A Generalized Framework for Evaluating Dzyaloshinskii–Moriya Interaction in Cr₁₊_δTe₂

Noncollinear spin textures, such as skyrmions, have attracted considerable attention as key components in next-generation spintronic devices. A central mechanism underlying these textures is the Dzyaloshinskii-Moriya interaction (DMI), which induces spin canting through spin–orbit coupling (SOC). To analyze DMI, various computational approaches based on density functional theory (DFT) have been proposed. However, the resulting DMI values are typically confined to specific crystal structures used in the calculations, which limits their general applicability. This limitation becomes noticeable in compounds with non-stoichiometric compositions, where small variations in the model configuration can lead to changes in the calculated DMI, even for the same material. To address this limitation, we propose a generalized approach for evaluating DMI that extends beyond a single structural configuration. Using first-principles DFT calculations, we analyze the spin-configuration-energy relationships across a range of compositions in self-intercalated Cr_1+δTe₂. From these data, we extract a unified set of DMI parameters that effectively capture the average response of the Cr-Te system. This generalized framework supports more accurate simulations of noncollinear spin textures across the CrTe family.