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arxiv: 2606.26921 · v1 · pith:H5T7T2U6new · submitted 2026-06-25 · ❄️ cond-mat.str-el · cond-mat.mtrl-sci

Coexistence of static order and spin dynamics in an S = 5/2 frustrated triangular antiferromagnet

U. Jena , B. Sana , Satish Kumar , M. Pregelj , A. Bandyopadhyay , P. Manuel , J. S. Lord , D. T. Adroja
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P. Khuntia
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classification ❄️ cond-mat.str-el cond-mat.mtrl-sci
keywords triangular lattice antiferromagnetmuon spin rotationpersistent spin dynamicsMnSnB2O6Ising antiferromagnetfrustrated magnetismspecific heat
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The pith

Muon spin rotation detects static magnetic order coexisting with persistent spin dynamics in the S=5/2 triangular antiferromagnet MnSnB2O6 below 1 K.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines MnSnB2O6, in which Mn2+ ions form a nearly ideal two-dimensional triangular lattice without anti-site disorder. Thermodynamic, neutron diffraction, and first-principles results establish antiferromagnetic order below approximately 1 K driven by intraplane exchange. Muon spin rotation spectra reveal a static internal field that appears at the ordering temperature while a dynamic relaxation channel remains active down to 50 mK. The temperature dependence of the ordered moment follows a power law consistent with three-dimensional Ising antiferromagnetism. Specific heat below the transition decays as T to the power 1.37, pointing to low-energy excitations beyond conventional spin waves.

Core claim

In MnSnB2O6 the Mn2+ moments order antiferromagnetically below approximately 1 K. Neutron diffraction and specific-heat data confirm the transition to long-range order. Zero-field muon spin rotation spectra show that a static internal field develops below TN while a dynamic relaxation component remains present down to 50 mK. The order parameter extracted from neutron data follows a power law consistent with three-dimensional Ising criticality. Specific heat below TN decays as T^1.37, indicating additional low-energy excitations beyond conventional spin waves.

What carries the argument

Zero-field muon spin rotation that separates the development of a static local field from a remaining dynamic relaxation channel at the muon site.

If this is right

  • Persistent spin dynamics inside long-range order are compatible with the classical high-spin triangular lattice once disorder is removed.
  • The T^1.37 specific-heat law implies gapless or weakly gapped excitations that survive deep inside the ordered phase.
  • Weak interplane couplings dictate three-dimensional Ising critical behavior despite the two-dimensional lattice geometry.
  • The clean triangular network isolates the effects of geometric frustration on low-energy excitations without random-bond complications.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar coexistence of order and dynamics may appear in other high-spin triangular compounds once anti-site disorder is minimized.
  • Inelastic neutron scattering at millikelvin temperatures could test whether the specific-heat exponent arises from magnon decay or from an emergent continuum of excitations.
  • The system offers a reference point for numerical simulations of classical frustrated magnets that must reproduce both static order and residual fluctuations.

Load-bearing premise

The triangular Mn network is free of significant anti-site disorder, allowing the observed dynamics to be interpreted as intrinsic rather than disorder-induced.

What would settle it

A controlled introduction of anti-site disorder that eliminates the dynamic muon relaxation component while preserving the static order would falsify the claim that the coexistence is intrinsic to the clean frustrated lattice.

Figures

Figures reproduced from arXiv: 2606.26921 by A. Bandyopadhyay, B. Sana, D. T. Adroja, J. S. Lord, M. Pregelj, P. Khuntia, P. Manuel, Satish Kumar, U. Jena.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) The Rietveld refinement of the powder X-ray diffraction pattern of MnSnB [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Temperature dependence of the [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) Neutron powder diffraction patterns for MnSnB [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) ZF- [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

