Exchange distortion and spin Jahn-Teller effect for triangular and   tetrahedral spin clusters of spin-1/2
  We study the effects of magneto-elastic coupling on the degenerate ground state of the antiferromagnetic Heisenberg model on regular triangle and tetrahedron clusters of spin-1/2. Both give very similar results. Static distortion lifts the degeneracy of the ground state through the distance dependence of the exchange coupling. On the contrary, quantum-mechanical or dynamical distortion does not. The tetragonal distortion at the non-magnetic phase transition of spinels is discussed. 
Kiyosi Terao and Ikumi Honda