Effective spin-1/2 exchange interactions in Tb$_2$Ti$_2$O$_7$

TL;DR

This paper derives an effective spin-1/2 exchange model for Tb$_2$Ti$_2$O$_7$, revealing it as a quantum spin ice system by calculating anisotropic exchange interactions beyond simple models.

Contribution

It introduces a comprehensive derivation of exchange constants for Tb$_2$Ti$_2$O$_7$, considering all nearest-neighbour paths, advancing understanding of its quantum spin ice behavior.

Findings

Tb$_2$Ti$_2$O$_7$ is described by a quantum spin ice Hamiltonian.

All relevant exchange constants are explicitly derived.

The model surpasses previous independent tetrahedra approximations.

Abstract

We derive an effective spin-1/2 exchange model for non-Kramers Tb$^{3+}$ states in the pyrochlore Tb$_2$Ti$_2$O$_7$. The four anisotropic nearest-neighbour exchange constants, as well as next-neighbour exchange constants are derived for the effective model. This work goes beyond the independent tetrahedra model by considering all nearest-neighbour exchange paths on the pyrochlore lattice. Estimates of the exchange constants reveal that Tb$_2$Ti$_2$O$_7$ is described by a quantum spin ice Hamiltonian.