Pith. sign in

REVIEW 3 major objections 7 minor 60 references

Multistage development of short-range spin correlations and weak magnetic order in the two coupled trillium lattices of K2Fe2(MoO4)(PO4)2

T0 review · 3 major / 7 minor · reviewed 2026-07-09 · glm-5.2

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Weak order and persistent spin dynamics in a 3D trillium lattice

desk verdict Solid experimental characterization of a new double-trillium frustrated magnet; the field-induced spin-liquid claim is unsupported and should be dropped or heavily qualified. read the letter →

arxiv 2607.07681 v1 pith:6H2BWO3P submitted 2026-07-08 cond-mat.str-el

J. Khatua , Sritharan Krishnamoorthi , Changhyun Koo , Gyungbin Ban , Taeyun Kim , Yugo Oshima , Marc Uhlarz , John Wilkinson
show 6 more authors
Peter J. Baker Kyeong Jun Lee Mani Shankar Seo Hyoung Chang R. Sankar Kwang-Yong Choi
This is my paper
classification cond-mat.str-el PACS 75.25.-j75.40.Cx76.30.-v75.50.Ee
keywords trilliumlatticegeometricfrustrationspinliquidmuonrelaxationpersistentdynamicsweakmagneticorderlangbeinitehypertrillium
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper reports that K₂Fe₂(MoO₄)(PO₄)₂, a compound whose Fe³⁺ ions form two interpenetrating trillium lattices (a chiral 3D network of corner-sharing triangles), develops short-range spin correlations in two distinct stages at 34 K and 10 K before settling into weak magnetic order at T_N = 5.2 K. Using magnetization, specific heat, electron spin resonance, and muon spin relaxation measurements on single crystals, the authors show that only about 13% of the magnetic entropy is released at the ordering transition, meaning the vast majority of spin degrees of freedom remain disordered well above T_N. Crucially, muon spin relaxation reveals that spins continue to fluctuate dynamically even below T_N, down to 150 mK, indicating that the ordered state is not a conventional frozen antiferromagnet but coexists with persistent spin dynamics. The paper further reports that the ordering temperature is suppressed by applied magnetic fields of 2 T and above, which the authors interpret as a possible route toward a field-induced spin-liquid state. The compound is notable for being relatively free of the site-mixing disorder that plagues related Fe-based trillium compounds, while exhibiting a larger antiferromagnetic exchange scale (|θ_CW| ≈ 104 K) and a frustration parameter f ≈ 20.

What carries the argument

The double trillium lattice of Fe³⁺ (S = 5/2) ions in the noncentrosymmetric P2₁₃ space group, connected via Fe–O–Mo/P–O–Fe super-superexchange pathways forming a hypertrillium network with multiple competing exchange interactions (dimer J₁, inter-dimer J₂, trillium J₃/J₄, inter-trillium J₅). The frustration parameter f = |θ_CW|/T_N ≈ 20 quantifies the gap between the dominant exchange energy scale and the ordering temperature. Muon spin relaxation serves as the key local probe distinguishing persistent dynamics from spin-glass freezing, through the absence of a 1/3-tail recovery and the persistence of a finite Lorentzian relaxation component at the lowest temperatures.

What would settle it

If field-dependent neutron scattering or specific heat measurements above 2 T show conventional magnon modes or a standard polarized paramagnetic response with no continuum of fractionalized excitations, the field-induced spin-liquid interpretation would not hold.

Watch

Extended reading notes

Core claim

The central finding is that a double trillium lattice with minimal disorder can host a multistage magnetic evolution: two distinct short-range correlation regimes at 34 K and 10 K, weak canted antiferromagnetic order at 5.2 K that coexists with persistent GHz spin fluctuations, a spin reorientation at 3.2 K, and field-suppression of the ordering temperature above 2 T. The hierarchy of exchange interactions in the hypertrillium network (dimer, inter-dimer, trillium, and inter-trillium couplings) is proposed as the mechanism producing the two separate correlation scales, while subleading anisotropic or residual interactions are responsible for lifting the frustrated degeneracy only weakly, as

Load-bearing premise

The claim that suppression of T_N under fields ≥2 T 'suggests' field-induced spin-liquid behavior assumes that the field-suppressed ordered state gives way to a cooperative fluctuating spin regime, but the paper provides no direct evidence (neutron scattering, field-dependent specific heat showing a continuum of excitations, or entanglement witnesses) for a spin-liquid state under field; the data are equally consistent with a simple polarized paramagnet.

