Abstract
Magneto-electric multiferroics exemplified by TbMnO(3) possess both magnetic and ferroelectric long-range order. The magnetic order is mostly understood, whereas the nature of the ferroelectricity has remained more elusive. Competing models proposed to explain the ferroelectricity are associated respectively with charge transfer and ionic displacements. Exploiting the magneto-electric coupling, we used an electric field to produce a single magnetic domain state, and a magnetic field to induce ionic displacements. Under these conditions, interference between charge and magnetic x-ray scattering arose, encoding the amplitude and phase of the displacements. When combined with a theoretical analysis, our data allow us to resolve the ionic displacements at the femtoscale, and show that such displacements make a substantial contribution to the zero-field ferroelectric moment.
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