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The Dzyaloshinskii-Moriya (D-M) spin-orbit interaction is an important coupling mechanism between ferroelectricity and magnetism in multiferroics [1]. Therefore it is interesting to find novel methods for quantitative studies of this interaction including its relation with crystal and electronic structure. Specifically, such methods would allow detailed comparison with available theoretical predictions based on ab initio simulations. After an introductory survey, two examples of recent development will be presented in detail. First, different experimental techniques sensitive to the sign of the D-M interaction are discussed: neutron diffraction, Mössbauer -ray diffraction, and resonant x-ray scattering. In all these cases, the sign can be determined from interference between magnetic and structural scattering (resonant and non-resonant) [2] and can be calculated from the first principles [3]. The techniques discussed have their advantages and drawbacks. Classical examples of antiferromagnets with weak ferromagnetism (FeBO3 and hematite, -Fe2O3) are considered in detail. Recent experimental determination of the D-M sign in FeBO3 using resonant x-ray scattering and comparison of this result with ab initio simulations will be also presented. Another example deals with chiral structures in ferromagnetic and multiferroic materials with the space group P213 (MnSi, Cu2OSeO3, etc.). It is shown how the wave vector and the sign of magnetic helices can be related with the D-M vectors of interatomic bonds [4]. Symmetry analysis of the D-M interaction reveals a non-trivial antiferromagnetic pattern of tilted Mn moments in MnSi remaining even after unwinding of the ground-state helix by the strong magnetic field. It is shown [5] that the tilting can be observed via pure magnetic reflections in neutron or x-ray magnetic scattering. In addition, the D-M-induced antiferromagnetic ordering could be important for the Skyrmion structures, for the spectra of magnetic resonances, and for a better understanding of magnetism-structure interplay in ferroics. This work was supported by the RFBR Grant No. 10-02-00768 and by two projects of the Presidium of the Russian Academy of Sciences: “Thermophysics and Mechanics of Extreme Energy Actions and the Physics of a Strongly Compressed Substance” and “Diffraction of Synchrotron Radiation in Multiferroics and Chiral Magnetics”.

Diffraction methods for detailed studies of the Dzyaloshinskii–Moriya ferroics