  Magnetism - the spontaneous alignment of atomic moments in a material - is
driven by quantum-mechanical `exchange' interactions which operate over atomic
distances as a result of the fundamental symmetry of electrons. Currently, one
of the most active fields of condensed matter physics involves the study of
magnetic interactions that cause, or are caused by a twisting of nearby atoms.
This can lead to the magnetoelectric effect that couples electric and magnetic
properties, and is predicted to play a prominent role in future technology.
Here, we discuss the complex relativistic interplay between magnetism and
atomic crystal structure in a class of materials called `weak ferromagnets'.
The sign of the underpinning Dzyaloshinskii--Moriya interaction has been
determined for the first time, by using synchrotron radiation to study iron
borate (FeBO3). We present a novel experimental technique based on interference
between two x-ray scattering processes (one acts as a reference wave) which we
combine with a second unusual approach of turning the atomic antiferromagnetic
motif with a small magnetic field. We show that the experimental results
provide a clear validation of state-of-the-art theoretical calculations. These
experimental and theoretical approaches open up new possibilities for
exploring, modelling and exploiting novel magnetic and magnetoelectric
materials.
