Co-existence of {\it ac} and {\it bc}-cycloidal phases, giant magnetocapacitance and polarization in the multiferroic R$_{0.5}$Dy$_{0.5}$MnO$_3$ (R = Eu and Gd)

In the cycloidal RMnO$_3$ (R = Tb and Dy) multiferroic compounds, the cycloidal spin propagates along the bc plane and polarization appears along c-direction. In the case of GdMnO$_3$, it appears that the cycloidal plane is along the ab plane and the polarization points in the a-direction. In my talk, I will demonstrate the emergence of these two cycloidal ordered phases with temperature and their co-existence from the measurements of pyroelectric current and dielectric properties in mixed rare-earth compounds, Eu$_{0.5}$Dy$_{0.5}$MnO$_3$ and Gd$_{0.5}$Dy$_{0.5}$MnO$_3$. The obtained value of polarization is in the same order of magnitude as in the E-type magnetic multiferroic (HoMnO$_3$). Further, these compound show giant magnetic field enhancement of ferroelectric polarization (up to +150\% in Gd$_{0.5}$Dy$_{0.5}$MnO$_3$) in contrast to TbMnO$_3$ (up to -10\%). Also, the value of magneto-capacitance is nearly twenty times higher than that of TbMnO$_3$. We attribute this high value of polarization and magneto-capacitance to the coexistence of ab and bc cycloidal phases. The isothermal current observed upon change of magnetic field with time, demonstrates giant magnetoelectric coupling for a number of cycle without any training effect.