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Motivated by recent experimental and theoretical progress on the Er2Ti2O7 pyrochlore XY antiferromagnet, we study the problem of quantum order-by-disorder in pyrochlore XY systems. We consider the most general nearest-neighbor pseudo spin-1/2 Hamiltonian for such a system characterized by anisotropic spin-spin couplings J_e = [J_pm, J_{pmpm}, J_{zpm}, J_{zz}] and construct zero-temperature phase diagrams. Combining symmetry arguments and spin-wave calculations, we show that the ground state phase boundaries between the two candidate ground states of the Gamma_5 irreducible representation, the psi_2 and psi_3 (basis) states, are rather accurately determined by a cubic equation in J_{pm}J_{pmpm})/J_{zpm}^2. Depending on the value of J_{zz}, there can be one or three phase boundaries that separate alternating regions of psi_2 and psi_3 states. In particular, we find for sufficiently small J_{zz}/J_{pm} a narrow psi_2 sliver sandwiched between two psi_3 regions in the J_{pmpm}/J_pm vs J_{zpm}/J_pm phase diagram. Our results further illustrate the very large potential sensitivity of the ground state of XY pyrochlore systems to minute changes in their spin Hamiltonian. Using the experimentally determined J_3 and g-tensor values for Er2Ti2O7, we show that the heretofore neglected long-range 1/r^3 magnetostatic dipole-dipole interactions do not change the conclusion that Er2Ti2O7 has a psi_2 ground state induced via a quantum order-by-disorder mechanism. We propose that the CdDy2Se4 chalcogenide spinel, in which the Dy^{3+} ions form a pyrochlore lattice and may be XY-like, could prove interesting to investigate.
We report neutron scattering and muon spin relaxation measurements (muSR) on the pyrochlore antiferromagnet Yb2Ge2O7. Inelastic neutron scattering was used to probe the transitions between crystal electric field levels, allowing us to determine the e
There is a growing family of rare-earth kagome materials with dominant nearest-neighbor interactions and strong spin orbit coupling. The low symmetry of these materials makes theoretical description complicated, with six distinct nearest-neighbor cou
The dipolar-octupolar pyrochlore oxides R$_2$M$_2$O$_7$ (R=Ce, Sm, Nd) represent an important opportunity in the search for three dimensional Quantum Spin Liquid (QSL) ground states. Their low energy physics is governed by an alluringly simple XYZ Ha
We explore the field-temperature phase diagram of the XY pyrochlore antiferromagnet Er$_2$Ti$_2$O$_7$, by means of magnetization and neutron diffraction experiments. Depending on the field strength and direction relative to the high symmetry cubic di
Conclusive evidence of order by disorder is scarce in real materials. Perhaps one of the strongest cases presented has been for the pyrochlore XY antiferromagnet Er2Ti2O7, with the ground state selection proceeding by order by disorder induced throug