Quantum Ferroelectric Magnets in Underdoped Manganites

Using the degenerate double exchange Hamiltonian with on-site Coulomb interactions we show that there is an instability towards the displacement of the manganese ion in La_{1-x}Ca_{x}MnO_{3}. The result is a dipole moment due to the charge disproportionation and the lattice distortions that gives rise to the predicted magnetic ferroelectric phase for dopings in between x=4 and x=5. The instability is stabilized by the phonons of the lattice, resulting in a stable configuration of the degrees of freedom of the system.