Microscopic theory of Dzyaloshinskii–Moriya coupling and related exchange-relativistic effects

•We overview the microscopic theory of Dzyaloshinskii–Moriya (DM) coupling.•We consider the direction and sense of the Dzyaloshinskii vector.•We discuss the dependence of the Dzyaloshinskii vector on the superexchange geometry.•We consider the effective symmetric spin anisotropy due to DM coupling.•We discuss related exchange-relativistic effects.

I present a short overview of the results of the microscopic theory of the Dzyaloshinskii–Moriya coupling and other related exchange-relativistic effects such as exchange anisotropy, antisymmetric magnetoelectric coupling, antisymmetric magnetogyrotropic effects, and electron-nuclear antisymmetric supertransferred hyperfine interactions in strongly correlated 3d compounds.