Editorial extensions

If this is right

  • If the field suppression of T_N genuinely produces a spin-liquid regime rather than a polarized paramagnet, inelastic neutron scattering under field should reveal a continuum of excitations rather than sharp magnon modes, which is directly testable.
  • The two-stage short-range correlation regime (T_H = 34 K, T_L = 10 K) implies that different sub-networks of the hypertrillium lattice order at different energy scales; neutron diffraction could resolve whether the two trillium sublattices or the dimer vs. trillium correlations dominate at each stage.
  • The persistent spin dynamics below T_N, combined with only 13% entropy release at the transition, suggests that the ordered moment is a small fraction of the full S = 5/2 moment; neutron diffraction should be able to quantify the ordered moment size directly.
  • The comparison across Fe-based trillium compounds (Table III) shows that T_N remains in the 2–5 K range regardless of disorder type, suggesting that the ordering is intrinsically pinned by the lattice geometry rather than by impurity effects — a pattern that could be tested by systematic isovalent substitution studies.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 7 minor

Summary. This manuscript reports a multi-probe study (magnetization, specific heat, ESR, μSR) of single crystals of K₂Fe₂(MoO₄)(PO₄)₂, a compound in which Fe³⁺ (S=5/2) ions form a double trillium lattice. The authors identify weak magnetic order at T_N = 5.2 K, two short-range correlation regimes at T_H = 34 K and T_L = 10 K, a spin reorientation anomaly at T* = 3.2 K, and persistent spin dynamics in the ordered state. The compound is notable for having minimal disorder (only Mo/P site mixing) and a large frustration parameter f ≈ 20. The paper concludes by suggesting that field suppression of T_N (μ₀H ≥ 2 T) makes this a candidate for field-induced spin-liquid behavior.

Significance. The study is valuable for the frustrated magnetism community as it presents a relatively clean 3D trillium-lattice compound with a large |θ_CW| and multiple correlation regimes, adding to the growing body of work on langbeinite-family magnets. The multi-probe approach is internally consistent in establishing the characteristic temperature scales. The high-field magnetization data (up to 55 T) and the μSR data down to 110 mK provide useful constraints on the ground state. The identification of two distinct short-range correlation regimes is a worthwhile observation that motivates future neutron scattering work.

major comments (3)
  1. §V (Conclusion) and Abstract: The claim that suppression of T_N under μ₀H ≥ 2 T 'suggests' or 'raises the possibility of' field-induced spin-liquid behavior is not supported by the evidence presented. Field suppression of a λ-anomaly in χ(T) is generic to weak canted antiferromagnets and does not distinguish a cooperative spin liquid from a trivially polarized paramagnet. The authors themselves attribute the weak ordering to 'subleading anisotropic or residual interactions' atop dominant Heisenberg exchange (§I, §V), in which case Zeeman suppression of T_N is expected regardless of the nature of the field-suppressed phase. No field-dependent specific heat, neutron scattering under field, or entanglement witness is provided. This claim should be either removed or substantially softened to a statement that the field suppression reflects the weakness of the ordering interaction, not that it
  2. §III E: The μSR data underpinning the 'persistent spin dynamics' claim are subject to two acknowledged limitations that weaken the conclusion. First, the Gaussian rate σ ≈ 14 μs⁻¹ reaches the instrument resolution limit at ISIS (acknowledged by the authors), so the low-T σ plateau may reflect instrumental limits rather than a physical saturation. Second, the LF decoupling field of 3200 Oe is below the estimated internal field width (~3800 Oe), so the persistence of relaxation at 110 mK is expected from incomplete decoupling alone and does not uniquely demonstrate active dynamics. The authors should explicitly state these as caveats on the persistent-dynamics conclusion rather than presenting it as firmly established.
  3. §III C, Eq. (1): The lattice specific heat fit uses fixed weighting coefficients (C_D=3, C_E1=15, C_E2=18, C_E3=21) and is performed over 100–220 K, but the magnetic specific heat C_mag is extracted and analyzed down to 2 K and up to 100 K. The validity of the lattice subtraction outside the fit range is not discussed. Given that the weak anomalies at T_H, T_L, and T_N are all identified from C_mag, the sensitivity of these features to the choice of lattice model and fit range should be addressed.
minor comments (7)
  1. §III E, Fig. 5(c) caption: The text refers to 'Fig. 2(c)' when discussing the Gaussian relaxation rate σ(T), but this should be 'Fig. 5(c)'.
  2. §III B: The Curie–Weiss temperature is reported as θ_CW = −104 K in the text but −102 K in Table II. Please reconcile.
  3. §III B: The frustration parameter is given as f ≈ 20 in the text but the abstract and Table III should be checked for consistency (Table III lists f ≈ 20 for KFMPO, which is consistent).
  4. §III D: The ESR g-factor reaches g = 2.56 at 9 K. The authors note this should be taken as an 'effective parameter,' but the physical meaning of such a large effective g-value for Fe³⁺ could be briefly elaborated.
  5. §IV, Table III: The entry for Pb₁.₅Fe₂(PO₄)₃ lists T_N and C_mag broad peak with dashes; if these quantities are unknown, stating 'not reported' would be clearer.
  6. §III E: The mean-field estimate J = 3k_B θ_CW / [2zS(S+1)] = 2.97 K uses z=6. The choice of z=6 should be justified given the multiple exchange paths (J1–J5) discussed in §III A.
  7. The abstract uses 'suggests' for the field-induced spin-liquid claim while the conclusion uses 'raises the possibility.' The language should be consistent and appropriately hedged throughout.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for a careful and constructive report. The referee raises three major comments concerning: (1) the field-induced spin-liquid claim, (2) limitations of the μSR persistent-spin-dynamics conclusion, and (3) the validity of the lattice specific heat subtraction outside the fit range. We address each point below. In brief, we agree that the spin-liquid claim should be substantially softened and that the μSR caveats should be stated explicitly; we also provide additional justification for the lattice subtraction and will add further discussion in the revised manuscript.

