Electron correlation and dynamical Jahn-Teller effect in an orbitally degenerate system

Motivated by recent experiments on Ba3CuSb2O9, we study the dynamical Jahn-Teller effect in a spin-orbital coupled system. We analyze a low-energy model Hamiltonian which includes the superexchange-type interaction and the Jahn-Teller interaction by using a combined method of the mean-field approximation and the quantum Monte-Carlo simulation. We find that magnetic orders do not appear in a wide parameter region and that the spin-dimer state with an orbital order is realized. The orbital order is strongly suppressed by the dynamical Jahn-Teller effect.