Unexpected Precursor Effects to the Structural Phase Transition in EuTiO₃

Abstract

Abstract. The dynamical properties of EuTiO 3 are investigated to gain insight into its precursor effects analogous to those observed in many other perovskite oxides. In spite of the fact that a competition between the long wave length transverse optic mode and the zone boundary 63.70.+h,In view of the fact that EuTiO 3 (ETO) has been discovered more than 60 years ago, [1] its dynamical, structural, and magnetic properties are much less investigated as compared to, for example, SrTiO 3 , BaTiO 3 , PbTiO 3 and related systems. It is, however, well established that ETO exhibits a G-type antiferromagnetic (AFM) order below T N = 5.5 K. Results and Discussion[2] In addition, strong magneto-electric coupling has been established at low temperatures, [3] accompanied by the softening of a transverse optic mode. [4,5] The structure was believed to be cubic at all temperatures until recently, when a detailed experimental and theoretical study showed that a structural phase transition to a low temperature tetragonal phase takes place at T S = 282 K. [6] From an analysis of the dynamics of this instability, it became apparent that it is analogous to the one in SrTiO 3 (STO) at T S = 105 K, namely, it is driven by the condensation of a zone boundary transverse acoustic mode, [7] which has been quickly confirmed after this prediction.[8] The transition temperature itself remained a matter of controversy since different groups reported different values ranging from as low as 160 [9] to 245 [10] and even to 308 K. [11] In addition, structural modulations below T S have been implicitly deduced in the synchrotron radiation study, [10] but have been claimed to be absent in another structural study.[12] Theoretically, first principles density functional calculations [7,13] arrived at the conclusion that the structure below T S must be distorted due to rotations of TiO 6 octahedra. The very close energetic proximity of different rotational possibilities left some ambiguity in clearly deciding which structural distortion corresponds to the lowest energy state. In addition, various work was done within a Landau free energy expansion, [14][15][16] in which coupling of various order parameters was included. These studies suggested that an AFM order might change to a FM order under strain, and indicated the possibility for simultaneous ferroelectric order. For solid solutions (ETO) 1-x (STO) x , it was proposed that a ferrimagnetic order is followed by ferromagnetism. Experimentally this could not be confirmed. Instead, it was found that AFM order remains robust for all doping levels [17] and is even stabilized under pressure. [18] In the present study we focus on the high temperature phase transition of ETO. This transition appears to be displacive and second order in nature according to its zone boundary transverse acoustic mode. [7,8] For the related one of STO, similar conclusions were drawn, [19] but soon this was questioned since substantial order/disorder dynamics precede the transition. [20] More recently, results from birefring...

Pressure-temperature phase diagram of multiferroicEuTiO3

“…Moreover, according to DFT+U calculations 6,32 , the octahedral rotations are also affected by the hybridization of Eu 4f states with Ti 3d states, which is strong in EuTiO 3 and absent in SrTiO 3 . The coupling between Eu 4f states and Ti 3d electrons is very sensitive to local breaking of symmetry and therefore the octahedral tilts will change the covalent bonding strength between Eu and O ions 42 , making the tetragonal lattice the most favourable energy state.…”

Structural and magnetic phase transitions inEuTi1−xNbxO3

“…tetragonal twinning segments form along three crystallographic orientations. This unexpected precursor effect in ETO has been analyzed by normalizing the transverse modes and taking the derivatives of the modes with respect to momentum, yielding the softening of the transverse acoustic mode as a function of temperature [33]. The coupling between the TA mode and the elastic constants gives rise to the elastic softening as the SPT is approached.…”

Pressure-Temperature phase diagram of multiferroic EuTiO$_3$

“…Moreover, according to DFT+U calculations 6,32 , the octahedral rotations are also affected by the hybridization of Eu 4f states with Ti 3d states, which is strong in EuTiO 3 and absent in SrTiO 3 . The coupling between Eu 4f states and Ti 3d electrons is very sensitive to local breaking of symmetry and therefore the octahedral tilts will change the covalent bonding strength between Eu and O ions 42 , making the tetragonal lattice the most favourable energy state.…”