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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.

Bibtex (Click to Show/Hide)

@article{PhysRevLett.109.167201,
title = {Order by Quantum Disorder in ${\mathrm{Er}}_{2}{\mathrm{Ti}}_{2}{\mathbf{O}}_{7}$},
author = {Savary, Lucile and Ross, Kate A. and Gaulin, Bruce D. and Ruff, Jacob P. C. and Balents, Leon},
journal = {Phys. Rev. Lett.},
volume = {109},
issue = {16},
pages = {167201},
numpages = {5},
year = {2012},
month = {Oct},
doi = {10.1103/PhysRevLett.109.167201},