  We report a giant linear magnetoelectric coupling in strained BiMnO3 thin
films in which the disorder associated with an islanded morphology gives rise
to extrinsic relaxor ferroelectricity that is not present in bulk
centrosymmetric ferromagnetic crystalline BiMnO3. Strain associated with the
disorder is treated as a local variable which couples to the two ferroic order
parameters, magnetization M and polarization P. A straightforward "gas under a
piston" thermodynamic treatment explains the observed correlated temperature
dependencies of the product of susceptibilities and the magnetoelectric
coefficient together with the enhancement of the coupling by the proximity of
the ferroic transition temperatures close to the relaxor freezing temperature.
Our interpretation is based on a trilinear coupling term in the free energy of
the form L(PXM) where L is a hidden antiferromagnetic order parameter,
previously postulated by theory for BiMnO3. This phenomenological invariant not
only preserves inversion and time reversal symmetry of the strain-induced
interactions but also explains the pronounced linear magnetoelectric coupling
without using the more conventional higher order biquadratic interaction
proportional to (PM)^2.
