  The incommensurate magnetic structures and phase diagrams of multiferroics
has been explored on the basis of accurate micromagnetic analysis taking into
account the spin flexoelecric interaction (Lifshitz invariant). The objects of
the study are BiFeO_3-like single crystals and epitaxial films grown on the
<111> substrates. The main control parameters are the magnetic field, the
magnetic anisotropy, and the epitaxial strain in the case of films. We predict
novel quasi-cycloidal structures induced by external magnetic field or by
epitaxial strain in the BiFeO_3-films. Phase diagrams representing the regions
of homogeneous magnetic states and incommensurate structures stability are
constructed for the two essential geometries of magnetic field (magnetic field
oriented parallel to the principal crystal axis C_3 and perpendicular to this
direction C_3). It is shown that the direction of applied magnetic field
substantially affects a set of magnetic phases, properties of incommensurate
structures, character of phase transitions. Novel conical type of cycloidal
ordering is revealed during the transition from incommensurate cycloidal
structure into homogeneous magnetic state. Elaborated phase diagrams allow
estimate appropriate combination of control parameters (magnetic field,
magnetic anisotropy, exchange stiffness) required to the destruction of
cycloidal ordering corresponding to the transition into homogeneous structure.
The results show that the magnitude of critical magnetic field suppressing
cycloid is lowered in multiferroics films comparing to single crystals, it can
be also lowered by the selection of orientation of magnetic field. Our results
can be useful for strain engineering of new multiferroic functional materials
on demand.
