Using a first-principles approach based on density functional theory and dynamical mean field theory, we study the electronic properties of a new candidate polar metal SrEuMo$_2$O$_6$. Its electronic structure shares similarities with centrosymmetric
SrMoO$_3$ and EuMoO$_3$, from which it may be considered an ordered derivative, but ferroelectric-like distortions of the divalent cations and oxygen anions lift inversion symmetry mediated by an anharmonic lattice interaction in the metallic state. We find that Hunds coupling promotes the effects of electronic correlations owing to the Mo$^{4+}$ $d^{2}$ electronic configuration, producing a correlated metallic phase far from the Mott state. The contraindication between metallicity and polar distortions is thereby alleviated through the renormalized quasiparticles, which are unable to fully screen the ordered local dipoles.
The effect of octahedral tilting on the acentric structural transitions in AGaO$_{3}$/AGaO$_{3}$ [001], [110], and [111] superlattices (A, A = La, Pr, Nd) is studied using density functional theory. We find the displacive transitions are driven by tw
o octahedral rotations modes (a$^{-}$a$^{-}$c$^{0}$ and a$^{0}$a$^{0}$c$^{+}$ tilting), with amplitudes that depend on the A and A chemistry and cation ordering direction. We find the ground states structures of the [001] and [111] ordered superlattices are polar. The coupling of octahedral tilting modes through a hybrid improper ferroelectric mechanism induces the polar displacements and produces the macroscopic electric polarizations.
High-temperature electronic materials are in constant demand as the required operational range for various industries increases. Here we design $(A,A^prime)B_2$O$_6$ perovskite oxides with [111] ``rock salt $A$-site cation order and predict them to b
e potential high-temperature piezoelectric materials. By selecting bulk perovskites which have a tendency towards only out-of-phase $B$O$_6$ rotations, we avoid possible staggered ferroelectric to paraelectric phase transitions while also retaining non-centrosymmetric crystal structures necessary for ferro- and piezoelectricity. Using density functional theory calculations, we show that (La,Pr)Al$_2$O$_6$ and (Ce,Pr)Al$_2$O$_6$ display spontaneous polarizations in their polar ground state structures; we also compute the dielectric and piezoelectric constants for each phase. Additionally, we predict the critical phase transition temperatures for each material from first-principles to demonstrate that the piezoelectric responses, which are comparable to traditional lead-free piezoelectrics, should persist to high temperature. These features make the rock salt $A$-site ordered aluminates candidates for high-temperature sensors, actuators, or other electronic devices.
Nuclear site analysis methods are used to enumerate the normal modes of $ABX_{3}$ perovskite polymorphs with octahedral rotations. We provide the modes of the fourteen subgroups of the cubic aristotype describing the Glazer octahedral tilt patterns,
which are obtained from rotations of the $BX_{6}$ octahedra with different sense and amplitude about high symmetry axes. We tabulate all normal modes of each tilt system and specify the contribution of each atomic species to the mode displacement pattern, elucidating the physical meaning of the symmetry unique modes. We have systematically generated 705 schematic atomic displacement patterns for the normal modes of all 15 (14 rotated + 1 unrotated) Glazer tilt systems. We show through some illustrative examples how to use these tables to identify the octahedral rotations, symmetric breathing, and first-order Jahn-Teller anti-symmetric breathing distortions of the $BX_{6}$ octahedra, and the associated Raman selection rules. We anticipate that these tables and schematics will be useful in understanding the lattice dynamics of bulk perovskites and would serve as reference point in elucidating the atomic origin of a wide range of physical properties in synthetic perovskite thin films and superlattices.
