Quantum distortion caused by magneto-elastic coupling for   antiferromagnetic tetrahedral cluster of spin-1/2
  We study the effects of magneto-elastic coupling on the degenerate ground spin-state of the antiferromagnetic Heisenberg model on a regular tetrahedron of spin-1/2.   When displacement of spin is considered as a classical variable, the degeneracy is lifted through the distance dependence of exchange coupling, i.e., a kind of Jahn-Teller effect.   On the other hand, when displacement is considered as a quantum variable, the degeneracy of the ground spin-state is not lifted although the tetrahedron is distorted by quantum fluctuation caused by magneto-elastic coupling for a component of the normal coordinates of the degenerate mode. We propose a new model for the structural phase transition of vanadium and nickel spinels: the tetragonal distortion is caused by quantum fluctuation and there exists a kind of hidden order with respect to the non-magnetic ground spin-states. 
Ikumi Honda and Kiyosi Terao