read point-by-point responses

  1. Referee: §V (Conclusion) and Abstract: The claim that suppression of T_N under μ₀H ≥ 2 T 'suggests' or 'raises the possibility of' field-induced spin-liquid behavior is not supported by the evidence presented. Field suppression of a λ-anomaly in χ(T) is generic to weak canted antiferromagnets and does not distinguish a cooperative spin liquid from a trivially polarized paramagnet. The authors themselves attribute the weak ordering to 'subleading anisotropic or residual interactions' atop dominant Heisenberg exchange (§I, §V), in which case Zeeman suppression of T_N is expected regardless of the nature of the field-suppressed phase. No field-dependent specific heat, neutron scattering under field, or entanglement witness is provided. This claim should be either removed or substantially softened to a statement that the field suppression reflects the weakness of the ordering interaction, not that it

    Authors: The referee is correct. We agree that field suppression of T_N in a weak canted antiferromagnet is expected from Zeeman competition with a subleading ordering interaction and does not, by itself, constitute evidence for a field-induced spin liquid. Our manuscript does not provide field-dependent specific heat, field-dependent neutron scattering, or any entanglement witness that would distinguish a cooperative spin liquid from a trivially polarized paramagnet. We will revise both the abstract and the conclusion to remove the claim that field suppression 'suggests' or 'raises the possibility of' field-induced spin-liquid behavior. The revised text will state that the field suppression reflects the weakness of the ordering interaction relative to the dominant Heisenberg exchange, and that further experiments (field-dependent specific heat, neutron scattering under field) would be needed to determine the nature of the field-suppressed phase. We will retain the statement that KFMPO is a promising candidate for future studies of field-tuned magnetism on the trillium lattice, but without implying that the present data establish or even suggest a spin-liquid regime. revision: yes

  2. Referee: §III E: The μSR data underpinning the 'persistent spin dynamics' claim are subject to two acknowledged limitations that weaken the conclusion. First, the Gaussian rate σ ≈ 14 μs⁻¹ reaches the instrument resolution limit at ISIS (acknowledged by the authors), so the low-T σ plateau may reflect instrumental limits rather than a physical saturation. Second, the LF decoupling field of 3200 Oe is below the estimated internal field width (~3800 Oe), so the persistence of relaxation at 110 mK is expected from incomplete decoupling alone and does not uniquely demonstrate active dynamics. The authors should explicitly state these as caveats on the persistent-dynamics conclusion rather than presenting it as firmly established.

    Authors: We agree that both limitations should be stated explicitly as caveats on the persistent-spin-dynamics conclusion. In the current manuscript, we do acknowledge that σ ≈ 14 μs⁻¹ approaches the ISIS time-resolution limit and that the 3200 Oe longitudinal field is below the estimated internal field width of ~3800 Oe. However, these caveats are embedded in the body of the text and are not clearly flagged as constraints on the persistent-dynamics conclusion itself. In the revised manuscript, we will add an explicit caveat statement, likely at the end of §III E or in §IV, noting that: (i) the σ plateau at low temperatures may partly reflect the instrumental resolution limit of the pulsed muon source rather than a purely physical saturation, and (ii) the persistence of relaxation at 110 mK under 3200 Oe is consistent with incomplete decoupling given the estimated internal field width, and therefore does not uniquely demonstrate active spin dynamics. We will accordingly soften the conclusion from 'confirm the persistence of dynamic spin fluctuations' to language indicating that the μSR data are 'consistent with' persistent spin dynamics but cannot unambiguously establish it given these experimental limitations. We note that the finite Lorentzian fraction f at low temperatures provides a complementary indication of a dynamic relaxation channel, but we agree this is not definitive given the decoupling issue. revision: yes

  3. Referee: §III C, Eq. (1): The lattice specific heat fit uses fixed weighting coefficients (C_D=3, C_E1=15, C_E2=18, C_E3=21) and is performed over 100–220 K, but the magnetic specific heat C_mag is extracted and analyzed down to 2 K and up to 100 K. The validity of the lattice subtraction outside the fit range is not discussed. Given that the weak anomalies at T_H, T_L, and T_N are all identified from C_mag, the sensitivity of these features to the choice of lattice model and fit range should be addressed.

