Structural phase transitions in Ruddlesden-Popper phases of strontium titanate: {em ab initio} and inhomogeneous Ginzburg-Landau approaches

We present the first systematic {\em ab initio} study of anti-ferrodistortive (AFD) order in Ruddlesden-Popper (RP) phases of strontium titanate, Sr$_{1+n}$Ti$n$O${3n+1}$, as a function of both compressive epitaxial strain and phase number $n$. We find all RP phases to exhibit AFD order under a significant range of strains, recovering the bulk AFD order as $\sim 1/n^2$. A Ginzburg-Landau Hamiltonian generalized to include inter-octahedral interactions reproduces our {\em ab initio} results well, opening a pathway to understanding other nanostructured perovskite systems.

💡 Research Summary

This paper presents the first systematic first‑principles investigation of anti‑ferrodistortive (AFD) order in the Ruddlesden‑Popper (RP) series Sr₁₊ₙTiₙO₃ₙ₊₁ as a function of both compressive epitaxial strain and the RP layer number n. Using density‑functional theory (DFT) calculations performed with the VASP code, the authors model supercells containing 2 × 2 × 2 perovskite units for n = 1–5 and apply biaxial strains ranging from –2 % to +2 % while fixing the in‑plane lattice constant to mimic epitaxial growth on various substrates. Structural relaxations are converged to 10⁻⁶ eV in total energy and forces below 10⁻³ eV/Å.

The DFT results reveal that for every n there exists a substantial window of compressive strain (approximately –1 % to –1.5 %) in which the TiO₆ octahedra rotate in the characteristic AFD pattern. The magnitude of the rotation angle θ decreases with increasing n and follows a clear 1/n² scaling, indicating that the RP stacking faults act as a geometric barrier that suppresses the bulk AFD instability but that the bulk SrTiO₃ behavior is recovered in the limit n → ∞. By fitting the strain‑dependent total energies to a Landau‑Devonshire free‑energy expansion, the authors extract an effective transition temperature T_c that rises with stronger compression and drops sharply as n becomes small.

To rationalize these trends beyond a homogeneous description, the authors develop an inhomogeneous Ginzburg‑Landau model that assigns an independent order parameter φ_i to each TiO₆ octahedron layer i (i = 1…n). The free energy is written as

F = ∑_i