Highly tunable magnetic spirals and electric polarization in Gd$_{0.5}$Dy$_{0.5}$MnO$_3$

Recent progress in the field of multiferroics led to the discovery of many new materials in which ferroelectricity is induced by cycloidal spiral orders. The direction of the electric polarization is typically constrained by spin anisotropies and magnetic field. Here, we report that the mixed rare-earth manganite, Gd$_{0.5}$Dy$_{0.5}$MnO$_3$, exhibits a spontaneous electric polarization along a general direction in the crystallographic ac-plane, which is suppressed below 10 K but re-emerges in an applied magnetic field. Neutron diffraction measurements show that the polarization direction results from a large tilt of the spiral plane with respect to the crystallographic axes and that the suppression of ferroelectricity is caused by the transformation of a cycloidal spiral into a helical one, a unique property of this rare-earth manganite. The freedom in the orientation of the spiral plane allows for a fine magnetic control of ferroelectricity, i.e. a rotation as well as a strong enhancement of the polarization depending on the magnetic field direction. We show that this unusual behavior originates from the coupling between the transition metal and rare-earth magnetic subsystems.