Valence bond crystal in a pyrochlore antiferromagnet with orbital degeneracy

TL;DR

This paper investigates the ground state of a pyrochlore lattice with orbitally-degenerate magnetic ions, revealing a valence bond crystal stabilized by spin-orbital interactions and lattice distortions, explaining experimental observations in MgTi₂O₄.

Contribution

It derives an effective spin-orbital Hamiltonian showing how orbital degeneracy influences spin exchange, leading to a valence bond crystal state with lattice distortion.

Findings

Orbital degrees of freedom modulate spin exchange, removing degeneracy.

Ground state is a valence bond crystal of spin-singlet dimers.

Magneto-elastic interactions induce tetragonal distortion.

Abstract

We discuss the ground state of a pyrochlore lattice of threefold-orbitally-degenerate $S=1/2$ magnetic ions. We derive an effective spin-orbital Hamiltonian and show that the orbital degrees of freedom can modulate the spin exchange, removing the infinite spin-degeneracy characteristic of pyrochlore structures. The resulting state is a collection of spin-singlet dimers, with a residual degeneracy due to their relative orientation. This latter is lifted by a magneto-elastic interaction, induced in the spin-singlet phase-space, that forces a tetragonal distortion. Such a theory provides an explanation for the helical spin-singlet pattern observed in the B-spinel MgTi$_2$O$_4$.