Heisenberg exchanges in tetragonal-like BiFeO₃ from first principles

Bismuth ferrite (BiFeO₃, BFO), one of the most well-known multiferroics at room temperature, has generated growing interest in the research community over the past two decades. Understanding the magnetism of BFO is crucial for exploring magnetoelectric coupling effects. Here, we focus on the non-relativistic Heisenberg exchanges, which affect the critical behavior. Compared to the previous works, we calculate the Heisenberg exchanges to the long range of 8.92 Å (the eighth closest shell) to incorporate all the non-negligible interactions. The automated workflow aids the calculations to analyze the spin-lattice of BFO and generate plausible collinear magnetic configurations. Our results indicate that J 5 (0.21 meV) is approximately 1 / 10 of J 4 and the Heisenberg exchanges beyond the fifth nearest neighbor can be neglected in BFO. Further, the electron structures and Heisenberg exchanges of BFO under different epitaxial strains are investigated. The bandgaps and Heisenberg exchanges decrease monotonically as the lattice constant of BFO increases.