Definitive Evidence for Order-by-Quantum-Disorder in Er2Ti2O7
  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. 
Lucile Savary, Kate A. Ross, Bruce D. Gaulin, Jacob P. C. Ruff, and   Leon Balents
cond-mat.str-el