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

Abstract

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. *

Microscopic description of twisted magnet Cu2OSeO3

“…If the magnetic moment density changes slowly along the crystal, a transition can be performed from discrete spins to smooth continuous spin functions s r ( ) î , whose number coincides with the number of magnetic atoms in the crystal unit cell. Then, the magnetic energy can be rewritten in integral form [29] …”

“…on observation of forbidden Bragg reflections of antiferromagnetic origin [25]. twist in ferromagnets [26,29]. In fact, the local canting of antiferromagnetic nature is the part of the spin tilts, which is additional to the global spiralling.…”

Chirality of structure and magnetism in the magnetoelectric compound <span class="aps-inline-formula"><math><msub><mi>Cu</mi><mn>2</mn></msub><msub><mi>OSeO</mi><mn>3</mn></msub></math></span>

“…Alternatively, the effect of next-nearest neighbors and outer shells on the sign of the DMI was suggest in the theoretical analysis of Ref. [11].…”

“…There, a multishell Heisenberg-like model was implemented for calculating the expected sign of the DMI based on the chirality of the crystal structure [11]. The expectations of the model successfully describe the relationship between the two chiralities for MnSi observed experimentally (Table III) [11,32] yet predicts the opposite chiral interrelation for the case of Cu 2 OSeO 3 ; the right-handed structure is expected to conjugate with the left-handed magnetic helix [32]. The experimental findings reported here show that this conjecture does not meet reality and so calls for a theoretical revision.…”

Antiferromagnetic spin cantings as a driving force of ferroelectricity in multiferroic Cu2OSeO3

“…Because the electric polarization is an additive vector, we can consider only one of the equivalent bonds within the unit cell. In order to calculate the spins, we will replace the discrete magnetic moments by continuous spin fields [17,31]. So, the polarization will also be a continuous function of the spatial coordinates.…”