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

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.

10 pages, 2 figures

References in corpus (10)

• Dynamically-Induced Frustration as a Route to a Quantum Spin Ice State in Tb2Ti2O7 via Virtual Crystal Field Excitations and Quantum Many-Body Effects
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Cited by in corpus (1)

• Antiferro-quadrupolar correlations in the quantum spin ice candidate Pr2Zr2O7