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Exact Nematic and Mixed Magnetic Phases Driven by Competing Orders on the Pyrochlore Lattice

Niccolò Francini, Lukas Schmidt, Lukas Janssen, and Daniel Lozano-Gómez

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Phys. Rev. X 16, 031070 – Published 16 September, 2026

DOI: https://doi.org/10.1103/vwx8-mdtw

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 Jz±, 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 mixed magnetic phase. This realizes a q=0 long-range-ordered phase in a pyrochlore magnet characterized by two distinct order parameters, which we denote as the A2⊕ψ2 phase. Furthermore, at Jz±=1/2, 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 Jz±=1/2.

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Popular Summary

Determining ground-state magnetic order in geometrically frustrated pyrochlore lattices remains difficult because competing interactions prevent atomic spins from settling into a single low-energy configuration. We investigated this degeneracy by studying a pyrochlore spin model with three competing magnetic phases and found that thermal fluctuations systematically select a composite ordered configuration.

We showed that tuning specific interaction parameters generates additional emergent symmetries that prevent conventional long-range magnetic ordering. Instead, we discovered that these emergent constraints stabilize a nematic state driven by the interplay of frustration and fluctuations. Our work illuminates how symmetry and fluctuations conspire to stabilize exotic phases, providing a theoretical framework to guide the search for unconventional states in frustrated quantum materials.

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Phys. Rev. X 16, 031070– Published 16 September, 2026
  • Received 9 December 2025
  • Revised 1 April 2026
  • Accepted 5 August 2026
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