Orbital ordering and spin-singlet formation in a pyroxene compound NaTiSi₂O₆

We analyse the ground state of the one-dimensional Ti-O network of NaTiSi₂O₆. First, we make the Hartree-Fock calculation of the original d-p model and obtain the ground-state phase diagram. We find that the orbital ferro and spin antiferro state is realized when the effect of lattice distortion is taken into account. We derive the effective spin-pseudospin Hamiltonian by the perturbation theory up to the fourth order of hoppings and its ground state is calculated by the density matrix renormalization (DMRG) method. We find that without the effect of distortion the orbital ordering occurs and the system is in the state of spin singlet, which indicates that the spin fluctuation plays an essential role in this phase transition.