Quantum order by disorder and accidental soft mode in Er2Ti2O7.

Motivated by recent neutron scattering experiments, we derive and study an effective "pseudodipolar" spin-1/2 model for the XY pyrochlore antiferromagnet Er(2)Ti(2)O(7). While a bond-dependent in-plane exchange anisotropy removes any continuous symmetry, it does lead to a one-parameter 'accidental' classical degeneracy. This degeneracy is lifted by quantum fluctuations in favor of the noncoplanar spin structure observed experimentally-a rare experimental instance of quantum order by disorder. A non-Goldstone low-energy mode is present in the excitation spectrum in accordance with inelastic neutron scattering data. Our theory also resolves the puzzle of the experimentally observed continuous ordering transition, absent from previous models.

Magnetic phase diagrams of classical triangular and kagome antiferromagnets.

We investigate the effect of geometrical frustration on the H-T phase diagrams of the classical Heisenberg antiferromagnets on triangular and kagome lattices. The phase diagrams for the two models are obtained from large-scale Monte Carlo simulations. For the kagome antiferromagnet, thermal fluctuations are unable to lift degeneracy completely and stabilize translationally disordered multipolar phases. We find a substantial difference in the temperature scales of the order by disorder effect related to different degeneracy of the low- and the high-field classical ground states in the kagome antiferromagnet. In the low-field regime, the Kosterlitz-Thouless transition into a spin-nematic phase is produced by unbinding of half-quantum vortices.