We consider theoretically the paramagnetic phases of EuTiO3 that represent configurations created by two sets of microscopic degrees of freedom (m-DOF): positional symmetry breaking due to octahedral rotations and magnetic symmetry breaking due to spin disorder. The effect of these sets of m-DOFs on the electronic structure and properties of the para phases is assessed by considering sufficiently large (super) cells with the required nominal global average symmetry, allowing, however, the local positional and magnetic symmetries to be lowered. We find that tendencies for local symmetry breaking can be monitored by following total energy lowering in mean-field like density functional theory, without recourse for strong correlation effects. While most nominally cubic ABO3 perovskites are known for their symmetry breaking due to the B-atom sublattice, the case of f-electron magnetism in EuTiO3 is associated with A- sublattice symmetry breaking and its coupling to structural distortions. We find that (i) paramagnetic cubic EuTiO3 has an intrinsic tendency for both magnetic and positional symmetry breaking, while paramagnetic tetragonal EuTiO3 has only magnetic symmetry lowering and no noticeable positional symmetry lowering with respect to low-temperature antiferromagnetic tetragonal phase. (ii) Properly modeled paramagnetic tetragonal and cubic EuTiO3 have a nonzero local magnetic moment on each Eu ion, consistent with the experimental observations of local magnetism in the para phases of EuTiO3 significantly above the Neel temperature. Interestingly, (iii) the local positional distortion modes in the short-range ordered para phases are inherited from the long-range ordered low-temperature antiferromagnetic ground state phase.
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