Exchange distortion and spin Jahn–Teller effect for triangular and tetrahedral spin clusters of spin

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-. Both give very similar results because of the characteristics of their symmetry. Quantum-mechanical distortion appears through fluctuation of normal modes and the degeneracy of the ground state is not lifted. The tetragonal distortion at the non-magnetic phase transition of vanadium spinels is discussed.