Ab-initio calculation of magnetic exchange interactions using the spin-spiral method in VASP: Self-consistent versus magnetic force theorem approaches

Abstract: We present an ab initio investigation of magnetic exchange interactions using the spin-spiral method implemented in the VASP code, with a comparative analysis of the self-consistent (SC) and magnetic force theorem (MFT) approaches. Using representative 3d ferromagnets (Fe, Co, Ni) and Mn-based full Heusler compounds, we compute magnon dispersion relations directly from spin-spiral total energies and extract real-space Heisenberg exchange parameters via Fourier transformation. Curie temperatures are subsequently estimated within both the mean-field and random-phase approximations. The SC spin-spiral calculations yield exchange parameters and magnon spectra in excellent agreement with previous theoretical data, confirming their quantitative reliability across different classes of magnetic systems. In contrast, the MFT approach exhibits systematic quantitative deviations: it overestimates spin-spiral energies and exchange couplings in high-moment systems such as bcc Fe and the Mn-based Heuslers, while underestimating them in low-moment fcc Ni. The magnitude of these discrepancies increases strongly with magnetic moment size, exceeding several hundred percent in the high-moment compounds. These findings underscore the decisive role of self-consistency in accurately determining magnetic exchange parameters and provide practical guidance for future first-principles studies of spin interactions and excitations using the spin-spiral technique.