Real-space Classification of Non-collinear Spin DFT Solutions

Traditional density functional theory (DFT) remains a cornerstone of electronic structure calculations. Many modern DFT codes offer the capability of describing spin textures, current densities, and non-collinear magnetism. In this work, we present a computational framework to identify and analyze the geometric structure of different types of solutions from non-collinear DFT calculations. In contrast to existing approaches that utilize the density matrix, our method employs real-space quantities to determine the collinearity and coplanarity of the magnetization, the current density, and the spin-current density. Using rank-based linear dependence tests, we categorize the solutions akin the Fukutome classification. One clear advantage of our approach is that it can be straightforwardly implemented in real-space grid-based or plane-wave codes that explicitly avoid the use of the density matrix.