  Magnetoelectric coupling permits a magnetic order parameter to be addressed
electrically or vice versa, and could find use in data storage, field sensors
and actuators. Coupling constants for single phase materials such as chromium
dioxide, boracites and manganites are typically as low as 10^{-12} - 10^{-9}
s/m, e.g. because the polarisations and magnetisations are small. Two phase
multiferroics with strain mediated coupling, such as laminates, composites and
epitaxial nanostructures, are more promising because each phase may be
independently optimised. The resulting magnetoelectric switching can be larger,
e.g. 10^{-8} s/m, but it is not sharp because clean coupling is precluded by
the complexity of the microstructures and concomitant strain fields. Here we
report a giant sharp magnetoelectric effect at a single epitaxial interface
between a 40 nm ferromagnetic stress-sensitive La_{0.67}Sr_{0.33}MnO_3 film,
and a 0.5 mm BaTiO_3 substrate that is ferroelectric, piezoelectric and
ferroelastic. By applying a small electric field (4-10 kV/cm) across the entire
structure, we achieve persistent changes in film magnetisation of up to 65%
near the BaTiO_3 structural phase transition at around 200 K. This represents a
giant magnetoelectric coupling (2.3*10-7 s/m) that arises from strain fields
due to ferroelastic non-180 degree domains whose presence we confirm using
x-ray diffraction. The coupling persists over a wide range of temperatures
including room temperature, and could therefore inspire a range of sensor and
memory applications.
