Magnetic-configuration design for reliable Heisenberg exchange parameters

The determination of magnetic exchange interactions is essential for the quantitative description and predictive modeling of magnetic materials. In this work, we present a neighbor-shell-based screening method for selecting magnetic configurations suitable for extracting Heisenberg exchange parameters beyond nearest-neighbor from density functional theory (DFT) calculations. Using only the structure, the proposed approach identifies the linear independence of neighbor-shell contributions before any first-principles calculations instead of relying on trial-and-error generation of magnetic configurations. We apply the proposed approach to two representative classes of magnetic configurations: random spin states and spin spirals, and validate its predictions against direct DFT fitting for Fe and MnF$_2$. We show that only parameters obtained when all relevant neighbor-shell contributions are linearly independent remain transferable to other magnetic configurations. The proposed method provides practical guidance for selecting magnetic configurations for reliable exchange-parameter extraction and may also benefit other neighbor-shell-based models.