Order Induced by Dilution in Pyrochlore XY Antiferromagnets

TL;DR

This paper investigates how non-magnetic ion substitution affects the magnetic order in pyrochlore XY antiferromagnets, revealing that dilution can induce a different ordered state than thermal or quantum fluctuations, with potential experimental implications.

Contribution

It introduces a novel understanding of how dilution influences order-by-disorder in pyrochlore XY antiferromagnets, especially near line degeneracy points, and predicts a disorder-driven phase transition.

Findings

Dilution favors a state opposite to thermal and quantum order-by-disorder.

Line defects from vacancies can cross, leading to a one-dimensional spin texture.

Potential for a second phase transition in Er$_{2-x}$Y$_x$Ti$_2$O$_7$ due to quenched disorder.

Abstract

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 non-magnetic ions onto the magnetic sites in a pyrochlore XY model with generally anisotropic exchange tuned by a single parameter $J^{\pm\pm}/J^\pm$. The physics is controlled by two points in this space of parameters $J^{\pm\pm}/J^\pm=\pm 2$ 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 Er$_{2-x}$Y$_x$Ti$_2$O$_7$ for small $x$ exhibits a second phase transition within the thermally selected $\psi_2$ state into a $\psi_3$ state selected by the quenched disorder.