[Paper Review] Quantum paraelectricity and structural phase transitions in strontium titanate beyond density-functional theory

Carla Verdi, Luigi Ranalli+2 more|arXiv (Cornell University)|Nov 17, 2022

Ferroelectric and Piezoelectric Materials4 citations

TL;DR

This study develops a machine-learned force field combined with the stochastic self-consistent harmonic approximation (SSCHA) to enable beyond-density-functional theory (beyond-DFT) calculations of temperature-dependent anharmonic and quantum effects in strontium titanate (SrTiO3). It demonstrates that the random phase approximation (RPA) is essential for accurately capturing the soft ferroelectric mode and quantum paraelectric behavior, while standard DFT functionals fail to reproduce experimental phonon frequencies and dielectric response.

ABSTRACT

We demonstrate an approach for calculating temperature-dependent quantum and anharmonic effects with beyond density-functional theory accuracy. By combining machine-learned potentials and the stochastic self-consistent harmonic approximation, we investigate the cubic to tetragonal transition in strontium titanate and show that the paraelectric phase is stabilized by anharmonic quantum fluctuations. We find that a quantitative understanding of the quantum paraelectric behavior requires a higher-level treatment of electronic correlation effects via the random phase approximation. This approach enables detailed studies of emergent properties in strongly anharmonic materials beyond density-functional theory.

Motivation & Objective

• To develop a general framework for accurately modeling temperature-dependent anharmonic and quantum lattice dynamics in strongly correlated perovskite oxides beyond standard DFT.
• To investigate the origin of quantum paraelectricity in SrTiO3, particularly the role of anharmonic quantum fluctuations in stabilizing the paraelectric phase.
• To assess the accuracy of various electronic structure functionals—especially PBEsol, rSCAN, HSE06, and RPA—in describing the ferroelectric soft mode and its temperature dependence.
• To determine whether beyond-DFT methods like RPA are necessary to correctly describe the energy landscape and phase transition in quantum paraelectrics.
• To establish a reliable computational protocol for studying emergent quantum phenomena such as quantum criticality and dilute superconductivity in complex oxides.

Proposed method

• Employ machine-learned interatomic potentials (MLFFs) trained on RPA-calculated forces using Δ-machine learning to achieve first-principles accuracy.
• Apply the stochastic self-consistent harmonic approximation (SSCHA) to non-perturbatively treat anharmonic lattice dynamics and calculate temperature-dependent phonon frequencies.
• Use the RPA-level MLFF to compute the free energy landscape and identify the stability of the cubic and tetragonal phases in SrTiO3.
• Perform finite-temperature calculations to capture the renormalization of phonon modes, lattice parameters, and internal degrees of freedom due to anharmonicity.
• Compare results from different exchange-correlation functionals (PBEsol, rSCAN, HSE06, RPA) to isolate the role of electronic correlation in soft mode behavior.
• Analyze the dielectric function and energy splitting of E_u and A_2u modes to validate against experimental data on quantum critical scaling and mode softening.

Experimental results

Research questions

• RQ1 Can beyond-DFT methods accurately describe the temperature-dependent softening of the ferroelectric mode in SrTiO3, which is central to its quantum paraelectric behavior?
• RQ2 Why do standard DFT functionals such as PBEsol and rSCAN fail to reproduce the experimentally observed soft mode frequencies and their temperature dependence?
• RQ3 To what extent does the random phase approximation (RPA) improve the description of the ferroelectric instability and anharmonic lattice dynamics compared to semilocal functionals?
• RQ4 How do anharmonic lattice distortions and quantum fluctuations collectively stabilize the paraelectric phase in SrTiO3?
• RQ5 Is the RPA sufficient to describe the AFD transition temperature, or are higher-level correlation effects required to correct for its tendency to overestimate bond lengths and volumes?

Key findings

• The RPA-based MLFF accurately reproduces the experimentally observed plateau in the ferroelectric soft mode frequency below ~25 K and its subsequent increase with temperature.
• Standard semilocal functionals (PBEsol, rSCAN) and hybrid functionals (HSE06) significantly overestimate the ferroelectric mode frequency, predicting values too hard by 8–10 meV at 0 K.
• The RPA correctly captures the energy splitting between the E_u and A_2u ferroelectric modes, which is governed by anharmonic relaxation of the c/a ratio.
• Anharmonic lattice expansion, when included via rSCAN, reduces the ferroelectric mode frequency by only ~2 meV, indicating that the main failure of DFT lies in electronic correlation, not lattice dynamics.
• The RPA predicts a transition temperature for the antiferrodistortive (AFD) transition that is too high, suggesting that even beyond-RPA methods are needed to correct for systematic underbinding.
• The study establishes that the RPA is essential for modeling quantum critical effects in SrTiO3, as it reproduces the quantum critical scaling of the dielectric function observed experimentally.