Crystalline and spin chiralities in multiferroics with langasite-type structure and Fe1–xCoxSi crystals

It is shown that, when magnetic ordering occurs in layered iron-containing langasites (sp. gr. P321), one of the reasons for spin chiralities of different signs is the presence of structural chirality (the existence of inversion twins), which, in turn, is due to the nonsymmetricity of these crystals. Spin helicoids arise in these multiferroics at split sites of Fe3+ ions below the Néel point. The direction of electric polarization vectors coincides with the direction of the magnetic helicoid axes because of the piezoelectric properties of these materials. Due to the magnetostriction effects, structural chirality wave vector kz exceeds the magnetic helicoid wave vector by a factor of 2: kz = 2qz. The temperatures of transitions to the chiral structural and chiral magnetic states may differ. In particular, if the structural transition initial temperature exceeds the magnetic transition temperature (ТU> ТМ), structural displacements may arise in the absence of magnetism at ТМ < Т < ТU. In noncentrosymmetric Fe1–xCoxSi crystals (sp. gr. P213), which are not multiferroics, magnetic chirality is due to the Dzyaloshinski–Moriya interaction. The dependence of the moduli of incommensurate wave number of the corresponding helicoid on the atomic composition of the crystals under consideration is nonmonotonic.