Can magnets show the long-sought superradiant phase transition?
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.
Source
Observation of the magnonic Dicke superradiant phase transition
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.
What they did
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.
What they found
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.
The limits
What it doesn't show
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.
Key terms
- Dicke model
- A model of many two-level systems coupled equally to one bosonic mode; above a critical coupling it predicts a superradiant phase.
- Superradiant phase transition
- A transition where, beyond a critical coupling, a static field and a collective polarisation appear spontaneously at the same time.
- Magnon
- A quantised collective spin wave in an ordered magnet, here the iron spin mode that plays the role of the cavity photon.
- Mode softening
- A vibration or resonance frequency falling toward zero as a phase boundary is approached, a classic sign of a continuous transition.
- No-go theorem
- The argument that the diamagnetic A-squared term in light-matter coupling prevents an equilibrium superradiant transition for real photons.
- Electron paramagnetic resonance
- Absorption of microwaves by unpaired spins at a frequency set by the magnetic field via the Zeeman effect.
Flashcards
0 of 11 answers reviewed
Research intelligence for this paper
See its role on concept claims, tensions it is part of, placement history, and related discoveries.
Quiz yourself
In the zero-detuning simple Dicke model, what normalized coupling is critical?
Common questions
Why use a magnet instead of atoms in a cavity?
In photon-atom systems the diamagnetic term blocks the equilibrium transition; here the coupling is a spin exchange interaction with no such term, so the transition can actually happen.
How does a magnetic field tune the transition?
The field shifts the erbium resonance frequency via the Zeeman effect while barely changing the iron magnon or the coupling, so it changes the frequency ratio that controls whether the system is superradiant.
How is this different from an ordinary spin-flop transition?
A spin-flop is usually first order and shows softening without a kink, with the field along the easy axis; here the field is perpendicular, the change is continuous, and both modes change together.
More on Phase transitions