Related Experiment Video
Updated: Jun 24, 2026

Visualizing Uniaxial-strain Manipulation of Antiferromagnetic Domains in Fe1+YTe Using a Spin-polarized Scanning Tunneling Microscope
Published on: March 24, 2019
Symmetry rules and strain/order-parameter relationships for coupling between octahedral tilting and cooperative
Michael A Carpenter1, Christopher J Howard
1Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ, England. mc43@esc.cam.ac.uk
Abstract:
Space groups, order-parameter and strain/order-parameter coupling relationships in ABX3 perovskite structures which combine cooperative Jahn-Teller distortions and octahedral tilting have been investigated from the perspective of group theory using the computer program ISOTROPY. Two common Jahn-Teller ordering schemes are associated with the irreducible representations M2+ and R3+ of the space group Pm3m. A third, less-common ordering scheme is associated with Gamma3+. These combine with tilting instabilities associated with M3+ and R4+ to generate a predicted suite of Jahn-Teller structure types that includes many of the known structures of manganites, vanadates, Cu and Cr halides. Order-parameter coupling and possible phase transitions are described using Landau free-energy expansions, and general expressions for the relationships between symmetry-adapted spontaneous strains and particular order-parameter components are presented. These provide a general formal framework for determining structural evolution across multi-component order-parameter space and for characterizing the influence of tilting instabilities on Jahn-Teller instabilities or of Jahn-Teller ordering on octahedral tilting.
Related Concept Videos
Crystal Field Theory - Tetrahedral and Square Planar Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
Woodward–Hoffmann Selection Rules and Microscopic Reversibility
Transformation of Plane Strain
Under plane strain conditions, typical for members where one dimension significantly exceeds the others, deformations and resultant strains are...
Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)
The extent of coupling depends on the C‑C bond length, the two H‑C‑C angles, any electron-withdrawing substituents, and the dihedral angle between the involved orbitals. The...
Three-Dimensional Analysis of Strain
Symmetry Elements in a Crystal

