Orbital Ordering — Cooperative Jahn-Teller
eg Orbital Patterns · Q₂/Q₃ Distortion Modes · Orbital-Lattice Coupling
Parameters
JT coupling g (eV/Å):
0.5
Elastic constant K (eV/Ų):
1.0
Orbital mixing angle θ (°):
0
Temperature T (K):
100
H = g(Q₂σ_x+Q₃σ_z) + K(Q₂²+Q₃²)/2
Optimal: Q_eq = g/K (JT distortion)
E_JT = g²/(2K) (stabilization)
Cooperative: alternating x²-y²/3z²-r²
Mn³⁺ (d⁴, one eg electron) distorts its MnO₆ octahedron via the Jahn-Teller effect. Cooperative ordering of these distortions across the lattice creates the A-type orbital order seen in LaMnO₃.