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Microscopic structural instabilities of EuTiO3 single crystal wereinvestigated by synchrotron x-ray diffraction. Antiferrodistortive (AFD) oxygenoctahedral rotational order was observed alongside Ti derived antiferroelectric(AFE) distortions. The competition between the two instabilities is reconciledthrough a cooperatively modulated structure allowing both to coexist. Theelectric and magnetic field effect on the modulated AFD order shows that theorigin of large magnetoelectric coupling is based upon the dynamic equilibriumbetween the AFD - antiferromagnetic interactions versus the electricpolarization - ferromagnetic interactions.

Emergence of a Dynamic Super-Structural Order Integrating Antiferroelectric and Antiferrodistortive Competing Instabilities in EuTiO3