A DMI Guide to Magnets Micro-World

Dzyaloshinskii-Moriya interaction, DMI in short, represents an antisymmetric type of magnetic interactions that favour orthogonal orientation spins and competes with Heisenberg exchange. Being introduced to explain weak ferromagnetism antiferromagnets without inversion center between atoms such anisotropic interaction can be used analyze other non-trivial structures technological importance including spin spirals skyrmions. Despite the fact corresponding contribution energy system has a very compact form vector product spins, determination from first-principles electronic structure is challenging methodological technical problem whose solution opens door into fascinating microscopic world complex materials. In this paper we review few methods developed by us for calculating their applications study properties real