Influence of vacancy type defects on the exchange integrals in ferromagnetic metals: a Monte-Carlo-based approach

Estimating exchange interactions in real systems, particularly with defects like vacancies and impurities, poses significant challenges. A classical Monte-Carlo spin simulation within an atomistic machine-learning framework is utilized to predict the pairwise exchange interactions in ideal and defective bcc Fe and fcc Ni systems. The results closely replicate the experimental Curie temperature, with a reduction in exchange interaction by ∼1 meV for the system with cluster vacancy concentration up to 6%. An exponential relationship is established between the classical rescaling parameter <?CDATA α?> α and microscopic exchange interaction enhancing <?CDATA α?> α up to 3.35 and 2.5 in Fe and Ni, respectively. Additionally, the spin wave stiffness constant calculated using the near neighbor Heisenberg model demonstrates a dampening in both Fe and Ni with the inclusion of cluster vacancies.