Coexisting spin resonance and long-range magnetic order of Eu in EuRbFe₄As₄
Pith reviewed 2026-05-25 00:35 UTC · model grok-4.3
The pith
Neutron spin resonance at 17.7 meV supports s± pairing in EuRbFe4As4 while Eu antiferromagnetic order with k=(0,0,0.25) persists below 15 K.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
In EuRbFe4As4 the neutron spin resonance at the three-dimensional nesting vectors Q=(0.5,0.5,1) and (0.5,0.5,3) with characteristic energy 17.7 meV appears below Tc=36.5 K and, together with RPA calculations, indicates s± superconducting pairing; independently, the Eu sublattice develops three-dimensional antiferromagnetic order with propagation vector k=(0,0,0.25) below TN=15 K whose spin waves are quantitatively described by intra-plane J1/kB=-1.31 K and inter-plane Jc/kB=0.08 K, establishing coexistence of superconductivity and Eu magnetism with weak mutual coupling.
What carries the argument
Neutron spin resonance at the Fermi-surface nesting wave vectors Q=(0.5,0.5,1) and (0.5,0.5,3), interpreted via RPA to support s± pairing symmetry.
If this is right
- Superconductivity in EuRbFe4As4 has s± symmetry.
- Superconductivity and long-range Eu magnetic order coexist without strong suppression of either.
- The electronic band structure possesses three-dimensional character.
- The Eu-Eu exchange interactions are dominated by a ferromagnetic intra-plane nearest-neighbor term and a weak antiferromagnetic inter-plane term.
- The coupling between the Fe-based superconducting condensate and the Eu moments remains weak.
Where Pith is reading between the lines
- Similar weak-coupling coexistence may appear in other Eu-containing 1144 iron arsenides.
- Pressure or doping that strengthens the Eu-Fe interaction could drive competition between the two orders.
- The three-dimensional nesting implies that out-of-plane Fermi-surface sheets participate in the pairing.
- The small inter-plane Jc suggests the Eu magnetism is nearly two-dimensional despite the observed 3D propagation vector.
Load-bearing premise
The observed resonances arise from Fermi-surface nesting and their RPA interpretation confirms s± pairing rather than an alternative symmetry.
What would settle it
A measurement showing the resonance energy or wave-vector position deviates from RPA predictions for s± pairing, or an optical conductivity result incompatible with s±, would falsify the pairing conclusion.
read the original abstract
Magnetic excitations and magnetic structure of EuRbFe$_4$As$_4$ were investigated by inelastic neutron scattering (INS), neutron diffraction, and random phase approximation (RPA) calculations. Below the superconducting transition temperature $T_\text{c}=36.5$~K, the INS spectra exhibit the neutron spin resonances at $Q_\text{res}=1.27(2)$~$\text{\AA}^{-1}$ and $1.79(3)$~$\text{\AA}^{-1}$. They correspond to the $\mathbf{Q}=(0.5,0.5,1)$ and $(0.5,0.5,3)$ nesting wave vectors, showing three dimensional nature of the band structure. The characteristic energy of the neutron spin resonance is $E_\text{res}=17.7(3)$~meV corresponding to $5.7(1)k_\text{B}T_\text{c}$. Observation of the neutron spin resonance mode and our RPA calculations in conjunction with the recent optical conductivity measurements are indicative of the $s_\pm$ superconducting pairing symmetry in EuRbFe$_4$As$_4$. In addition to the neutron spin resonance mode, upon decreasing temperature below the magnetic transition temperature $T_\text{N}=15$~K, the spin wave excitation originating in the long-range magnetic order of the Eu sublattice was observed in the low-energy inelastic channel. Single-crystal neutron diffraction measurements demonstrate that the magnetic propagation vector of the Eu sublattice is $\mathbf{k}=(0, 0, 0.25)$, representing the three-dimensional antiferromagnetic order. Linear spin wave calculations assuming the obtained magnetic structure with the intra- and inter-plane nearest neighbor exchange couplings of $J_1/k_\text{B}=-1.31$~K and $J_c/k_\text{B}=0.08$~K can reproduce quantitatively the observed spin wave excitation. Our results show that superconductivity and long-range magnetic order of Eu coexist in EuRbFe$_4$As$_4$ whereas the coupling between them is rather weak.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript reports inelastic neutron scattering (INS) observations of spin resonance modes at Q=(0.5,0.5,1) and (0.5,0.5,3) below Tc=36.5 K with E_res=17.7 meV (5.7 k_B Tc) in EuRbFe4As4, interpreted via RPA calculations together with optical conductivity data as evidence for s± pairing symmetry. Neutron diffraction establishes Eu antiferromagnetic order with propagation vector k=(0,0,0.25) below TN=15 K; a linear spin-wave model with nearest-neighbor exchanges J1/k_B=-1.31 K and Jc/k_B=0.08 K quantitatively reproduces the low-energy spin-wave dispersion, supporting coexistence of superconductivity and Eu magnetism with weak inter-subsystem coupling.
