  Microscopic structural instabilities of EuTiO3 single crystal were
investigated by synchrotron x-ray diffraction. Antiferrodistortive (AFD) oxygen
octahedral rotational order was observed alongside Ti derived antiferroelectric
(AFE) distortions. The competition between the two instabilities is reconciled
through a cooperatively modulated structure allowing both to coexist. The
electric and magnetic field effect on the modulated AFD order shows that the
origin of large magnetoelectric coupling is based upon the dynamic equilibrium
between the AFD - antiferromagnetic interactions versus the electric
polarization - ferromagnetic interactions.
