$S = 1$ pyrochlore magnets with competing anisotropies: A tale of two Coulomb phases, $Z_2$ flux confinement and $XY$-like transitions

Jay Pandey; Kedar Damle

Paper

$S = 1$ pyrochlore magnets with competing anisotropies: A tale of two Coulomb phases, $Z_2$ flux confinement and $XY$-like transitions

Abstract

We argue that the low-temperature physics of

pyrochlore magnets with a predominantly Ising-like easy-axis exchange coupling

that favors the local tetrahedral body diagonals, and a comparably large easy-plane single-ion anisotropy

(

) that favors the plane perpendicular to these local axes will exhibit interesting new phenomena due to the competition between

and

. In the

limit, we find three low temperature phases as a function of

: a short-range correlated paramagnetic phase, and two topologically-distinct Coulomb liquids separated by a

flux confinement transition. Both Coulomb liquids are described at long-wavelengths by a fluctuating divergence-free polarization field and have characteristic pinch-point singularities in their structure factor. In one Coulomb phase, the flux of this polarization field is confined to {\em even} integers, while it takes on all integer values in the other Coulomb phase. Experimental realizations with

and negative are predicted to exhibit signatures of a transition from a flux-deconfined Coulomb phase to the flux-confined Coulomb phase as they are cooled below

, while realizations with positive

will show signatures of a transition from a flux-deconfined Coulomb liquid to a short-range correlated paramagnet via a continuous

-like transition at