Local positional and spin symmetry breaking as a source of magnetism and insulation in paramagnetic EuTiO3

We consider theoretically the paramagnetic phases of $\mathrm{EuTi}{\mathrm{O}}_{3}$ that represent configurations created by two sets of microscopic degrees of freedom (m-DOFs): 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-fieldlike density-functional theory, without recourse for strong correlation effects. While most nominally cubic $AB{\mathrm{O}}_{3}$ perovskites are known for their symmetry breaking due to the B-atom sublattice, the case of $f$-electron magnetism in $\mathrm{EuTi}{\mathrm{O}}_{3}$ is associated with $A$-sublattice symmetry breaking and its coupling to structural distortions. We find that (i) paramagnetic $cubic$ $\mathrm{EuTi}{\mathrm{O}}_{3}$ has an intrinsic tendency for both magnetic and positional symmetry breaking, while paramagnetic $tetragonal$ $\mathrm{EuTi}{\mathrm{O}}_{3}$ 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 $\mathrm{EuTi}{\mathrm{O}}_{3}$ have a nonzero local magnetic moment on each Eu ion, consistent with the experimental observations of local magnetism in the para phases of $\mathrm{EuTi}{\mathrm{O}}_{3}$ significantly above the N\'eel 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.