Definitive Evidence for Order-by-Quantum-Disorder in Er₂Ti₂O₇

In this paper (arXiv and PRL), we exhibit for the first time definitive evidence of order-by-disorder in a real material, namely Er₂Ti₂O₇. This is done by showing (1) a very general proof of the existence of a robust U(1) degeneracy of mean-field states on the pyrochlore lattice, (2) by extracting the Hamiltonian parameters by fitting spin-wave theory with high-field inelastic neutron scattering measurements, which (3) places Er₂Ti₂O₇ in a region of parameter space where it is described by its classical ground states which are precisely those of the degenerate U(1) manifold. The proof of order-by-disorder resides precisely within the robustness of the degeneracy. Order-by-disorder driven by quantum fluctuations is shown to describe all accessible experimental features. Several other predictions, in particular the existence of a measurable gap, are described, and many comparisons with experiments are made.

Facts and FAQs

• This is the only demonstration of order-by-disorder in a material.
• We show this is because the classical degeneracy enjoys unprecedented symmetry protection.
• We are looking forward to experimental measurements of the spin wave gap and comparison to the value we predict, Δ ≅ 0.02 meV = 260 mK.
• Activated behavior of the specific heat at very low temperatures would also be good evidence of the existence of this nonzero gap.