  We have elucidated the spin, lattice, charge and orbital coupling mechanism
underlying the multiferroic character in tensile strained EuTiO3 films.
Symmetry determined by oxygen octahedral tilting shapes the hybridization
between the Eu 4f and Ti 3d orbitals and this inhibits predicted Ti
displacement proper ferroelectricity. Instead, phonon softening emerges at low
temperatures within the pseudo-cube (110) plane, orthogonal to the anticipated
ferroelectric polarization symmetry. Additionally, the magnetic anisotropy is
determined by orbital distortion through hybridization between the Ti 3d and
typically isotropic Eu2+ 4f. This unique scenario demonstrates the critical
role symmetry plays in the coupling of order parameters defining multiferroic
behaviour.
