Microscopic description of twisted magnetic Cu2OSeO3

Twisted structures of chiral cubic ferromagnetics MnSi and Cu$_2$OSeO$_3$ can be described both in the frame of the phenomenological Ginzburg-Landau theory and using the microscopical Heisenberg formalism with a chirality brought in by the Dzyaloshinskii-Moriya (DM) interaction. Recent progress in quantum first-principal methods allows to calculate interatomic bond parameters of the Heisenberg model, namely, isotropic exchange constants $J_{ij}$ and DM vectors $\mathbf{D}_{ij}$, which can be used for simulations of observed magnetic textures and comparison of their calculated characteristics, such as magnetic helix sense and pitch, with the experimental data. In the present work, it is found that unaveraged microscopical details of the spin structures (the local canting) have a strong impact on the global twist and can notably change the helix propagation number. Coefficients ${\cal J}$ and ${\cal D}$ of the phenomenological theory and helix propagation number $k={\cal D}/2{\cal J}$ are derived from interatomic parameters $J_{ij}$ and $\mathbf{D}_{ij}$ of individual bonds for MnSi and Cu$_2$OSeO$_3$ crystals and similar cubic magnetics with almost collinear spins.