    Authors: This is a fair concern. The lattice fit is performed over 100–220 K, where the magnetic contribution is small relative to the phonon contribution (|θ_CW| ≈ 104 K, but the magnetic entropy above 100 K is a small fraction of R ln 6, as shown in the entropy plot). The use of fixed weighting coefficients (C_D = 3, C_E1 = 15, C_E2 = 18, C_E3 = 21) is motivated by the expected distribution of 3 acoustic modes and (3n − 3) optical phonon branches for n atoms per formula unit; these coefficients are not freely varied but are constrained by the crystal structure. The extrapolation of this phonon model to temperatures below 100 K is standard practice for insulating magnets where the phonon contribution is smooth and monotonic. Nevertheless, we agree that the sensitivity of the weak C_mag features to the lattice model choice should be discussed. In the revised manuscript, we will add the following: (i) a statement justifying the extrapolation of the lattice model below 100 K based on the smooth, monotonic phonon contribution and the negligible magnetic entropy above 100 K; (ii) a note that the qualitative features in C_mag (the hump near T_H, the broad maximum near T_L, and the change of slope near T_N) are robust against reasonable variations in the lattice parameters, as they appear as deviations from a smooth background; and (iii) an acknowledgment that the quantitative magnitude of C_mag at low temperatures depends on the lattice subtraction and that the weak anomalies at T_N and T* are small perturbations on top of the extracted C_mag. If the referee or editors consider it necessary, we can also add a supplementary figure showing C_mag obtained with slightly varied lattice parameters to demonstrate the robustness of the qualitative features. revision: partial

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity found; the paper is primarily experimental with self-citations used for context, not as load-bearing premises.

full rationale

The paper reports independent experimental measurements (magnetization, specific heat, ESR, μSR) on K₂Fe₂(MoO₄)(PO₄)₂. The key results—T_N = 5.2 K, T_H = 34 K, T_L = 10 K, persistent spin dynamics, field suppression of T_N—are all directly observed quantities, not predictions derived from fitted parameters. The Curie-Weiss fit (θ_CW = -104 K) is a standard analysis of high-temperature susceptibility data. The mean-field θ_CW estimate in Sec. IV uses exchange constants from an external group (Ref. [28], KSrFe₂(PO₄)₃) and is presented as a qualitative cross-check, not a first-principles prediction. The μSR internal field width estimate (Δ/γ_μ ≈ 3800 Oe) derives from θ_CW via a standard mean-field expression, but the persistent-dynamics conclusion comes from the direct observation of incomplete decoupling at 3200 Oe, not from the estimate itself. Self-citations (Refs. [8], [25], [29]) involve overlapping authors but are used for phenomenological comparison and background context; none define the present results. The field-induced spin-liquid claim is explicitly hedged as a suggestion ('raises the possibility'), not a derivation. No step in the chain reduces to its inputs by construction. The minor self-citation (Ref. [29]) for μSR phenomenology comparison warrants a score of 1 rather than 0, but it is not load-bearing for any central claim.

Assumptions & free parameters 3 free parameters · 3 assumptions · 0 invented entities

No new particles, forces, or entities are postulated. The analysis relies on standard condensed matter physics models and the known crystal structure.

free parameters (3)
  • Lattice specific heat weights (C_D, C_E1, C_E2, C_E3) = 3, 15, 18, 21 (fixed)
    Fixed weighting coefficients in the Debye+Einstein fit to phonon specific heat (Sec. III C, Eq. 1), affecting the extraction of C_mag.
  • Debye and Einstein temperatures = θ_D=162 K, θ_E1=583 K, θ_E2=264 K, θ_E3=1306 K
    Fitted parameters in the lattice specific heat model (Sec. III C).
  • μSR asymmetry parameters A_0 and A_bg = 0.293 and 0.079 (fixed)
    Fixed in the μSR fit (Sec. III E, Eq. 2-3) to reduce free parameters.
assumptions (3)
  • domain assumption Fe³⁺ ions (S=5/2) form a double trillium lattice in the P2₁3 space group.
    Structural basis for the entire analysis, established by Rietveld refinement (Sec. III A).
  • domain assumption The Goodenough-Kanamori-Anderson rules provide qualitative indication of exchange hierarchy despite not being directly applicable to super-superexchange.
    Used to infer the hierarchy of J1-J5 interactions from bond angles (Sec. III A, Table II).
  • domain assumption The two-component μSR relaxation function (Eq. 3) correctly separates quasistatic and dynamic relaxation channels.
    The interpretation of persistent spin dynamics depends on this model choice (Sec. III E).

how reviews work

0 comments
Cite this review

Pith. "Pith review of Multistage development of short-range spin correlations and weak magnetic order in the two coupled trillium lattices of K2Fe2(MoO4)(PO4)2." pith.science (2026). https://pith.science/paper/6H2BWO3P

@misc{pith2026260707681,
  author       = {Pith},
  title        = {Pith review of: Multistage development of short-range spin correlations and weak magnetic order in the two coupled trillium lattices of K2Fe2(MoO4)(PO4)2},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6H2BWO3P}},
  note         = {Machine review of arXiv:2607.07681}
}
abstract

