David J. Srolovitz

Atomistic machine learning is a powerful tool for accurate and efficient investigation of material behavior at the atomic scale. While attempts have been made to construct models directly within Cartesian space, they face challenges in providing a systematic framework based on irreducible representations—a core feature of widely used spherical models. Here we propose Cartesian Natural Tensor Networks to overcome these limitations and thus offer a general, symmetry-preserving framework for atomistic machine learning. We present a theory of irreducible representations using Cartesian natural tensors, comprising their construction, their products, and a systematic scheme to decompose and reconstruct high-rank physical tensors. Leveraging this machinery, we develop equivariant machine learning interatomic potentials for materials and molecular systems with performance on par with leading spherical models. It further captures accurate structure–property relationships for tensorial quantities ranging from low-rank dipole moments to high-rank tensors with complex symmetries, such as the elastic constant tensor.

We provide atomistic insights into the microscopic mechanism of polarization switching in wurtzite ferroelectric AlScN by integrating advanced thin-film fabrication, ferroelectric switching dynamics characterizations, high-resolution scanning transmission electron microscopy (STEM), and large-scale molecular dynamics simulations enabled by a deep neural network-based interatomic potential. Contrary to earlier interpretations proposing a transient nonpolar intermediate phase, our Letter provides strong evidence that the broad transitional regions previously observed in STEM images are consistent with projection artifacts resulting from the intrinsic three-dimensional zigzag morphology of 180° domain walls, which are a characteristic form of inversion domain boundary. This is further confirmed by STEM imaging of strategically prepared, partially switched Al_{0.75}Sc_{0.25}N thin films. Our simulations reveal that switching proceeds through collective, column-by-column atomic displacements, directly explaining the emergence of zigzag-shaped domain walls, and is consistent with the nucleation-limited switching behavior observed in experimental switching dynamic measurements. Furthermore, we show that increasing Sc content systematically lowers domain wall energy and associated nucleation barrier, thereby reducing the switching field in agreement with experimental trends. These findings establish a direct connection between local domain wall structure, switching dynamics, and macroscopic ferroelectric behavior.

Heterostructures are composed of spatially distinct zones with differing mechanical and/or physical properties. When carefully engineered, these architectures can exhibit superior performance compared with their homogeneous counterparts. However, not all heterostructures inherently lead to a pronounced improvement in properties. Realizing the full potential of complex heterostructures requires a rigorous understanding of the structure–property relationships and mechanisms related to inter-zone interactions. This knowledge is essential if the heterostructure effect is to be effectively harnessed and the overall performance of the material optimized. Here we examine the fundamental mechanisms underlying the unusual mechanical properties of heterostructured materials, highlighting the important role of interactive coupling in the heterozone boundary-affected regions. We outline strategies for evaluating the effects that arise from heterostructures, in particular the heterodeformation-induced stress. We also provide guidelines for designing heterostructured materials with optimal mechanical properties, and discuss future directions for property design and characterization development.