  Magneto-electric multiferroics exemplified by TbMnO3 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 use an electric field to produce a single magnetic domain state,
and a magnetic field to induce ionic displacements. Under these conditions,
interference charge-magnetic X-ray scattering arises, 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 significant contribution to the zero-field
ferroelectric moment.