Trillium lattices, where magnetic ions form a chiral network of corner-sharing triangles, offer a three-dimensional magnetic framework that can host fragile classical spin-liquid states. Herein, we report on the magnetization, specific heat, electron spin resonance (ESR), and muon spin relaxation ($\mu$SR) of K$_{2}$Fe$_{2}$(MoO$_{4}$)(PO$_{4}$)$_{2}$ single crystals. Magnetization measurements reveal strong antiferromagnetic interactions coexisting with weak magnetic order at $T_{\rm N} = 5.2$~K, as evidenced by a $\lambda$-like anomaly observed in the magnetic susceptibility, a critical enhancement of the muon spin relaxation rate and the wipeout of the ESR signal as the temperature approaches $T_{\rm N}$. Above $T_{\rm N}$, two distinct developments of short-range spin correlations are identified at $T_{\rm H} = 34$~K and $T_{\rm L} = 10$~K, supported by magnetic specific heat anomalies and the temperature dependence of the ESR linewidth and $g$-factor. Upon cooling below $T_{\rm N}$, an anomaly appears at $T^{*} = 3.2$~K in thermodynamic observables and the muon spin relaxation rate, indicative of spin reorientation driven by residual interactions. Despite the presence of magnetic order, $\mu$SR experiments reveal dynamically fluctuating spins persisting even in the ordered state. Moreover, the suppression of $T_{\rm N}$ under applied magnetic fields ($\mu_{0}H \geq 2$~T) suggests that K$_{2}$Fe$_{2}$(MoO$_{4}$)(PO$_{4}$)$_{2}$ constitutes a promising candidate for exploring field-induced spin-liquid behavior in three-dimensionally coupled trillium lattices.

Figures

Figures reproduced from arXiv: 2607.07681 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Rietveld refinement of the powder X-ray diffraction pattern collected at room temperature. The colored curves [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) Temperature dependence of the magnetic susceptibility [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a)Temperature dependence of the specific heat at several magnetic fields. The solid orange line represents the lattice [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Selected ESR spectra at [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. (a) Time evolution of the zero-field muon spin asymmetry at selected temperatures. (b) Temperature dependence of [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

60 extracted references · 60 canonical work pages

  1. [1]

    crystal orientation (Fig. 4(a)). A single resonance feature is observed atT= 280 K and it gets broader as the temperature decreases toT L. BelowT= 9 K, close toT L whereC mag(T) exhibits a broad maximum, the signal becomes excessively broadened over the entire field range, and no well-defined resonance is observed, indicating the development of critical s...

    work page 2023

  2. [2]

    Khatua, B

    J. Khatua, B. Sana, A. Zorko, M. Gomilˇ sek, K. Sethu- pathi, M. R. Rao, M. Baenitz, B. Schmidt, and P. Khuntia, Experimental signatures of quantum and topological states in frustrated magnetism, Phys. Rep. 1041, 1 (2023)

    work page 2023

  3. [3]

    Balents, Spin liquids in frustrated magnets, Nature 464, 199 (2010)

    L. Balents, Spin liquids in frustrated magnets, Nature 464, 199 (2010)

    work page 2010

  4. [4]

    P. W. Anderson, Resonating valence bonds: A new kind of insulator?, Mater. Res. Bull.8, 153 (1973)

    work page 1973

  5. [5]

    Savary and L

    L. Savary and L. Balents, Quantum spin liquids: a re- view, Rep. Prog. Phys.80, 016502 (2016)

    work page 2016

  6. [6]

    Broholm, R

    C. Broholm, R. J. Cava, S. A. Kivelson, D. G. Nocera, M. R. Norman, and T. Senthil, Quantum spin liquids, Science367, eaay0668 (2020)

    work page 2020

  7. [7]

    Glittum, A

    C. Glittum, A. ˇStrkalj, D. Prabhakaran, P. A. Goddard, C. D. Batista, and C. Castelnovo, A resonant valence bond spin liquid in the dilute limit of doped frustrated mott insulators, Nat. Phys.21, 1211 (2025)

    work page 2025

  8. [8]

    J. M. Hopkinson and H.-Y. Kee, Geometric frustration inherent to the trillium lattice, a sublattice of the B20 structure, Phys. Rev. B74, 224441 (2006)

    work page 2006

Show all 60 references
  1. [9]

    Khatua and K.-Y

    J. Khatua and K.-Y. Choi, Frustration and chirality in three-dimensional trillium lattices: insights and perspec- tives, J. Phys.: Condens. Matter37, 483001 (2025)

    2025

  2. [10]

    J. M. Bulled, J. A. M. Paddison, A. Wildes, E. Lhotel, S. J. Cassidy, B. Pato-Dold´ an, L. C. G´ omez-Aguirre, P. J. Saines, and A. L. Goodwin, Geometric frustration on the trillium lattice in a magnetic metal-organic framework, Phys. Rev. Lett.128, 177201 (2022)

    2022

  3. [11]

    ˇZivkovi´ c, V

    I. ˇZivkovi´ c, V. Favre, C. Salazar Mejia, H. O. Jeschke, A. Magrez, B. Dabholkar, V. Noculak, R. S. Freitas, M. Jeong, N. G. Hegde, L. Testa, P. Babkevich, Y. Su, P. Manuel, H. Luetkens, C. Baines, P. J. Baker, J. Wos- nitza, O. Zaharko, Y. Iqbal, J. Reuther, and H. M. Rønno...

