2005/01/12 by S. Di Matteo, G. Jackeli, N. B. Perkins
Physics and Astronomy · #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.72.024431
published as Phys. Rev. B 72, 024431 (2005) · 15 pages, 8 figures
arxiv created 2005/01/12 · arxiv updated 2009/12/01
We discuss the ground state properties of a spin 1/2 magnetic ion with threefold t2g orbital degeneracy on a highly frustrated pyrochlore lattice, like Ti3+ ion in B-spinel MgTi2O4. We formulate an effective spin-orbital Hamiltonian and study its low energy sector by constructing several exact-eigenstates in the limit of vanishing Hund's coupling. We find that orbital degrees of freedom modulate the spin-exchange energies, release the infinite spin-degeneracy of pyrochlore structure, and drive the system to a non-magnetic spin-singlet manifold. The latter is a collection of spin-singlet dimers and is, however, highly degenerate with respect of dimer orientations. This ``orientational'' degeneracy is then lifted by a magneto-elastic interaction that optimizes the previous energy gain by distorting the bonds in suitable directions and leading to a tetragonal phase. In this way a valence bond crystal state is formed, through the condensation of dimers along helical chains running around the tetragonal c-axis, as actually observed in MgTi2O4. The orbitally ordered pattern in the dimerized phase is predicted to be of ferro-type along the helices and of antiferro-type between them. Finally, through analytical considerations as well as numerical ab-initio simulations, we predict a possible experimental tool for the observation of such an orbital ordering, through resonant x-ray scattering.