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.
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