    2021

  4. [12]

    M.-H. Li, S. Biswas, and S. A. Parameswaran, Classifi- cation of spin- 1 2 fermionic quantum spin liquids on the trillium lattice, Phys. Rev. B112, 104429 (2025)

    2025

  5. [13]

    Biswas, Y

    S. Biswas, Y. H. Kwan, and S. A. Parameswaran, Be- yond the freshman’s dream: Classical fractal spin liquids from matrix cellular automata in three-dimensional lat- tice models, Phys. Rev. B105, 224410 (2022)

    2022

  6. [14]

    H. Yan, O. Benton, R. Moessner, and A. H. Nevidom- skyy, Classification of classical spin liquids: Typology and resulting landscape, Phys. Rev. B110, L020402 (2024)

    2024

  7. [15]

    H. Yan, O. Benton, A. H. Nevidomskyy, and R. Moess- ner, Classification of classical spin liquids: Detailed for- malism and suite of examples, Phys. Rev. B109, 174421 (2024)

    2024

  8. [16]

    Fancelli, R

    A. Fancelli, R. Flores-Calder´ on, O. Benton, B. Lake, R. Moessner, and J. Reuther, Fragile spin liquid in three dimensions, Phys. Rev. B111, 134413 (2025)

    2025

  9. [17]

    Castelnovo, R

    C. Castelnovo, R. Moessner, and S. Sondhi, Spin ice, fractionalization, and topological order, Annu. Rev. Con- dens. Matter Phys.3, 35 (2012)

    2012

  10. [18]

    M. G. Gonzalez and J. Reuther, Spin liquids on the tetra- trillium lattice, Phys. Rev. B113, 054430 (2026)

    2026

  11. [19]

    Matsumura, C

    T. Matsumura, C. Tabata, K. Kaneko, H. Nakao, M. Kakihana, M. Hedo, T. Nakama, and Y.¯Onuki, Single helicity of the triple-qtriangular skyrmion lattice state in the cubic chiral helimagnet EuPtSi, Phys. Rev. B109, 174437 (2024)

    2024

  12. [20]

    Yambe and S

    R. Yambe and S. Hayami, Anisotropic spin model and multiple-Q states in cubic systems, Phys. Rev. B107, 174408 (2023)

    2023

  13. [21]

    M¨ uhlbauer, B

    S. M¨ uhlbauer, B. Binz, F. Jonietz, C. Pfleiderer, A. Rosch, A. Neubauer, R. Georgii, and P. B¨ oni, Skyrmion lattice in a chiral magnet, Science323, 915 (2009)

    2009

  14. [22]

    Rousseau, G

    S. Rousseau, G. Seyfarth, G. Knebel, D. Aoki, Y. ¯Onuki, and A. Pourret, Metastability of the topological magnetic orders in the chiral antiferromagnet EuPtSi, Phys. Rev. B113, 115160 (2026)

    2026

  15. [23]

    N. Higa, T. U. Ito, M. Yogi, T. Hattori, H. Sakai, S. Kambe, Z. Guguchia, W. Higemoto, M. Nakashima, Y. Homma, A. Nakamura, F. Honda, Y. Shimizu, D. Aoki, M. Kakihana, M. Hedo, T. Nakama, Y. ¯Onuki, and Y. Tokunaga, Critical slowing-down and field- dependent paramagnetic fluct...

    2021

  16. [24]

    K. Boya, K. Nam, K. Kargeti, A. Jain, R. Kumar, S. K. Panda, S. M. Yusuf, P. L. Paulose, U. K. Voma, E. Ker- marrec, K. H. Kim, and B. Koteswararao, Signatures of spin-liquid state in a 3D frustrated lattice compound KSrFe2(PO4)3 with S = 5/2, APL Materials10, 101103 (2022)

    2022

  17. [25]

    W. Yao, Q. Huang, T. Xie, A. Podlesnyak, A. Brassing- ton, C. Xing, R. S. D. Mudiyanselage, H. Wang, W. Xie, 13 S. Zhang, M. Lee, V. S. Zapf, X. Bai, D. A. Tennant, J. Liu, and H. Zhou, Continuous spin excitations in the three-dimensional frustrated magnet K2Ni2(SO4)3, Phys. R...

    2023

  18. [26]

    Khatua, S

    J. Khatua, S. Lee, G. Ban, M. Uhlarz, G. S. Muru- gan, R. Sankar, B. Hitti, G. Morris, K.-Y. Choi, and P. Khuntia, Magnetism and spin dynamics of thes= 3 2 frustrated trillium lattice compound K 2CrTi(PO4)3, Phys. Rev. B109, 184432 (2024)

    2024

  19. [27]

    Magar, K

    A. Magar, K. Somesh, M. P. Saravanan, J. Sichelschmidt, Y. Skourski, M. T. F. Telling, V. A. Ginga, A. A. Tsirlin, and R. Nath, Proximate spin-liquid behavior in the dou- ble trillium lattice antiferromagnet K 2Co2(SO4)3, Phys. Rev. B113, L020409 (2026)

    2026

  20. [28]

    M. G. Gonzalez, V. Noculak, A. Sharma, V. Favre, J.-R. Soh, A. Magrez, R. Bewley, H. O. Jeschke, J. Reuther, H. M. Rønnow, Y. Iqbal, and I. ˇZivkovi´ c, Dynamics of K2Ni2(SO4)3 governed by proximity to a 3D spin liquid model, Nat. Commun.15, 7191 (2024)

    2024

  21. [29]

    S. J. Sebastian, Q.-P. Ding, A. A. Tsirlin, R. Nath, and Y. Furukawa, Short-range spin freezing in the double tril- lium lattice spin-liquid candidate KSrFe2(PO4)3 revealed via 31P NMR, Phys. Rev. B112, L220406 (2025)

    2025

  22. [30]

    Khatua, S

    J. Khatua, S. Krishnamoorthi, C. Koo, G. Ban, T. Kim, S. Kim, Y. Oshima, J. A. Krieger, T. J. Hicken, H. Luetkens, M. Uhlarz, E. Mun, K. J. Lee, S. H. Chang, R. Sankar, and K.-Y. Choi, Coexistence of anomalous spin dynamics and weak magnetic order in the chiral tril- lium latt...

