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We present an approach for simulating x-ray nanobeam Bragg coherent diffraction patterns based on the Takagi-Taupin equations. Compared to conventional methods, the current approach can be universally applied to any weakly strained system including semi-infinite crystals that diffract dynamically. It addresses issues such as the curved wave front and redivergence of the focused incident beam. We show excellent agreement with experimental data for a strained La0.7Sr0.3MnO3 thin film on a SrTiO3 substrate and a path to extracting physical information using automatic differentiation. 

Rare-earth nitrides, such as gadolinium nitride (GdN), have great potential for spintronic devices due to their unique magnetic and electronic properties. GdN has a large magnetic moment, low coercitivity and strong spin polarization suitable for spin transistors, magnetic memories and spin-based quantum computing devices. Its large spin splitting of the optical bandgap functions as a spin-filter that offers the means for spin-polarized current injection into metals, superconductors, topological insulators, 2D layers and other novel materials. As spintronics devices require thin films, a successful implementation of GdN demands a detailed investigation of the optical and magnetic properties in very thin films. With this objective, we investigate the dependence of the direct and indirect optical bandgaps (𝐸𝑔) of half-metallic GdN, using the trilayer structure AlN(10 nm)/GdN(t)/AlN(10 nm) for GdN film thickness t in the ranging from 6 nm to 350 nm, in both paramagnetic (PM) and ferromagnetic (FM) phases. Our results show a bandgap of 1.6 eV in the PM state, while in the FM state the bandgap splits for the majority (0.8 eV) and minority (1.2 eV) spin states. As the GdN film becomes thinner the spin split magnitude increases by 60%, going from 0.290 eV to 0.460 eV. Our results point to methods for engineering GdN films for spintronic devices.