Linear response theories for interatomic exchange interactions

The purpose of this review is to elaborate basic ideas of the linear response theories for the exchange interactions as well as more resent developments. The special attention is paid to the approximations underlying the original method in comparison with its more recent and more rigorous extensions, the roles of the on-site Coulomb interactions and the ligand states, and calculations of antisymmetric Dzyaloshinskii-Moriya interactions, which can be performed alongside with the isotropic exchange, within one computational scheme. The abilities of the linear response theories as well as many theoretical nuances, which may arise in the analysis of interatomic exchange interactions, are illustrated on magnetic van der Walls materials CrX3 (X= Cl, I), half-metallic ferromagnet CrO2, ferromagnetic Weyl semimetal Co3Sn2S2, and orthorhombic manganites AMnO3 (A= La, Ho), known for the peculiar interplay of the lattice distortion, spin, and orbital ordering.