NiO systems.

Experimental and theoretical section
10, 20 and 40 nm thin films of NiO were grown on single crystalline MgO(001) substrates (NiO/MgO) via molecular beam epitaxy (MBE). The base pressure in the MBE chamber was 10 À10 mbar. For the sample preparation oxygen (O 2 ) was led into the chamber via a leak valve until the pressure reached 5 Â 10 À7 mbar. In the O 2 atmosphere Ni metal was evaporated from a Knudsen cell with 1 Å min À1 onto the substrate resulting in epitaxial growth of NiO. Epi-polished MgO substrates were cleaned by annealing them in O 2 atmosphere at 600 1C. In addition, a 20 nm NiO film was grown on a 20 nm magnetite (Fe 3 O 4 ) film, which was itself epitaxially grown on MgO (NiO/ Fe 3 O 4 /MgO). The film thickness was determined with a quartzbalance thickness monitor during growth. The monitor was calibrated against X-ray reflectivity measurements of prepared films. Reflectivity data were also used to check for thickness variation, which were found to be well below one monolayer within the region of the sample. With lattice constants of a = 4.21 Å for MgO(001) and a = 8.4 Å for Fe 3 O 4 (001), the lattice mismatch for NiO (a = 4.18 Å) is 0.72% and 0.48% respectively. A bulk NiO single crystal from MaTeck was cleaved along the (001) direction before transferring it to the RIXS setup.
Nickel M 2,3 -edge RIXS measurements were performed with a predecessor of the SolidFlexRIXS-setup 21 attached to the UE-112/PGM1 beamline 22 at the BESSY-II synchrotron in Berlin, Germany. The Nickel M 2,3 -edge absorption spectra were recorded via sample drain current measurements. 23 The first M 3 resonance maximum occurred at 67.2 eV and was selected as excitation energy for the RIXS experiments, since it is sufficiently below the threshold of the 3p core ionization. The RIXS spectra for the nano-layer NiO-films required acquisition times of typically three to four hours with the used setup, while for the NiO bulk sample a measurement time of only 90 minutes was considered sufficient. The incident X-rays were horizontally polarized in order to reduce the elastic scattering contribution to the RIXS spectra and the samples were rotated with the sample normal around 601 to the incoming beam, resulting in the normal being 301 off the direction of the spectrometer mounted at a right angle to the incoming beam in the horizontal polarization plane.
The Quanty package [24][25][26] was used to calculate Ni M-edge horizontally polarized X-ray absorption spectra (XAS) and RIXS calculations with horizontal incoming polarization (X in) and the orthogonal outgoing polarizations (Y + Z out), thereby simulating the experimental geometry with the RIXS spectrometer in the plane of the incoming polarization. Simulations were performed for Ni 2+ in octahedral (O h ) symmetry with a crystal field value of 10Dq = +1.05 eV and with a negligible magnetic field of H = 0.000001 T. Distortions from O h symmetry were taken into account with two parameters called D 1 and D 2 , where D 1 splits the original t 2g levels and D 2 the original e g levels of the O h symmetry as shown in Fig. 1A.
The energetic splitting of the d-orbitals can be equivalently formulated with D 1 and D 2 or with the symmetry parameters Ds and Dt. The one-electron energies as function of Dq, Dt and Ds are shown in Fig. 1A. The D 1 and D 2 approach can be used to test the behavior of the t 2g and e g splitting independently.
In addition, this approach can be used in tests of symmetry distortions that are different from the D 4h -type. While ignoring Dt (Dt = 0 eV) to account only for small distortions to octahedral symmetry, for example due to Jahn-Teller distortions, the relationship between Ds and D 1 and D 2 is: As for such simulations with Ds distortions, the D 2 = 4/3 Â D 1 relationship was fixed.
The simulations for Ni 2+ with 10Dq = 1.05 eV and various distortions Ds in eV yield linearly polarized XAS and full RIXS maps. One set is shown in Fig. 1B and C for comparison with the experimental data. RIXS slices were taken at the vertical line indicated in the XAS spectrum of Fig. 1C. We chose a single value for 10Dq, for both ground and X-ray excited state for sake of simplicity, however it is known that 10Dq may be different in the ground state (and RIXS final state) and the X-ray excited state. 29 Overall, the first band in these simulations agreed with the chosen 67.2 eV excitation energy of the experimental data. In addition, the overall calculated XAS shape agreed well with the experimental XAS of bulk NiO. 30

Results and discussion
Slices from the calculated RIXS maps at the discussed excitation energy (vertical line in Fig. 1C) for a few values of the combined distortion parameters D 1 and D 2 in (their fixed D 2 = 4/3 Â D 1 relationship for) Ds are presented in Fig. 2A. The spectra in Fig. 2A show minor changes in the energetic positions as function of Ds, which would not be detectable within our experimental resolution. There are, however, pronounced changes in the spectral weights of the peaks at B1 eV and 1.76 eV (referred to further as peak 2 and 3 as indicated in Fig. 2B). These peaks can be identified as 3d-3d excitations from the Ni 2+ 3 A 2g ground state to 3 T 2g and 3 T 1g excited states. Note that the 3d-3d excitation corresponding to the peak around 1 eV is a t 2ge g excitation, so there is a direct relationship of this peak with the 10Dq splitting.
