Recent observations of gigantic magnetoelectric and magnetocapacitive effects in rare-earth manganites, TbMnO3 and DyMnO3 [1,2], provide a
novel approach to the mutual control of magnetization and electric polarization in magnetic ferroelectrics. We can control the magnitude and/or direction of the electric polarization vector by the application
of magnetic field in these manganites. In comparing the results from the both manganites, we noticed that a characteristic common to the both
materials is that they possess modulated magnetic structures with long wavelengths (as compared to the chemical unit cell) which arise from
competing magnetic interactions. Ferroelectricity in these materials appears to originate from the competing magnetic interactions which cause lattice modulations through magnetoelastic coupling. We extend our study to other modulated magnets with competing magnetic interactions.
In this talk, I show magnetic control of electric polarization in several modulated magnets , which may provide new route to design magnetoelectrics.
 T. Kimura, T.Goto, H. Shintani, K. Ishizaka, T. Arima, and Y.
Tokura, Nature 426, 55 (2003).
 T. Goto, T. Kimura, G. Lawes, A. P. Ramirez, and Y. Tokura, Phys.
Rev. Lett. 92, 257201 (2004).
 T. Kimura, G. Lawes, and A. P. Ramirez, Phys. Rev. Lett. (in press).