The spiral magnetic order in cubic MnSi-type crystals is considered using the model of classical Heisenberg ferromagnetics with an extra interaction of the Dzyaloshinskii-Moriya (DM) type between neighboring atoms. It is found how the wave vector of magnetic helices depends on DM vector. The wave number k determines both the sign and strength of global spiraling whereas locally, within a unit cell, the helical order can be strongly frustrated so that the twist angles between neighboring ferromagnetic layers may be even of different signs. Conical deformations of helices caused by an arbitrary directed external magnetic field is also considered within the same model. The critical field of helix unwinding is found and it is shown that even in the unwound state there remains a residual periodic splay of magnetic moments which can be measured by diffraction methods. It is also demonstrated how the usually used continuous picture of moment distribution can be obtained from the discrete one in a coarse grain approximation.Comment: 22 pages, 2 figure

A symmetry analysis of the Dzyaloshinskii-Moriya (DM) interaction in MnSi-type crystals reveals a nontrivial antiferromagnetic pattern of tilted Mn moments remaining even after an unwinding of the ground-state helix by a strong magnetic field. The remaining tilts are caused by that component of the DM vector which is perpendicular to the component responsible for helical spiraling; both components are evaluated and related to the atomic structure using a simple model. It is shown that the tilting should induce pure magnetic reflections 00ℓ(ℓ=2n+1) in neutron or x-ray magnetic scattering. In addition, the DM-induced antiferromagnetic ordering is important for the core structure of intrinsic defects, for the spectra of magnetic resonances, and generally for a better understanding of spin-orbit interaction in this type of magnetics.

a b s t r a c tTwisted structures of chiral cubic ferromagnets 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 arising from the Dzyaloshinskii-Moriya (DM) interaction. Recent progress in quantum firstprincipal methods allows us to calculate interatomic bond parameters of the Heisenberg model, namely isotropic exchange constants J ij and DM vectors 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 an experimental data. In the present work, it is found that unaveraged microscopical details of the spin structures (local canting) have a strong impact on the global twist and can significantly change the helix propagation number. Coefficients and of the phenomenological theory and helix propagation number k /2 = are derived from interatomic parameters J ij and D ij of individual bonds for MnSi and Cu 2 OSeO 3 crystals and similar cubic magnets with almost collinear spins.

The transition from the microscopic Heisenberg model to the macroscopic elastic theory is carried out for the chiral magnetics of MnSi-type with the 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 the Mn1−xFexGe crystals. PACS numbers: 75.25.-j, 75.10.Hk I. INTRODUCTIONChiral spin textures are studied now very actively for possible spin self-organization, unusual quantum transport phenomena and spintronic applications. A well established mechanism of spin chirality is the spin-orbit Dzyaloshinskii-Moriya (DM) interaction which is responsible for intricate magnetic patterns in the MnSi-type crystals. Even half a century after the discovery of the strange magnetic properties of MnSi [1,2], the magnetics with the B20 crystal structure still amaze us with the variety and complexity of their magnetic phases and electronic properties [3] contrasting the simplicity of the crystalline arrangement (only four magnetic atoms per a unit cell). Among the magnetic phases, both experimentally observed and hypothetical, are simple and cone helices [4,5], the Skyrmions and their lattices associated with the recently found A-phase [6-9], possible 3D structures [10-12] similar to the blue phases of liquid crystals, etc. This variety is due to, first, the lack of inverse and mirror symmetries, which gives rise to the chirality of the crystalline and spin structures; second, the frustrations [13,14] resulting from nontrivial topology of the trillium lattice, that introduces a competition of various interactions between different pairs of atoms.Beginning from the discovery of the chiral magnetic properties of MnSi in 1976 [4, 5] till present day the most used approach to describe and predict twisted magnetic structures remains the phenomenological theory based on the Ginsburg-Landau free energy with an additional term first introduced by Dzyaloshinskii [10,11,[15][16][17]. However, the approach, which uses our knowledge of the system symmetry, is not able to say anything about the values of coefficients in the free energy, for instance, how they are connected with the real interactions between atoms. *

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