In order to have an analysis of the areas of peak 2 and peak 3 in the simulated spectra that can directly be related to experimental data, were fitted six Voigt-profiles to the calculated spectra for a range of Ds-values in between À0.15 and +0.15 eV. An example of this analysis for a M 2,3 -edge RIXS slice of Ni 2+ with 10Dq = 1.05 and Ds = 0.0033333 eV is shown in Fig. 2B. Fig. 2C summarizes the obtained peak area fitting results for different values of Ds, displaying the trends in spectral weight of peak 2 and 3 as a function of Ds: the peak 2 weight increases, while the peak 3 decreases with increasing Ds. These trends are becoming less clear for Ds Z 0.07 eV as will be discussed shortly. The peak 2/peak 3 area ratio as a function of Ds is shown in Fig. 2D, which may be directly compared to the values found for experimental data shown below. The peak area ratio in panel D is roughly linear with the distortion Ds, up to Ds E 0.07 eV. For larger Ds values, the fitting procedure using six peaks begins to deviate from the simulated spectra, since peak 3 starts to split into two components starting around this value of Ds = 0.07 eV (for example, the green solid line with Ds = 0.1 eV in Fig. 2A shows a side-band component in peak 3). For the remaining discussion we restrict ourselves to Ds values where this splitting is small enough to be ignored.
We further mention that the energetic positions of peak 2 and 3, which for both peaks increase slightly with Ds (see e.g., Fig. 2A), yields additional qualitative information about the value and sign of the distortion parameter Ds, especially when symmetry distortions due to strain become large, e.g., when the value of Ds is on the order of Dq (= 10Dq/10).
The experimental Ni M 2,3 -edge XAS of all the investigated samples appear similar to the NiO bulk spectrum measured by Chiuzbȃian et al. 30 The 67.  Fig. 3A, the inelastic features at about 1 eV (peak 2) and 1.6-1.7 eV (peak 3) are enhanced for all the nano-layered NiO samples. The elastic line (peak 1) is about 100 to 1000 times higher than the energy loss features and has been cut off for clarity. Due to potential saturation effects in the elastic peak, its shape gets distorted. Therefore the peak analysis was performed as follows: the elastic line (peak 1) is assumed to be perfectly symmetric and the background found at negative energy loss is subtracted from the positive energy loss side before integrating the areas of peaks 2 or peak 3. The peak analysis results for the different samples are displayed in Fig. 3B and C. Both peak 2 and peak 3 areas in Fig. 3B are decreasing as function of increasing nano-layer film size on MgO and are approaching the peak areas obtained for NiO bulk.
The peak ratios of the experimental data in Fig. 3C for the 10, 20, 40 nm NiO/MgO and bulk samples are around 0.5-0.55. Comparing these ratios of the experimental data with the analyses of the Quanty calculations in Fig. 2D suggests negative values of Ds of about À0.10 AE 0.02 eV for all those samples, e.g., the ratios of 0.54, 0.52, 0.52 and 0.50 relate to rounded-off Ds values of À0.10, À0.11, À0.11 and À0.11 eV for the respective 10 nm, 20 nm, 40 nm NiO on MgO and bulk NiO samples. Observing that the sign of Ds is negative is logical, since the lattice constants of the MgO and Fe 3 O 4 substrates are larger than the NiO lattice constant. That allows the Ni-O bonds inplane to extend and in a crystal field description that leads to energy lowering of for example the 3d x 2 Ày 2 orbital (b 1 in Fig. 1A) compared to the 3d z 2 (a 1 ) orbital. In order to simulate such an effect of a lower relative energy for the b 1 orbital compared to the a 1 orbital, Ds should be negative.
