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.