Determining the Heisenberg exchange interaction is fundamental for performing the atomistic spin dynamics and micromagnetic simulations of magnetic materials. Usually, the exchange integrals Jij used to describe the interaction of spins in the Heisenberg model, are estimated from ab initio calculations performed for the bulk. One method to calculate the Jij is to apply the Korringa-Kohn-Rostoker (KKR)-Green’s function formalism by considering the rotation of two spin moments at sites i and j with opposite angles and calculating the total energy variation [1]. This method readily provides the magnetic exchange interaction within the muffin-tin or atomic sphere approximation for metals, as well as for binary alloys through KKR-CPA scheme [2]. Another method is to use the frozen-magnon approach by calculating the total energy for a spiral magnetic configuration [3]. Both methods are formally equivalent and complementary to each other [4]. Within the framework of frozen-magnon approximation, the magnetic configuration is constrained to a spin spiral with the wave vector q and the spin-wave energy E (q) is calculated. Then, the exchange parameters Jij are obtained by Fourier transformation. These two approaches, however, are difficult to implement in multilayered systems or nanomagnets in order to estimate the exchange interactions at the interfaces. Here we propose a basic approach to determine the Jij for which is independent of the implementation of the ab initio method used to calculate the total energy of a magnetic structure. It is based on mapping the Heisenberg Hamiltonian to a selected set of antiferromagnetic configurations modeled by supercells. We performed the supercell calculations by using the Vienna Ab initio Simulation Package (VASP) [5].

[1] Liechtenstein et al., J. Magn. Magn. Mater., 67 (1987), 65.
[2] Faulkner et al., Phys. Rev. B, 21 (1980), 3222.
[3] Rosengaard et al., Phys.Rev. B, 55 (1997), 14975.
[4] Pajda et al., Phys. Rev. B, 64 (2001), 174402.
[5] Kresse et al., Phys. Rev. B, 54 (1996), 11169.