Order induced by dilution in pyrochlore XY antiferromagnets

XY pyrochlore antiferromagnets are well-known to exhibit order-by-disorder through both quantum and thermal selection. In this paper, we consider the effect of substituting nonmagnetic ions onto the magnetic sites in a pyrochlore XY model with generally anisotropic exchange tuned by a single parameter J(+/-+/-)/J(+/-). The physics is controlled by two points in this space of parameters J(+/-+/-)/J(+/-) = +/- 2 at which there are line modes in the ground state and hence an O(L-2) ground-state degeneracy intermediate between that of a conventional magnet and a Coulomb phase. At each of these points, single vacancies seed pairs of line defects. Two line defects carrying incompatible spin configurations from different vacancies can cross leading to an effective one-dimensional description of the resulting spin texture. In the thermodynamic limit at finite density, we find that dilution selects a state "opposite" to the state selected by thermal and quantum disorder which is understood from the single vacancy limit. The latter finding hints at the possibility that Er2-xYxTi2O7 for small x exhibits a second phase transition within the thermally selected psi(2) state into psi(3) state selected by the quenched disorder.