The influence of an external static magnetic field (up to 480 mT)on the structural properties of EuTiO$_3$ (ETO) polycrystalline samples was examined by powder XRD at the Elettra synchrotron facilities in the temperature range 100-300K. While the cubic to tetragonal structural phase transition temperature in this magnetic field range remains almost unaffected, significant lattice effects appear at two characteristic temperatures (~200K and 250K), which becomes more pronounced at a critical threshold magnetic field. At ~200K a change in the sign of the magnetostriction is detected attributed to a modification of the local magnetic properties from intrinsic ferromagnetism to intrinsic antiferromagnetism. These data are a clear indication that strong spin-lattice interactions govern also the high temperature phase of ETO and trigger the appearance of magnetic domain formation and novel phase transitions
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