Exact nematic and mixed magnetic phases driven by competing orders on the pyrochlore lattice

TL;DR

This paper investigates a pyrochlore spin model revealing a novel mixed magnetic phase and a nematic phase driven by competing interactions, using analytical and numerical methods to understand their stability and properties.

Contribution

It provides the first demonstration of a $ extbf{q}=0$ long-range-ordered phase with two order parameters and characterizes a nematic phase arising at a specific interaction point.

Findings

Discovery of a mixed $A_2 igoplus oldsymbol{ ext{ extit{ extpsi}}}_2$ magnetic phase.

Identification of a nematic phase at $J_{z ext{ extpm}}=1/ ext{ extsqrt}2$.

Analysis of phase stability under temperature variations and parameter deviations.

Abstract

Pyrochlore magnets are a paradigmatic example of three-dimensional frustrated systems and provide an excellent platform for studying a variety of exotic many-body phenomena, including spin liquids, nematic phases, fragmentation, and order by disorder. In recent years, increasing attention has been devoted to bilinear spin models on this lattice, where multiple magnetic phases can be degenerate in energy, often stabilizing unconventional magnetic states. In this work, we focus on one such model, parametrized by the interaction coupling $J_{z\pm}$, which defines a line in parameter space corresponding to the phase boundary between three distinct magnetic phases. Using a combination of analytical and numerical methods, we show that this model exhibits an order-by-disorder mechanism at low temperatures, giving rise to a \emph{mixed} magnetic phase. This represents the first realization of a $\mathbf{q}=0$ long-range-ordered phase in a pyrochlore magnet characterized by two distinct order parameters, which we denote as the $A_2 \oplus \psi_2$ phase. Furthermore, at $J_{z\pm} = 1/\sqrt{2}$, the model acquires a subextensive number of discrete symmetries, which preclude the stabilization of conventional long-range order and instead lead to the emergence of a novel nematic phase. We characterize this nematic phase, describe how its ground-state configurations are constructed, and analyze its stability at higher temperatures and under small deviations from $J_{z\pm} = 1/\sqrt{2}$.