Ferroelectric, quantum paraelectric or paraelectric? Calculating the evolution from BaTiO$_3$ to SrTiO$_3$ to KTaO$_3$ using a single-particle quantum-mechanical description of the ions

Abstract

We present an inexpensive first-principles approach for describing quantum paraelectricity that combines density functional theory (DFT) treatment of the electronic subsystem with quantum mechanical treatment of the ions through solution of the single-particle Schrödinger equation with the DFT-calculated potential. Using BaTiO3, SrTiO3 and KTaO3 as model systems, we show that the approach can straightforwardly distinguish between ferroelectric, paraelectric and quantum paraelectric materials, based on simple quantities extracted from standard density functional and density functional perturbation theories. We calculate the influence of isotope substitution and strain on the quantum paraelectric behavior, and find that, while complete replacement of oxygen-16 by oxygen-18 has a surprisingly small effect, experimentally accessible strains can induce large changes. Finally, we collect the various choices for the phonon mass that have been introduced in the literature. We identify those that are most physically meaningful by comparing with our results that avoid such a choice through the use of mass-weighted coordinates.

Mesoscopic tunneling in strontium titanate

“…Up to now, the quantum paraelectric regime of SrTiO 3 was believed to be only driven by the soft TO Γ mode [8][9][10][11]. In this picture, the ferroelectric order is aborted due to quantum tunneling between two zero-point energy levels associated with two adjacent titanium-oxygen bonds [see Fig.…”

“…Ferroelectric ordering at low temperature is aborted in SrTiO 3 by zero-point quantum fluctuations [9][10][11]. The large dielectric constant in this state has made SrTiO 3 one of the most widely used substrates for growing oxide heterostructures [12].…”

Finite temperature dielectric properties of KTaO$_3$ from first principles and machine learning: Phonon spectra, Barrett law, strain engineering and electrostriction

“…In the previous section we have shown that our approach of QSCAILD combined with machine-learnt interatomic potentials is able to quite accurately reproduce the quantum behavior of the soft mode frequency and of the dielectric constant at ambient pressure and low temperatures, despite some discrepancies due to the high sensitivity of the dielectric constant close to the quantum critical point. We will now explore the pressure-and temperature-dependent behavior of the dielectric properties around this critical point, towards the transition to a ferroelectric phase, which can be introduced by both by the application of pressure [37] and epitaxial strain [13,24,38].…”

“…One is therefore often limited to use DFT-parametrized phenomenological theories and effective Hamiltonians to calculate temperature dependent phonon spectra and dielectric constants, see e.g. [11][12][13][14][15], However, obtaining quantitative agreement with experimental data has been a challenge due to the large spectrum of anharmonic interactions to be considered. This has been made possible by the development of new methods to calculate temperature dependent phonon anharmonicities, starting from the work of Souvatzis et al [16], who took into account classically averaged thermal displacements to self-consistently compute phonon frequencies at high temperatures (SCAILD).…”