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 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 limit the number of exchange parameters that can be extracted. To identify supercells that allow for more exchange parameters, we generate all possible supercell sizes within a specified range and apply null space analysis to the coefficient matrix derived from mapping DFT results to the Heisenberg Hamiltonian. By selecting optimal supercells, we significantly reduce computational time and resource consumption. This method, which involves generating and analyzing supercells before performing DFT calculations, has demonstrated a reduction in computational costs by 1-2 orders of magnitude in many cases.