Higher-Rank Spin Liquids and Spin Nematics from Competing Orders in Pyrochlore Magnets

TL;DR

This paper explores the rich phase diagram of pyrochlore magnets, revealing a transition from conventional magnetic order to a novel spin-nematic phase and a rank-2 U(1) spin liquid driven by competing interactions.

Contribution

It introduces a comprehensive analysis of competing orders in pyrochlore magnets, identifying a new spin-nematic phase and characterizing a rank-2 U(1) spin liquid using classical simulations.

Findings

Small $|J_{z\u2212}|$ favors thermal order-by-disorder with $f q=0$ order.

Large $|J_{z\u2212}|$ stabilizes a spin-nematic phase with characteristic structure factor lines.

Intermediate temperatures exhibit a rank-2 U(1) classical spin liquid.

Abstract

Pyrochlore magnets have proven to provide an excellent arena for the realization of a variety of many-body phenomena such as classical and quantum order-by-disorder, as well as spin liquid phases described by emergent gauge field theories. These phenomena arise from the competition between different symmetry-breaking magnetic orders. In this work, we consider a subspace of the most general bilinear nearest-neighbor Hamiltonian on the pyrochlore lattice, parameterized by the local interaction parameter $J_{z\pm}$, where three symmetry-breaking phases converge. We demonstrate that for small values of $|J_{z\pm}|$, a conventional $\mathbf q=0$ ordered phase is selected by a thermal order-by-disorder mechanism. For $|J_{z\pm}|$ above a certain finite threshold, a novel spin-nematic phase is stabilized at low temperatures. Instead of the usual Bragg peaks, the spin-nematic phase features lines of high intensity in the spin structure factor. At intermediate temperatures above the low-temperature orders, a rank-2 U(1) classical spin liquid is realized for all $J_{z\pm} \neq 0$. We fully characterize all phases using classical Monte-Carlo simulations and a self-consistent Gaussian approximation.