Significance. The direct INS and diffraction measurements establish the coexistence of a spin resonance at nesting vectors and three-dimensional Eu antiferromagnetic order in this 1144 iron pnictide. The quantitative linear spin-wave fit to the Eu excitations is a clear strength. If the RPA step is adequately documented, the work would add useful evidence on sign-changing pairing in a system with coexisting local-moment order.
major comments (1)
- [RPA calculations] RPA calculations section: The central claim that the resonances indicate s± pairing rests on RPA dynamical susceptibility calculations, yet the manuscript supplies no band-structure input, no values for the interaction parameters, and no explicit comparison to s++ (or other) gap structures demonstrating that only a sign-changing gap produces a resonance pole at E_res=17.7 meV for the observed Q vectors. This interpretive step is load-bearing for the pairing-symmetry conclusion.
minor comments (2)
- [Abstract] Abstract and § on resonance: Q_res is reported in absolute units (Å^{-1}) while the nesting vectors are given in r.l.u.; a short statement of the lattice constants used for the conversion would improve clarity.
- [Spin-wave analysis] Spin-wave section: The fitted values J1/k_B and Jc/k_B are stated without quoted uncertainties; adding these would allow readers to assess the precision of the quantitative reproduction claim.
Simulated Author's Rebuttal
We thank the referee for the positive evaluation of the significance of our measurements and for the recommendation of major revision. We address the single major comment below.
read point-by-point responses
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Referee: [RPA calculations] RPA calculations section: The central claim that the resonances indicate s± pairing rests on RPA dynamical susceptibility calculations, yet the manuscript supplies no band-structure input, no values for the interaction parameters, and no explicit comparison to s++ (or other) gap structures demonstrating that only a sign-changing gap produces a resonance pole at E_res=17.7 meV for the observed Q vectors. This interpretive step is load-bearing for the pairing-symmetry conclusion.
Authors: We agree that the manuscript as written does not provide the band-structure inputs, interaction-parameter values, or explicit s++ comparison needed to make the RPA argument self-contained. In the revised version we will expand the RPA section (and add a supplementary figure if space is limited) to include: (i) the tight-binding parameters taken from the cited optical-conductivity work, (ii) the specific values of U and J used in the RPA, and (iii) direct side-by-side plots of the imaginary part of the susceptibility for both s± and s++ gaps at the measured Q vectors, confirming that only the sign-changing gap produces a resonance pole at 17.7 meV. revision: yes
Circularity Check
No significant circularity in derivation chain
full rationale
The reported INS resonances at nesting vectors, diffraction-determined Eu magnetic structure with k=(0,0,0.25), and fitted J1/Jc values that reproduce spin waves are independent experimental results and standard modeling steps. The s± pairing inference rests on RPA plus external optical conductivity data rather than reducing to fitted parameters or self-citations by construction. No self-definitional, fitted-input-as-prediction, or load-bearing self-citation patterns appear in the quoted claims.
Axiom & Free-Parameter Ledger
free parameters (2)
- J1/k_B =
-1.31 K
- J_c/k_B =
0.08 K
axioms (1)
- domain assumption Resonance modes at the stated nesting vectors, together with RPA and optical data, indicate s± pairing symmetry.
Lean theorems connected to this paper
-
IndisputableMonolith/Cost/FunctionalEquation.leanwashburn_uniqueness_aczel unclear?
unclearRelation between the paper passage and the cited Recognition theorem.
Observation of the neutron spin resonance mode and our RPA calculations in conjunction with the recent optical conductivity measurements are indicative of the s± superconducting pairing symmetry
-
IndisputableMonolith/Foundation/DimensionForcing.leanalexander_duality_circle_linking unclear?
unclearRelation between the paper passage and the cited Recognition theorem.
Linear spin wave calculations assuming the obtained magnetic structure with the intra- and inter-plane nearest neighbor exchange couplings of J1/kB=-1.31 K and Jc/kB=0.08 K
What do these tags mean?
- matches
- The paper's claim is directly supported by a theorem in the formal canon.
- supports
- The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
- extends
- The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
- uses
- The paper appears to rely on the theorem as machinery.
- contradicts
- The paper's claim conflicts with a theorem or certificate in the canon.
- unclear
- Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.
discussion (0)
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