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Abstract The piezoelectric and ferroelectric applications of heterovalent ternary materials are not well explored. Epitaxial MgSiN₂films are grown at 600 °C on (111)Pt//(001)Al₂O₃substrates by the reactive sputtering method using metallic Mg and Si under the N₂atmosphere. Detailed X‐ray diffraction measurements and transmission electron microscopy observations revealed that the epitaxially grown films on the substrates have a hexagonal wurtzite structure withc‐axis out‐of‐plane orientation. The random occupation of this structure by Mg and Si differs from that of the previously reported structure in which these two cations periodically occupy the cationic sites. However, the lattice spacings closely approximate those that are previously reported, irrespective of the ordering, and they are almost comparable with those of (Al_0.8Sc_0.2)N. The wide bandgap of >5.0 eV in deposited MgSiN₂is compatible with that of AlN and suggests durability against the application of strong external electric fields, possibly to induce polarization switching. In addition, MgSiN₂is shown to have piezoelectric properties with an effectived₃₃value of 2.3 pm V⁻¹for the first time. This work demonstrates the compositional expansion of hexagonal wurtzite to heterovalent ternary nitrides for novel piezoelectric materials, whose ferroelectricity is expected. 

Abstract Optical second harmonic generation (SHG) is a nonlinear optical effect widely used for nonlinear optical microscopy and laser frequency conversion. Closed-form analytical solution of the nonlinear optical responses is essential for evaluating materials whose optical properties are unknown a priori. A recent open-source code, ♯SHAARP.si, can provide such closed form solutions for crystals with arbitrary symmetries, orientations, and anisotropic properties at asingleinterface. However, optical components are often in the form of slabs, thin films on substrates, and multilayer heterostructures with multiple reflections of both the fundamental and up to ten different SHG waves at each interface, adding significant complexity. Many approximations have therefore been employed in the existing analytical approaches, such as slowly varying approximation, weak reflection of the nonlinear polarization, transparent medium, high crystallographic symmetry, Kleinman symmetry, easy crystal orientation along a high-symmetry direction, phase matching conditions and negligible interference among nonlinear waves, which may lead to large errors in the reported material properties. To avoid these approximations, we have developed an open-source package named Second Harmonic Analysis of Anisotropic Rotational Polarimetry in Multilayers (♯SHAARP.ml). The reliability and accuracy are established by experimentally benchmarking with both the SHG polarimetry and Maker fringes using standard and commonly used nonlinear optical materials as well as twisted 2-dimensional heterostructures.