    2025

  23. [31]

    J. Khatua et al; (2025): Possible chiral classical spin liq- uid ground state in a tetra-trillium lattice antiferromag- net K2Fe2(MoO4)(PO4)2, STFC ISIS Neutron and Muon Source, https://doi.org/10.5286/ISIS.E.RB2510135

    2025 doi

  24. [32]

    Pratt, Wimda: a muon data analysis program for the windows pc, Physica B Condens

    F. Pratt, Wimda: a muon data analysis program for the windows pc, Physica B Condens. Matter289-290, 710 (2000)

    2000

  25. [33]

    N. S. Slobodyanik, K. V. Terebilenko, I. V. Ogorod- nyk, I. V. Zatovsky, M. Seredyuk, V. N. Baumer, and P. G¨ utlich, K2MIII 2(MVIO4)(PO4)2 (MIII = Fe, Sc; M vi = Mo, W), Novel members of the lagbeinite-related fam- ily: Synthesis, structure, and magnetic properties, Inorg. Ch...

    2012

  26. [34]

    Jeong and W

    T. Jeong and W. E. Pickett, Implications of the b20 crys- tal structure for the magnetoelectronic structure of MnSi, Phys. Rev. B70, 075114 (2004)

    2004

  27. [35]

    Kittel and P

    C. Kittel and P. McEuen,Introduction to solid state physics(Vol. 8, John Wiley & Sons, 1976)

    1976

  28. [36]

    Okuma, T

    R. Okuma, T. Yajima, D. Nishio-Hamane, T. Okubo, and Z. Hiroi, Weak ferromagnetic order breaking the threefold rotational symmetry of the underlying kagome lattice in CdCu 3(OH)6(NO3)2·H2O, Phys. Rev. B95, 094427 (2017)

    2017

  29. [37]

    Go˜ ni, L

    A. Go˜ ni, L. Lezama, N. O. Moreno, L. Fourn` es, R. Olazcuaga, G. E. Barberis, and T. Rojo, Spectro- scopic and magnetic properties ofα-Li 3Fe2(PO4)3: a two-sublattice ferrimagnet, Chem. Mater.12, 62 (2000)

    2000

  30. [38]

    Klingeler, N

    R. Klingeler, N. Leps, I. Hellmann, A. Popa, U. Stock- ert, C. Hess, V. Kataev, H.-J. Grafe, F. Hammerath, G. Lang, S. Wurmehl, G. Behr, L. Harnagea, S. Singh, and B. B¨ uchner, Local antiferromagnetic correlations in the iron pnictide superconductors LaFeAsO 1 –xFx and Ca(Fe1...

    2010

  31. [39]

    Aruga Katori and A

    H. Aruga Katori and A. Ito, Experimental study of the de almeida-thouless line by using typical ising spin-glass FexMn1 –xTiO3 withx= 0.41, 0.50, 0.55 and 0.57, J. Phys. Soc. Jpn.63, 3122 (1994)

    1994

  32. [40]

    Khatua, M

    J. Khatua, M. Gomilˇ sek, K.-Y. Choi, and P. Khuntia, Magnetism and field-induced effects in the s = 5/2 hon- eycomb lattice antiferromagnet FeP3SiO11, Phys. Rev. B 110, 184402 (2024)

    2024

  33. [41]

    P. Popp, A. P. Ramirez, and S. Syzranov, Origin of the hidden energy scale and thefratio in geometrically frus- trated magnets, Phys. Rev. Lett.134, 226701 (2025)

    2025

  34. [42]

    A. P. Ramirez, B. Hessen, and M. Winklemann, Entropy balance and evidence for local spin singlets in a kagom´ e- like magnet, Phys. Rev. Lett.84, 2957 (2000)

    2000

  35. [43]

    J. L. Mesa, A. Go˜ ni, A. L. Brandl, N. O. Moreno, G. E. Barberis, and T. Rojo, Structure and magnetic proper- ties of Li 3Fe2(AsO4)3 –x(PO4)x (x≈0,1,1.5,2): two sublattice weak ferromagnets, J. Mater. Chem.10, 2779 (2000)

    2000

  36. [44]

    Wulferding, K.-Y

    D. Wulferding, K.-Y. Choi, P. Lemmens, A. N. Pono- maryov, J. van Tol, A. T. M. Nazmul Islam, S. Toth, and B. Lake, Softened magnetic excitations in the s = 3/2 distorted triangular antiferromagnetα-CaCr2O4, J. Phys.: Condens. Matter24, 435604 (2012)

    2012

  37. [45]

