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• W2072488059 abstract "We discuss the ground state properties of a spin 1/2 magnetic ion with threefold $t_{2g}$ orbital degeneracy on a highly frustrated pyrochlore lattice, like Ti$^{3+}$ ion in B-spinel MgTi$_2$O$_4$. 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 MgTi$_2$O$_4$. 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." @default.
• W2072488059 created "2016-06-24" @default.
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• W2072488059 date "2005-07-14" @default.
• W2072488059 modified "2023-10-13" @default.
• W2072488059 title "Valence-bond crystal and lattice distortions in a pyrochlore antiferromagnet with orbital degeneracy" @default.
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• W2072488059 doi "https://doi.org/10.1103/physrevb.72.024431" @default.
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