  Ferroelectricity occurs in crystals with broken spatial inversion symmetry.
In conventional perovskite oxides, concerted ionic displacements within a
three-dimensional network of transition metal-oxygen polyhedra (MOx) manifest
spontaneous polarization. Meanwhile, some two-dimensional networks of MOx can
foster geometric ferroelectricity with magnetism, owing to the distortion of
the polyhedra. Because of the fundamentally different mechanism of
ferroelectricity in a two-dimensional network, one can further challenge an
uncharted mechanism of ferroelectricity in a one-dimensional channel of MOx and
estimate its feasibility. This communication presents ferroelectricity and
coupled ferromagnetism in a one-dimensional FeO4 tetrahedral chain network of a
brownmillerite SrFeO2.5 epitaxial thin film. The result provides a new paradigm
for designing low-dimensional MOx networks, which is expected to benefit the
realization of macroscopic ferro-ordering materials including ferroelectric
ferromagnets.