    Sperlich, K

    G. Sperlich, K. H. Janneck, and K. H. J. Buschow, Exchange narrowing in the ESR spectra of metallic GdxLa1 –xB6 (x= 1 to 0.01), Phys. Status Solidi b57, 701 (1973)

    1973

  38. [46]

    Y. J. Uemura, T. Yamazaki, D. R. Harshman, M. Senba, and E. J. Ansaldo, Muon-spin relaxation in AuFe and CuMn spin glasses, Phys. Rev. B31, 546 (1985)

    1985

  39. [47]

    Simutis, L

    G. Simutis, L. Su´ arez-Garc´ ıa, H. Zeroual, I. Villa, M. Georgopoulou, D. Boldrin, D. Chatterjee, C. N. Wang, C. Baines, T. Shiroka, R. Khasanov, H. Luetkens, B. F˚ ak, Y. Sassa, M. Bartkowiak, A. S. Wills, E. Kermar- rec, F. Bert, and P. Mendels, Fluctuating magnetism in zn...

    2025

  40. [48]

    M. L. Brooks, T. Lancaster, S. J. Blundell, W. Hayes, F. L. Pratt, and Z. Fisk, Magnetic phase separation in EuB6 detected by muon spin rotation, Phys. Rev. B70, 020401 (2004)

    2004

  41. [49]

    S. A. Dodds, G. A. Gist, D. E. MacLaughlin, R. H. Heffner, M. Leon, M. E. Schillaci, G. J. Nieuwenhuys, and J. A. Mydosh, Muon spin relaxation in a random ferromagnet: PdMn, Phys. Rev. B28, 6209 (1983)

    1983

  42. [50]

    J. Lago, M. J. Rosseinsky, S. J. Blundell, P. D. Battle, M. Diaz, I. Uriarte, and T. Rojo, Critical behavior in the inhomogeneous ferromagnet SrFe 0·80 Co0·20 O3·0, Phys. Rev. B83, 104404 (2011)

    2011

  43. [51]

    V. V. Krishnamurthy, I. Watanabe, K. Nagamine, H. Kuwahara, and Y. Tokura, Critical spin dynamics in Nd1 –xSrxMnO3 withx≈0.5, Phys. Rev. B61, 4060 (2000)

    2000

  44. [52]

    Y. J. Uemura, A. Keren, K. Kojima, L. P. Le, G. M. Luke, W. D. Wu, Y. Ajiro, T. Asano, Y. Kuriyama, M. Mekata, H. Kikuchi, and K. Kakurai, Spin fluctuations in frus- trated kagom´ e lattice system SrCr8Ga4O19 studied by muon spin relaxation, Phys. Rev. Lett.73, 3306 (1994)

    1994

  45. [53]

    K. Boya, V. Sahu, R. Kumar, P. Paulose, and B. Koteswararao, Spin disorder state in a site-depleted 3d coupled trillium spin-lattice system Pb 1.5Fe2(PO4)3, J. Magn. Magn. Mater.629, 173302 (2025). 14

    2025

  46. [54]

    Vojta, Disorder in quantum many-body systems, Annu

    T. Vojta, Disorder in quantum many-body systems, Annu. Rev. Condens. Matter Phys.10, 233 (2019)

    2019

  47. [55]

    Letouz´ e, P

    C. Letouz´ e, P. Viot, and L. Messio, Emergence of chiral order driven by quenched disorder, Phys. Rev. Lett.135, 186504 (2025)

    2025

  48. [56]

    Okada, H

    S. Okada, H. Suzuki, N. Higa, Y. Shimura, T. Taniguchi, and T. Onimaru, Ferromagnetic order of reduced mag- netic moments in a frustrated sawtooth chain of the mag- netic semiconductor ZnYb 2S4, J. Phys. Soc. Jpn.95, 074706 (2026)

    2026

  49. [57]

    H. Lane, K. Barros, and M. Mourigal, Classical signa- tures of quenched and thermal disorder in the dynamics of correlated spin systems, J. Phys.: Condens. Matter. 37, 265802 (2025)

    2025

  50. [58]

    P. D. Battle, A. K. Cheetham, W. T. Harrison, and G. J. Long, The crystal structure and magnetic properties of the synthetic langbeinite KBaFe 2(PO4)3, J. Solid State Chem.62, 16 (1986)

    1986

  51. [59]

    M. G. Gonzalez, Y. Iqbal, J. Reuther, and H. O. Jeschke, Field-induced spin liquid in the decorated square-kagome antiferromagnet nabokoite KCu 7TeO4(SO4)5Cl, Com- munications Materials6, 96 (2025)

    2025

  52. [60]

    Pokharel, H

    G. Pokharel, H. S. Arachchige, T. J. Williams, A. F. May, R. S. Fishman, G. Sala, S. Calder, G. Ehlers, D. S. Parker, T. Hong, A. Wildes, D. Mandrus, J. A. M. Pad- dison, and A. D. Christianson, Cluster frustration in the breathing pyrochlore magnet LiGaCr 4S8, Phys. Rev. Lett...

    2020

Pith tools

Reviewed July 9, 2026 · model on record in the stance chip above.