Phase transition and thermal order-by-disorder in the pyrochlore antiferromagnet Er sub(2) Ti sub(2) O sub(7): A high-temperature series expansion study

We use a high-temperature series expansion method to study the phenomenon of thermal order-by-disorder in the rare-earth pyrochlore material Er sub(2) Ti sub(2) O sub(7) on its approach to the critical temperature T sub(c). We show that its anisotropic exchange parameters, {J sub(e)}, characterizing an effective spin-1/2 model and recently determined from high-field inelastic neutron scattering spectra, describe very well the thermodynamic properties of the material in the paramagnetic phase and near T sub(c). While different q = 0 XY order-parameter susceptibilities show a high degree of degeneracy, a nonlinear susceptibility, related to the sixth power of the order parameter, reveals a thermal order-by-disorder selection of the same noncollinear "[psi] sub(2) state" as found in Er sub(2) Ti sub(2) O sub(7). Our results provide a rather definite quantitative demonstration that thermal order-by-disorder is operating at T sub(c) in this frustrated quantum spin-1/2 antiferromagnetic material.