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

Abstract

Here we establish the systematic existence of a U(1) degeneracy of all symmetry-allowed Hamiltonians quadratic in the spins on the pyrochlore lattice, at the mean-field level. By extracting the Hamiltonian of Er2Ti2O7 from inelastic neutron scattering measurements, we then show that the U(1)-degenerate states of Er2Ti2O7 are its classical ground states, and unambiguously show that quantum fluctuations break the degeneracy in a way which is confirmed by experiment. This is the first definitive observation of order-by-disorder in any material. We provide further verifiable consequences of this phenomenon, and several additional comparisons between theory and experiment.

4.5 pages, 3 figures, 7.5 pages of Supplemental Material, 8 supplemental figures

References in corpus (3)

• Quantum order by disorder and accidental soft mode Er2Ti2O7
• Structural distortion and the spin liquid state in Tb2Ti2O7
• Energetic selection of ordered states in a model of the Er2Ti2O7 frustrated pyrochlore XY antiferromagnet

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• Order by Disorder and Energetic Selection of the Ground State in the XY Pyrochlore Antiferromagnet Er2Ti2O7. An Inelastic Neutron Scattering Study
• Order from structural disorder in $XY$ pyrochlore antiferromagnet $\mathrm{E}{\mathrm{r}}_2\mathrm{T}{\mathrm{i}}_2{\mathrm{O}}_7$
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• Infinite Geometric Frustration in a Cubic Dipole Cluster
• Melting of Spin Ice state through structural disorder in Dy2Zr2O7
• Order Induced by Dilution in Pyrochlore XY Antiferromagnets
• Tuning order-by-disorder multiferroicity in CuO by doping
• Magnetic dilution and domain selection in the XY pyrochlore antiferromagnet Er${}_2$Ti${}_2$O${}_7$
• Experimental evidence for field induced emergent clock anisotropies in the XY pyrochlore Er${}_2$Ti${}_2$O${}_7$
• Doping-induced quantum cross-over in Er${}_2$Ti${}_{2-x}$Sn${}_x$O${}_7$
• Phase diagram of the frustrated quantum-XY model on the honeycomb lattice studied by series expansions: Evidence for proximity to a bicritical point
• Effective spin-1/2 exchange interactions in Tb${}_2$Ti${}_2$O${}_7$
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