Orbital-Peierls transition in the spin chains of NaTiSi2O6

The distinguishing feature of the pyroxene compound NaTiSi2O6 is the presence of quasi-one-dimensional arrays of edge sharing TiO6 octahedra. Besides its spin (s=12), each Ti3+ ion has an additional orbital degree of freedom. We determine the properties of the microscopic spin-orbital Hamiltonian for this compound by finite temperature Monte Carlo simulations. We show that for the spin and orbital ordering to occur at the same temperature, the orbital crystal field splitting should be smaller than or comparable to the inter-site superexchange integral. The simulations strongly indicate that in NaTiSi2O6 there is an orbital-Peierls transition, which is an orbital ordering transition that is accompanied by a lattice dimerization. Magnetically, in this case, the system goes from a high temperature quasi-one-dimensional antiferromagnet to a low-temperature valence bond solid. The experimentally observed spin gap and lattice anomalies are strong evidence for the presence of an orbital-Peierls transition in NaTiSi2O6.