Electronic correlations decimate the ferroelectric polarization of multiferroic HoMn2O5

We show that electronic correlations decimate the intrinsic ferroelectric polarization of the recently discovered class of multiferroic manganites RMn$_2$O$_5$, where R is a rare earth element. Such is manifest from {\it ab initio} bandstructure computations that account for the strong local Coulomb interactions between the manganese 3d electrons --the root of magnetism in these materials. When including these the computed electronic, magnetic and lattice structure of multiferroic HoMn$_2$O$_5$ results in an amplitude and direction of polarization that is in accordance with experiment. The microscopic mechanism behind the decimation is a near cancellation of the ionic polarization induced by ferroelectric lattice displacements and the electronic one caused by valence charge redistributions.