Different critical behaviors in cubic to trigonal and tetragonal perovskites

Understand

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.