Different critical behaviors in cubic to trigonal and tetragonal perovskites

TL;DR

This paper investigates the critical behaviors of cubic to trigonal and tetragonal phase transitions in perovskites, revealing universal features and crossover phenomena through renormalization group analysis and proposing experimental tests.

Contribution

It provides a theoretical framework connecting different critical behaviors to renormalization group fixed points and predicts crossover effects in effective critical exponents.

Findings

Crossover of effective exponents from Ising to cubic in trigonal transitions

Isotropic critical exponents can persist over wide temperature ranges in tetragonal transitions

Renormalization group calculations estimate effective exponents near the isotropic fixed point

Abstract

Perovskites like LaAlO3 (or SrTiO3) undergo displacive structural phase transitions from a cubic crystal to a trigonal (or tetragonal) structure. For many years, the critical exponents in both these types of transitions have been fitted to those of the isotropic three-components Heisenberg model. However, field theoretical calculations showed that the isotropic fixed point of the renormalization group is unstable, and renormalization group iterations flow either to a cubic fixed point or to a fluctuation-driven first-order transition. Here we show that these two scenarios correspond to the cubic to trigonal and to the cubic to tetragonal transitions, respectively. In both cases, the critical behavior is described by slowly varying effective critical exponents, which exhibit universal features. For the trigonal case, we predict a crossover of the effective exponents from their Ising values to their cubic values (which are close to the isotropic ones). For the tetragonal case, the effective exponents can have the isotropic values over a wide temperature range, before exhibiting large changes en route to the first-order transition. New renormalization group calculations near the isotropic fixed point in three dimensions are presented and used to estimate the effective exponents, and dedicated experiments to test these predictions are proposed. Similar predictions apply to cubic magnetic and ferroelectric systems.