Optimizing supercell structures for Heisenberg exchange interaction calculations

In this paper, we introduce an efficient, linear algebra-based method for optimizing supercell selection to determine Heisenberg exchange parameters from density functional theory (DFT) calculations. A widely used approach for deriving these parameters involves mapping DFT energies from various magnetic configurations within a supercell to the Heisenberg Hamiltonian. However, periodic boundary conditions in crystals constrain the number of extractable exchange parameters. To identify optimal supercell structures for extracting a target number of exchange parameters, we systematically generate supercells within a specified volume range using Hermite normal form matrices. Then, for each supercell, we perform a null space analysis on the coefficient matrix obtained by mapping magnetic configurations to the Heisenberg Hamiltonian. By analyzing the null space results for each supercell structure, we identify the optimal configuration for extracting a target number of exchange parameters. This optimal supercell selection approach significantly reduces computational time and resource requirements. This method, which involves generating and analyzing supercells before performing DFT calculations, has demonstrated a reduction in computational costs by one to two orders of magnitude in many cases.