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We report a giant linear magnetoelectric coupling in strained BiMnO3 thinfilms in which the disorder associated with an islanded morphology gives riseto extrinsic relaxor ferroelectricity that is not present in bulkcentrosymmetric ferromagnetic crystalline BiMnO3. Strain associated with thedisorder is treated as a local variable which couples to the two ferroic orderparameters, magnetization M and polarization P. A straightforward "gas under apiston" thermodynamic treatment explains the observed correlated temperaturedependencies of the product of susceptibilities and the magnetoelectriccoefficient together with the enhancement of the coupling by the proximity ofthe ferroic transition temperatures close to the relaxor freezing temperature.Our interpretation is based on a trilinear coupling term in the free energy ofthe form L(PXM) where L is a hidden antiferromagnetic order parameter,previously postulated by theory for BiMnO3. This phenomenological invariant notonly preserves inversion and time reversal symmetry of the strain-inducedinteractions but also explains the pronounced linear magnetoelectric couplingwithout using the more conventional higher order biquadratic interactionproportional to (PM)^2.

Proximate transition temperatures amplify linear magnetoelectric coupling in strain-disordered multiferroic BiMnO3