Multiferroic materials (in which electric and magnetic order coexist) that also display magneto-electric
coupling have recently raised considerable interest as candidate compounds for advanced
applications in electronics and data storage. In particular, the magneto-electric coupling is relevant
in those materials such as TbMnO3 and Ni3V2O8 in which the onset of a cycloidal magnetic order
drives the formation of a ferroelectric state. A key feature in these compounds is the possibility to
control the population of magnetic domains (de�fined by the handedness of the cycloids) by an in situ
electric fi�eld.
The combination of magnetic non-resonant di�ffraction by circularly polarised X-rays with the full
linear polarimetry of the scattered beam opens the way to a new class of experiments, in which the
magnetic order of complex magnetic materials under applied electric and magnetic �fields is probed.
This technique brings a strong experimental sensitivity to the imbalance in the domain populations,
since the handedness of the circular polarisation naturally couples to the sense of rotation of the
magnetic moments, leading to an accurate description of the domain state and to the re�finement of
the magnetic structure.
The results shed more light on the complex magnetic structure of TbMnO3, a challenging test
case due to its two magnetic sublattices on the Mn and Tb sites, by identifying components of the
ordering on the Tb sublattice and phase shifts that earlier neutron di�ffraction experiments could
not resolve. In the case of Ni3V2O8, the method not only facilitated the refi�nement of the magnetic
structure, but also allowed real space images of the magnetic cycloidal domains to be obtained. Their
evolution is followed as they are controlled via magneto-electric coupling by the applied electric fi�eld
and cycled through a hysteresis loop, thus collecting valuable information on domain formation,
inhomogeneities and domain wall movement
