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Phase transitions

Can magnets show the long-sought superradiant phase transition?

Kim D, Dasgupta S, Ma X, et al. · Science advances · 2025

Open access · cc by · source: Europe PMC

In the magnetic crystal ErFeO3, one coupled spin mode drops toward zero frequency while the other kinks at the same field, the signature of a Dicke superradiant phase transition.

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Study at a glance

Design
Other — Transmission and thermal-detection magnetospectroscopy of ErFeO3 single crystals at 2 K and 10 K, with a mean-field spin-Hamiltonian fit and derived extended Dicke model.
N
No sample count; a few single-crystal pieces cut along different axes were measured.
Population
Single crystals of the rare-earth orthoferrite ErFeO3
Outcome
Magnetic-field dependence of the upper and lower hybrid (polariton) mode frequencies

Structured fields used in claim comparison tables when every cited study has a complete layer.

Key findings

At 2 K the system leaves the superradiant phase at a critical field of 1.8 T: the upper (terahertz) mode shows a sharp kink in its frequency, while the lower (GHz) mode softens to below the measurable range and reappears, centred on the same field. At 10 K neither mode shows critical behaviour and they are much less mixed. The fitted model reproduces both features, and the derived Dicke model has no diamagnetic A-squared term, so the no-go theorem that forbids the photonic version does not apply.

Methodology

The authors grew single crystals of ErFeO3, where iron spin waves (magnons) couple strongly to erbium spins, mimicking light coupled to atoms in the Dicke model. At low temperature they swept a static magnetic field along the a axis and tracked the two hybrid modes using terahertz time-domain spectroscopy for the upper mode and GHz transmission and heating-based detection for the lower mode. They fitted a spin Hamiltonian that adds erbium anisotropy and derived an extended Dicke model from it.

Limitations

The lower mode could not be followed all the way to zero frequency because it fell below the lowest frequency they could measure, so complete softening is inferred rather than directly seen. The model is mean-field and relies on six fitted parameters, so agreement with data is partly by construction. The quantum features predicted for this phase, such as squeezing and entanglement, were not measured, and it is an analogue using magnons rather than real photons in a cavity.

How this study connects

Role on claims

Each row is a claim on a concept or method page where this paper supports, challenges, or qualifies the statement. Roles are hand-checked — not a model guess.

  • SupportsPhase transitions beyond melting and boilingconcept

    Coupled magnons can realise a Dicke-type superradiant transition that is forbidden for ordinary photons.

    In ErFeO3 at 2 K, the system left a superradiant phase at a critical field of 1.8 T: the upper mode's frequency kinked and the lower mode softened below the measurable range; at 10 K neither mode showed critical behaviour.

    Evidence for the claim as stated.

  • QualifiesPhase transitions beyond melting and boilingconcept

    Coupled magnons can realise a Dicke-type superradiant transition that is forbidden for ordinary photons.

    In ErFeO3 at 2 K, the system left a superradiant phase at a critical field of 1.8 T: the upper mode's frequency kinked and the lower mode softened below the measurable range; at 10 K neither mode showed critical behaviour.

    Scope note — Full mode softening is inferred, and the mean-field model has six fitted parameters.

    Limits the claim's scope: a different population, assay, or outcome.

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