Two-sublattice uniaxial systems with strong antisymmetric exchange: A model for some hexagonal ferrites

We solve rigorously the equilibrium equations for a system of two classical magnetic moments in a transverse field, coupled by Dzialoshinskii antisymmetric exchange, as well as isotropic and anisotropic exchange, in the presence of uniaxial second order anisotropy, whose easy axis is parallel to the Dzialoshinskii D vector. The system allows for planar, axial and conical phases (the latter were never reported before). In all the possible phases the equilibrium equations allow for an exact solution, without introducing any approximation steaming from the assumption of some definite hierarchy of the interaction strengths. We discuss the application of this model to the low field-low temperature transverse magnetization curves reported for some diamagnetically substituted hexagonal ferrites, paying special attention to the conical phases.