Optimizing Supercell Structures for Heisenberg Exchange Interaction Calculations

TL;DR

This paper presents a linear algebra-based method to optimize supercell selection for calculating Heisenberg exchange parameters from DFT, significantly reducing computational costs by enabling more exchange parameters to be extracted efficiently.

Contribution

The paper introduces a novel supercell optimization technique using null space analysis to enhance the extraction of exchange parameters from DFT calculations.

Findings

Reduces computational costs by 1-2 orders of magnitude.

Enables extraction of more exchange parameters with optimized supercells.

Demonstrates efficiency improvements in supercell selection process.

Abstract

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.