The origin of electromagnon excitations in cycloidal textit{R}MnO$_3$ is explained in terms of the Heisenberg coupling between spins despite the fact that the static polarization arises from the much weaker Dzyaloshinskii-Moriya (DM) exchange interac
tion. We present a model that incorporates structural characteristics of this family of manganites that is confirmed by far infrared transmission data as a function of temperature and magnetic field and inelastic neutron scattering results. A deep connection is found between the magnetoelectric dynamics of the spiral phase and the static magnetoelectric coupling in the collinear E-phase of this family of manganites.
We observe a seemingly complex magnetic field dependence of dielectric constant of hexagonal YbMnO3 near the spin ordering temperature. After rescaling, the data taken at different temperatures and magnetic fields collapse on a single curve describin
g the sharp anomaly in nonlinear magnetoelectric response at the magnetic transition. We show that this anomaly is a result of the competition between two magnetic phases. The scaling and the shape of the anomaly are explained using the phenomenological Landau description of the competing phases in hexagonal manganites.
Ferroelectric spiral magnets DyMnO3 and TbMnO3 show similar behavior of electric polarization in applied magnetic fields. Studies of the field dependence of lattice modulations on the contrary show a completely different picture. Whereas in TbMnO3 th
e polarization flop from P||c to P||a is accompanied by a sudden change from incommensurate to commensurate wave vector modulation, in DyMnO3 the wave vector varies continuously through the flop transition. This smooth behavior may be related to the giant magnetocapacitive effect observed in DyMnO3.
