Anisotropic interactions in magnetic crystals with S-state ions. Nanostructures

Anisotropy mechanisms in compounds with S-state ions are discussed, including the ‘single-ion’ exchange mechanism that was developed theoretically by Nikiforov and coworkers based on the two-ion model and which has only recently received detailed experimental study. Results demonstrating the significant role of the ‘single-ion’ source are presented. An independent generalized method for quantitatively describing and predicting the anisotropy of magnetically ordered crystals is discussed, and its potential for the investigation of the BiFeO$_3$ multiferroic in the region of the existence of a spin cycloid is examined. The anisotropic interactions responsible for the formation of nanostructures in the form of spin vortices (skyrmions) in MnSi and Cu$_2$OSeO$_3$ are analyzed.