Dzyaloshinskii – Moriya interaction, epitaxial strains, phase transitions in multiferroics with cycloidal structure

In this paper, we explore magnetic phases and spin reorientation phase transitions (SRPT) in the BiFeO ₃ – like multiferroics. We consider the Dzyaloshinskii – Moriya exchange interaction (DMI) as the principle mechanism responsible for appearance of spin space modulated structures (SSMS) in BiFeO ₃ and focus the peculiar features of the DMI manifestation in single crystals and films. As an example we take a (1 1 0) – oriented BiFeO ₃ film whose thickness is much lower than the period of SSMS ( d_film≪ λ) and construct phase diagram in terms “magnetic field H – perpendicular magnetic anisotropy (PMA) constant κ” accounting the PMA dependence on the strains, where the tensile strains correspond to the situation κ > 0; the compressive strains correspond to the situation κ < 0. Our findings shows that at the condition ( d_film≪ λ) the SSMS modulated along the [0 0 1] axis with spin rotating in a plane (1 1 0) exists as the ground magnetic state in a definite range of the control parameters ( H, ± κ ). We show that magnetic field applied along the normal to the film along with strains leads to the transition into homogeneous magnetic state of the “easy plane” type at κ > 0 and tilted phase at κ < 0. As well as in the single crystals at the positive values κ > 0 phase transition from SSMS into homogeneous “easy plane” phase goes through the cone SSMS whose existence was recently experimentally confirmed [S. Kawachi, et al, Phys. Rev. Mater. 1, 024, 408 (2017)]. We believe that our findings performed for the (1 1 0) BiFeO ₃ film will be of interest for further experimental and theoretical research and the implementations of BiFeO ₃ based technologies.