Since the signal in the M 2,3 -edge RIXS experiment is dominated by the topmost 15 nm, the peak area ratios show that the growth of NiO layers on MgO beyond a 20 nm thickness already becomes more bulk-like, e.g., the probed surface-near layers further away from the MgO substrate (e.g., the surface-near region of both the 20 and 40 nm NiO on MgO) are having a similar lattice as NiO bulk. Strain effects due to the substrate are expected to decrease with increasing layer thickness, ultimately leading to surfaces that resemble the electronic structure similar of the bulk material. This trend is indeed been found in our M-edge RIXS electronic structure analyses for NiO/ MgO, e.g., the average peak area ratio of 10 nm NiO/MgO is different from the NiO bulk, while the average peak area ratio of 40 nm NiO/MgO is already very similar to the NiO bulk, showing the robustness of the M-edge RIXS method for electronic structure characterization due to strain. Taking into account the error bars all nanolayered NiO films on MgO can be considered similar to bulk NiO. (Note that the error bars in Fig. 3C are rather large due to the analysis procedure applied to the experimental data and derives from the noise level of the acquired data.) Focusing on the experimental analysis obtained for the bulk NiO, the symmetry of bulk NiO is often considered to be Ni 2+ in an O h surrounding. However, it is known since the 1940s that crystalline bulk NiO has a small orthorhombic distortion. 31  .75 relating to a Ds distortion in the quanty calculations of À0.025 eV, e.g., a value which is much closer to zero than the previously discussed NiO/ MgO and bulk NiO samples. As mentioned before, the lattice parameter mismatch of Fe 3 O 4 with NiO (0.48%) should be smaller than the mismatch of MgO with NiO (0.72%). Thus, surprisingly, we observed that the obtained Ds distortion of 20 nm NiO/Fe 3 O 4 /MgO differs more from the bulk NiO than the 20 nm NiO/MgO does. We should point out here that the Fe 3 O 4 unit cell has to match two NiO unit cells so that could somewhat explain our unexpected observation. In addition, the fact that Fe 3 O 4 grown on MgO also has a lattice mismatch, which might not be compensated yet after 20 nm of Fe 3 O 4 layers, needs also to be taken into account. Ultimately this seems to lead to NiO nano-layer growth on top that is more O h -symmetric than the near-surface crystal structure of a bulk NiO crystal.
For the theoretical analyses shown above, 10Dq = 1.05 eV was fixed agreeing well with the experimental data (peak 2 energy loss position) and published values for NiO. 30 In order to analyze the robustness of our Ds calibration with respect to the choice of 10Dq, the dependence of the above analyses on different values of 10Dq is checked by varying the distortion Ds for fixed 10Dq = 0.8 and 10Dq = 1.2 eV. For 10Dq = 0.8 eV similar trends as above remain present, although absolute values for the peak ratios are somewhat different. Since 10Dq = 0.8 eV shows the energetic position of peak 2 at 0.8 eV and peak 3 at about 1.6 eV, this 10Dq is considered not to be realistic for matching the experimental data. For a 10Dq value of 1.2 eV, peak 3 generally shows a double structure, which is in disagreement with the experimental data shown in Fig. 3A, so the energetic position and shape of peaks 2 and 3 strongly depend on the choice of 10Dq and agreement with the experiment enforces values 1.05 AE 0.05 eV.
The provided multiplet analyses demonstrate the potential of obtaining lattice distortion related electronic structure information with M 2,3 -edge RIXS. Furthermore we performed M-edge RIXS calculations for other 3d-transition metal ions (e.g., Co 2+ , Fe 2+ ) and observe clear relationships between distortions of the ligand field around the metal ion and features in the RIXS spectra. Thus, a very similar M-edge analysis procedure for electronic structure modifications could also be used for analysis of, for example, cobalt oxide nano-films. 8,11 Although the SolidFlexRIXS setup that we used was not set to the optimal resolution in order to improve count rates, we want to stress here that for M-edge RIXS nowadays sub-100 meV resolutions are achieved with rather compact instruments, very much in contrast to L 2,3 -edge RIXS of 3d-transition metal materials, where such energy resolution can only be achieved with huge experimental effort. Also it should be noted that the energy range of the M 2,3 -edges of 3d-transition metal materials can be achieved with lab-high-harmonic-generation (HHG) sources. Although current HHG sources do not provide sufficient flux to perform the here presented RIXS experiments, we expect future developments increasing photon flux in combination with increased efficiency of RIXS optics, 33,34 such that one could foresee that this type of strain engineering analyses with M-edge RIXS may be performed in the lab in the future.

Summary and conclusions
Concluding, strain engineering of thin films by choosing the right combination of substrate and sample material is a key tactic for improving materials' functional properties. In this work we have shown that 3d-transition metal M 2,3 -edge RIXS is a powerful tool for analyzing the electronic structure resulting from the strained 3d-transition metal oxide films on different substrates: experimental Ni M 2,3 -edge RIXS spectra of several nanometer thicknesses of NiO on a substrate and of a bulk NiO crystal were presented and analyzed in terms of the two most intense inelastic features. The experimental results were compared with analyses of RIXS calculations with Ni 2+ using a fixed crystal field of 10Dq = 1.05 eV in O h symmetry and on top of that distortions with the Ds parameter leading to splitting of both the e g and t 2g 3d-orbital sets. We observed trends in the analyses from calculated spectra as function of distortion, e.g., the ratio between the areas of the two most intense inelastic features was shown to provide a measurement of the structural distortion Ds and could be used for quantitatively deriving distortions from experimental data.

Conflicts of interest
There are no conflicts to declare.