Unexpected long-range ferromagnetic coupling in MnBi

Ferromagnetism in MnBi is commonly attributed to long-range exchange interaction that extends to the sixth nearest neighbors around Mn atoms. In this study, we demonstrate that the exchange interaction in MnBi persists far beyond the known range with significant coupling between Mn atoms separated by more than 9 Å, corresponding to the eleventh nearest neighbors. Density functional theory calculations show that while direct Mn-Mn pairs at this separation exhibit negligible exchange coupling (0.24 meV), indirect Mn-Mn pairs bridged by Bi-2Mn-Bi chains yield a much stronger interaction of 2.21 meV. This unusually long-range exchange originates from multistep ferromagnetic superexchange interaction which is mediated by intermediate Bi and Mn atoms along the body diagonal. Atomistic spin dynamics simulations further reveal that the extended couplings play a decisive role in correctly reproducing the appropriate Curie temperature (600.7 K). These findings provide a key insight into the long-range exchange interaction in MnBi and establish its close connection to the crystal structure.