Theory of multiple--phase competition in pyrochlore magnets with anisotropic exchange, with application to Yb2Ti2O7, Er2Ti2O7 and Er2Sn2O7

TL;DR

This paper develops a comprehensive symmetry-based theory for anisotropic exchange interactions in pyrochlore magnets, explaining diverse phenomena in materials like Yb2Ti2O7, Er2Ti2O7, and Er2Sn2O7 through classical and Monte Carlo analyses.

Contribution

It introduces a general model for anisotropic exchange in pyrochlore magnets, identifying multiple classical ordered states and explaining complex behaviors in key materials.

Findings

Identification of four classical ordered states with q=0

Explanation of order-by-fluctuations in Er2Ti2O7

Insights into the absence of magnetic order in Er2Sn2O7

Abstract

The family of magnetic rare-earth pyrochlore oxides R2M2O7 plays host to a diverse array of exotic phenomena, driven by the interplay between geometrical frustration and spin-orbit interaction, which leads to anisotropy in both magnetic moments and their interactions. In this article we establish a general, symmetry--based theory of pyrochlore magnets with anisotropic exchange interactions. Starting from a very general model of nearest-neighbour exchange between Kramers ions, we find four distinct classical ordered states, all with q=0, competing with a variety of spin-liquids and unconventional forms of magnetic order. The finite-temperature phase diagram of this model is determined by Monte Carlo simulation, supported by classical spin-wave calculations. We pay particular attention to the region of parameter space relevant to the widely studied materials Er2Ti2O7, Yb2Ti2O7, and Er2Sn2O7. We find that many of the most interesting properties of these materials can be traced back to the "accidental" degeneracies where phases with different symmetries meet. These include the ordered ground state selection by fluctuations in Er2Ti2O7, the dimensional-reduction observed in Yb2Ti2O7, and the lack of reported magnetic order in Er2Sn2O7. We also discuss the application of this theory to other pyrochlore oxides.