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We report a detailed study of high-order harmonic generation (HHG) in helium. When comparing predictions from a single-active-electron model with those from all-electron simulations, such as the ATTOMESA code and R-matrix-with-time-dependence method, which can include different numbers of states in the close-coupling expansion, it seems imperative to generate absolute numbers for the HHG spectrum in a well-defined framework. While qualitative agreement in the overall frequency dependence of the spectrum, including the cutoff frequency predicted by a semiclassical model, can be achieved by many models in arbitrary units, only absolute numbers can be used for benchmark comparisons between different approaches. 

We report on the x-ray absorption spectra (XAS) and x-ray magnetic circular dichroism (XMCD) of a series of NiFe2O4 (Ni ferrite) films grown on symmetry matched substrates and measured in two geometries: out-of-plane and near in-plane. The Ni ferrite films, grown by pulsed laser deposition, are epitaxial and the substrates used (ZnGa2O4, CoGa2O4, MgGa2O4, and MgAl2O4) introduce a systematic variation in the lattice mismatch between the substrate and the film. Modeling of the XAS and XMCD spectra, both measured with the surface sensitive total electron yield mode, indicates that the Ni2+ cations reside on the octahedrally coordinated lattice sites in the spinel structure. Analyses of the Fe XAS and XMCD spectra are consistent with Fe3+ cations occupying a subset of the octahedral and tetrahedral sites in the spinel oxide lattice with the addition of a small amount of Fe2+ located on octahedral sites. The Ni2+ orbital to spin moment ratio (μℓ/μs), derived from the application of XMCD sum rules, is enhanced for the substrates with a small lattice mismatch relative to NiFe2O4. The results suggest a path for increasing the orbital moment in NiFe2O4 by applying thin film growth techniques that can maintain a highly strained lattice for the NiFe2O4 film.