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The magnetic structure of multiferroic Ni$_3$V$_2$O$_8$ has been investigatedusing non-resonant X-ray magnetic scattering. Incident circularly polarizedX-rays combined with full polarization analysis of the scattered beam is shownto yield high sensitivity to the components of the cycloidal magnetic order,including their relative phases. New information on the magnetic structure inthe ferroelectric phase is obtained, where it is found that the magneticmoments on the "cross-tie" sites are quenched relative to those on the "spine"sites. This implies that the onset of ferroelectricity is associated mainlywith spine site magnetic order. We also demonstrate that our technique enablesthe imaging of multiferroic domains through polarization enhanced topography.This approach is used to image the domains as the sample is cycled by anelectric field through its hysteresis loop, revealing the gradual switching ofdomains without nucleation.

Electric field control of multiferroic domains in Ni$_3$V$_2$O$_8$ imaged by X-ray polarization enhanced topography