  In multiferroic BiFeO$_3$ a cycloidal antiferromagnetic structure is coupled
to a large electric polarization at room temperature, giving rise to
magnetoelectric functionality that may be exploited in novel multiferroic-based
devices. In this paper, we demonstrate that by substituting samarium for 10% of
the bismuth ions the periodicity of the room temperature cycloid is increased,
and by cooling below $\sim15$ K the magnetic structure tends towards a simple
G-type antiferromagnet, which is fully established at 1.5 K. We show that this
transition results from $f-d$ exchange coupling, which induces a local
anisotropy on the iron magnetic moments that destroys the cycloidal order - a
result of general significance regarding the stability of non-collinear
magnetic structures in the presence of multiple magnetic sublattices.