Frustrated triangular-lattice antiferromagnets in the classical high-spin limit provide a paradigmatic setting in which the interplay of competing exchange interactions, anisotropy, and collective degrees of freedom can lead to unconventional low-energy excitations, anomalous criticality, and persistent dynamical responses. Here, we present comprehensive thermodynamic, $\mu$SR, and neutron diffraction experiments, along with first-principles calculations, on a triangular-lattice antiferromagnet, MnSnB$_2$O$_6$, where Mn$^{2+}$ ($S=5/2$) moments form a nearly perfect 2D triangular network without any anti-site disorder. The Curie-Weiss fit to the magnetic susceptibility yields a moderate Curie-Weiss temperature of $-12$ K, indicating dominant antiferromagnetic interactions between Mn$^{2+}$ moments, which is supported by first-principles calculations. Specific-heat measurements reveal the onset of long-range magnetic order at $T_{\rm N}\approx 1$ K, which is ascribed to intraplane exchange interactions. The specific heat exhibits pronounced short-range correlations above $T_{\rm N}$ and an unconventional power-law behavior, $C\propto T^{1.37}$, deep in the ordered state, suggesting the presence of non-trivial low-energy excitations. Zero-field $\mu$SR experiments down to 50~mK confirm the presence of magnetic ordering below $T_{\rm N}$, in agreement with thermodynamic and neutron diffraction experiments. The $\mu$SR measurements detect persistent spin dynamics coexisting with static magnetic order. The temperature evolution of the order parameter down to 50~mK from neutron diffraction suggests that the ordered state is consistent with a 3D Ising-like antiferromagnet. This family of archetypal frustrated magnets offers a promising venue for the experimental realization of emergent phenomena governed by competing exchange interactions and exotic low-energy excitations.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript presents thermodynamic, μSR, and neutron diffraction measurements, together with DFT calculations, on the S=5/2 triangular antiferromagnet MnSnB2O6. It reports a Curie-Weiss temperature of −12 K, long-range order at TN≈1 K, an unconventional specific-heat power law C∝T^1.37 below TN, μSR evidence for static order coexisting with persistent spin dynamics down to 50 mK, and an order-parameter temperature dependence consistent with 3D Ising antiferromagnetism. The central claim is that these features occur in a clean, nearly perfect 2D triangular lattice free of anti-site disorder.

Significance. If the lattice cleanliness is quantitatively established, the work supplies a well-characterized classical high-spin example in which static order and persistent dynamics coexist, with multiple independent probes converging on TN and the order-parameter evolution. The combination of thermodynamics, local-probe dynamics, and diffraction data on a geometrically frustrated S=5/2 system would be a useful addition to the literature on low-energy excitations in triangular antiferromagnets.

major comments (1)
  1. [Abstract] Abstract (and structural characterization section): the assertion that the Mn2+ moments form a 'nearly perfect 2D triangular network without any anti-site disorder' is stated as fact but is not accompanied by quantitative site-occupancy refinements or upper limits (with error bars) from neutron diffraction. This information is load-bearing for the interpretation that the observed μSR relaxation arises from intrinsic dynamics rather than from local random fields or inhomogeneity induced by even modest Mn/Sn mixing.
minor comments (2)
  1. [Abstract] Abstract: numerical values (TN, CW temperature, exponent 1.37) are given without uncertainties or explicit statements of data-selection criteria.
  2. The specific-heat power-law fit and the μSR relaxation-rate analysis would benefit from explicit statements of the temperature ranges used and goodness-of-fit metrics.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address the single major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract (and structural characterization section): the assertion that the Mn2+ moments form a 'nearly perfect 2D triangular network without any anti-site disorder' is stated as fact but is not accompanied by quantitative site-occupancy refinements or upper limits (with error bars) from neutron diffraction. This information is load-bearing for the interpretation that the observed μSR relaxation arises from intrinsic dynamics rather than from local random fields or inhomogeneity induced by even modest Mn/Sn mixing.

    Authors: We agree that quantitative site-occupancy refinements with error bars are necessary to substantiate the claim of a clean lattice and to support the interpretation of the μSR data. Although the original manuscript asserted the absence of anti-site disorder on the basis of synthesis conditions and the quality of the diffraction patterns, explicit numerical limits were not provided. In the revised manuscript we have added the Rietveld refinement results from the neutron diffraction data, including refined site occupancies together with their uncertainties and a stated upper bound on Mn/Sn anti-site mixing. These additions directly address the referee’s concern and reinforce that the persistent dynamics are intrinsic. The abstract has been updated to incorporate the quantitative characterization. revision: yes

Circularity Check

0 steps flagged

No circularity; central claims are direct experimental observations

full rationale

The paper reports thermodynamic, μSR, neutron diffraction, and first-principles results on MnSnB2O6. Its strongest claims (persistent spin dynamics coexisting with static order below TN ≈ 1 K, order-parameter temperature dependence consistent with 3D Ising antiferromagnetism) are stated as direct measurements without any model equations, parameter fitting, or predictions that reduce to the fitted inputs by construction. No self-citation load-bearing steps, uniqueness theorems, or ansatz smuggling appear in the provided text. The assertion of a clean 2D triangular network without anti-site disorder is presented as a structural premise rather than a derived result, and the paper does not contain any derivation chain that would trigger the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work rests on standard domain assumptions for interpreting μSR asymmetry and neutron Bragg peaks as signatures of static order versus dynamics; no free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Standard condensed-matter assumptions that μSR relaxation rates and neutron diffraction intensities can be unambiguously partitioned into static and dynamic contributions
    Invoked to conclude coexistence from the μSR data.

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