Orbital-driven spin-singlet formation in NaTiSi₂O₆

A Ti-oxide compound in the pyroxene family NaTiSi₂O₆ containing a one-dimensional Ti-O network exhibits a phase transition at T=210K, for which it has been anticipated that the spin-singlet formation is driven by the orbital ordering. We develop a theory that describes the mechanism of this phase transition. We use the Hartree-Fock approximation to the multiband d-p model and derive the groundstate phase diagram in the parameter space. We also use the perturbation theory in the strong correlation limit up to the fourth order of electron hoppings to derive the effective spin-orbital Hamiltonian. We then apply the density-matrix renormalization group method to the derived Hamiltonian and obtain the groundstate phase diagram. Experimental relevance of our results is discussed.