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

TL;DR

This paper provides the first definitive experimental evidence of order-by-disorder driven by quantum fluctuations in the magnetic material Er2Ti2O7, combining theoretical analysis and neutron scattering data.

Contribution

It demonstrates the existence of U(1) degeneracy in the Hamiltonian of Er2Ti2O7 and shows quantum fluctuations select a unique ground state, confirming order-by-disorder experimentally.

Findings

U(1) degeneracy exists in the Hamiltonian of Er2Ti2O7

Quantum fluctuations lift the degeneracy, selecting a specific ground state

Experimental neutron scattering confirms the theoretical predictions

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.