title: Order by disorder spin wave gap in the XY pyrochlore magnet Er2Ti2O7.
abstract: The recent determination of a robust spin Hamiltonian for the antiferromagnetic XY pyrochlore Er2Ti2O7 reveals a most convincing case of the "Order-by-Quantum-Disorder" mechanism for ground state selection. This mechanism relies on quantum fluctuations to remove an accidental symmetry of the magnetic ground state, and selects a particular ordered spin structure below TN=1.2 K. The removal of the continuous degeneracy results in an energy gap in the spectrum of spin wave excitations, long wavelength pseudo-Goldstone modes. We have measured the Order-by-Quantum-Disorder spin wave gap at a zone center in Er2Ti2O7, using low incident energy neutrons and the time-of-flight inelastic scattering method. We report a gap of Δ=0.053±0.006  meV, which is consistent with upper bounds placed on it from heat capacity measurements and roughly consistent with the theoretical estimate of ∼0.02  meV, further validating the spin Hamiltonian that led to that prediction. The gap is observed to vary with the square of the order parameter, and goes to zero for T∼TN.
authors.affiliation: Institute for Quantum Matter and Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA and NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA.
authors.forename: K A
authors.initials: KA
authors.lastname: Ross
authors.affiliation: NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA and Department of Materials Science and Engineering, University of Maryland, College Park, Maryland 20742, USA.
authors.forename: Y
authors.initials: Y
authors.lastname: Qiu
authors.affiliation: NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA.
authors.forename: J R D
authors.initials: JR
authors.lastname: Copley
authors.affiliation: Brockhouse Institute for Materials Research, McMaster University, Hamilton, Ontario L8S 4M1, Canada.
authors.forename: H A
authors.initials: HA
authors.lastname: Dabkowska
authors.affiliation: Brockhouse Institute for Materials Research, McMaster University, Hamilton, Ontario L8S 4M1, Canada and Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S 4M1, Canada and Canadian Institute for Advanced Research, 180 Dundas Street West, Toronto, Ontario M5G 1Z8, Canada.
authors.forename: B D
authors.initials: BD
authors.lastname: Gaulin