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Using neutron diffraction, we have studied the magnetic field effect oncharge structures in the charge-ordered multiferroic material LuFe$_2$O$_4$. Anexternal magnetic field is able to change the magnitude and correlation lengthsof the charge valence order even before the magnetic order sets in. Thisaffects the dielectric and ferroelectric properties of the material and inducesa giant magneto-electric effect. Our results suggest that the magneto-electriccoupling in LuFe$_2$O$_4$ is likely due to magnetic field effect on localspins, in clear contrast to the case in most other known multiferroic systemswhere the bulk magnetic order is important.

Magnetic field control of charge structures in the magnetically disordered phase of the multiferroic LuFe$_2$O$_4$