A Theory of Ferroelectric Phase Transition in SrTiO$_3$ induced by Isotope Replacement

TL;DR

This paper develops a quantum model explaining the ferroelectric phase transition in SrTiO$_3$ caused by oxygen isotope substitution, reconciling macroscopic dielectric and microscopic lattice measurements.

Contribution

It introduces a 3-state quantum order-disorder model incorporating isotope effects via tunneling frequency, providing a unified explanation of experimental observations.

Findings

Qualitative agreement with dielectric measurements across isotope concentrations

Phase diagram consistent with quantum Monte Carlo simulations

Reconciliation of macroscopic and microscopic experimental results

Abstract

A theory to describe the dielectric anomalies and the ferroelectric phase transition induced by oxygen isotope replacement in SrTiO$_3$ is developed. The proposed model gives consistent explanation between apparently contradictory experimental results on macroscopic dielectric measurements versus microscopic lattice dynamical measurements by neutron scattering studies. The essential feature is described by a 3-state quantum order-disorder system characterizing the degenerated excited states in addition to the ground state of TiO$_6$ cluster. The effect of isotope replacement is taken into account through the tunneling frequency between the excited states. The dielectric properties are analyzed by the mean field approximation (MFA), which gives qualitative agreements with experimental results throughout full range of the isotope concentration.The phase diagram in the temperature-tunneling frequencycoordinate is studied by a QMC method to confirm the qualitative validity of the MFA analysis.