Different critical behaviors in cubic to trigonal and tetragonal perovskites

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.

arXiv commentNew solutions of the renormalization group recursion relations are added. arXiv admin note: substantial text overlap with arXiv:2107.13971

References in corpus (10)

• Critical Phenomena and Renormalization-Group Theory
• Minimally subtracted six loop renormalization of $O(n)$-symmetric ${\varphi }^4$ theory and critical exponents
• The N-component Ginzburg-Landau Hamiltonian with cubic anisotropy: a six-loop study
• Bootstrapping Heisenberg Magnets and their Cubic Instability
• Anisotropic perturbations in three-dimensional O(N)-symmetric vector models
• Six-loop $\epsilon$ expansion study of three-dimensional $n$-vector model with cubic anisotropy
• Comment on "Bicritical and Tetracritical Phenomena and Scaling Properties of the SO(5) Theory"
• Six-loop beta functions in general scalar theory
• Fractal dimension of critical curves in the $O(n)$-symmetric ${\varphi }^4$-model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY and Heisenberg models
• Interplay between antiferrodistortive, ferroelectric and superconducting instabilities in Sr_{1-x}Ca_{x}$TiO_{3-δ}

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• The puzzle of bicriticality in the XXZ antiferromagnet
• Anomalous Dimensions in Hypercubic Theories
• Bi- and tetracritical phase diagrams in three dimensions
• ${\varphi }^4$ lattice model with cubic symmetry in three dimensions: RG-flow and first order phase transitions
• Cubic ferromagnet and emergent $U(1)$ symmetry on its phase boundary
• Cubic* criticality emerging from a quantum loop model on triangular lattice
• Phonon-induced modification of quantum criticality
• Phase transitions and remnants of fractionalization at finite temperature in the triangular lattice quantum loop model