Jahn-Teller effect in multi-spin systems with high exchange interaction: Ground state problem forV15nanocluster

We study the ground state stability of the magnetic subsystem of the low spin molecular cluster ${V}_{15},$ which has two degenerated doublets in its ground state governed by isotropic antiferromagnetic couplings of an odd number of magnetic ions ${V}^{4+}.$ We show that the ground state degeneracy of the cluster can be lifted off by the spin-phonon interactions of the exchange origin in the spin subsystem. This effect is connected to the break of the permutation symmetry of the exchange Hamiltonian of the cluster. The ground state splitting caused by the static Jahn-Teller effect is analyzed. The considered effect depends on the temperature and has a critical temperature proportional to the splitting gap ${T}_{0}\ensuremath{\sim}{\ensuremath{\Delta}}_{0},$ over which the Jahn-Teller effect disappears. The estimated splitting gap for the molecular cluster ${V}_{15}$ at zero temperature has an order of ${\ensuremath{\Delta}}_{0}\ensuremath{\sim}{10}^{\ensuremath{-}1}--{10}^{\ensuremath{-}3}\mathrm{K}$ which correlates with the experimentally observed value $\ensuremath{\Delta}=10--50\mathrm{mK}.$