Effect of non-Heisenberg magnetic interactions on defects in ferromagnetic iron

Fundamental flaws in the Heisenberg Hamiltonian are highlighted in the context of its application to bcc Fe, including the particular issues arising when modeling lattice defects using spin dynamics. Exchange integrals are evaluated using the magnetic force theorem. The bilinear exchange coupling constants are calculated for all the interacting pairs of atomic magnetic moments in large simulation cells containing defects, enabling a direct mapping of the magnetic energy onto the Heisenberg Hamiltonian and revealing its limitations. We provide a simple procedure for extracting the Landau parameters from density-functional theory calculations to construct a Heisenberg-Landau Hamiltonian. We quantitatively show how the Landau terms correct the exchange-energy hypersurface, which is essential for the accurate evaluation of energies and migration barriers of defects.