Multishell contribution to the Dzyaloshinskii-Moriya spiraling in MnSi-type crystals

The transition from the microscopic Heisenberg model to the macroscopic elastic theory is carried out for MnSi-type chiral magnetics with $B20$ crystal structure. Both exchange and Dzyaloshinskii-Moriya (DM) interactions are taken into account for the first, second, and third magnetic neighbors. The particular components of the DM vectors of bonds are found, which are responsible for (i) the global magnetic twist and (ii) the canting between four different spin sublattices. A possible mechanism for effective reinforcement of the global magnetic twist is suggested: it is demonstrated that the components of the DM vectors normal to corresponding interatomic bonds become very important for the twisting power. The Ruderman-Kittel-Kasuya-Yosida (RKKY) theory is used for model calculation of exchange parameters. It is found that just the interplay between the exchange parameters of several magnetic shells rather than the signs of DM vectors can be responsible for the concentration-induced reverse of the magnetic chirality recently observed in Mn_1-xFeₓGe crystals.