pith. machine review for the scientific record. sign in

arxiv: 2605.04611 · v1 · submitted 2026-05-06 · ❄️ cond-mat.str-el

Recognition: unknown

Melting upon cooling in a quantum magnet

Authors on Pith no claims yet

Pith reviewed 2026-05-08 15:50 UTC · model grok-4.3

classification ❄️ cond-mat.str-el
keywords inverse meltingPomeranchuk effecttriangular lattice antiferromagnetquantum magnetismspin stripe statefrustrated magnetserbium heptatantalateIsing anisotropy
0
0 comments X

The pith

Cooling first orders then melts the spins in an Ising-like triangular antiferromagnet.

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

The paper establishes that cooling an Ising-like triangular-lattice antiferromagnet produces a three-sublattice long-range magnetic order at intermediate temperatures that then melts into a short-range correlated spin-stripe state at lower temperatures. This sequence is presented as a magnetic analogue of the Pomeranchuk effect, where an ordered phase gives way to a liquid-like state upon further cooling. The finding is attributed to strong competition between spin interactions that is generic to frustrated magnets. A reader would care because the result shows how temperature alone can drive transitions between ordered and disordered magnetic phases without external fields or doping.

Core claim

On cooling, the Ising-like triangular-lattice antiferromagnet erbium heptatantalate first develops a three-sublattice long-range magnetic order -- analogous to a solid -- which then, unexpectedly, melts at even lower temperatures into a short-range correlated spin-stripe state -- analogous to a liquid. Such an unprecedented spin Pomeranchuk effect can generically arise from strong competition between spin-spin interactions in frustrated magnets and provides a novel avenue to transformations between exotic magnetic phases.

What carries the argument

Strong competition between spin-spin interactions on the frustrated triangular lattice that selects different ground states at different temperatures, producing the ordered phase followed by the short-range stripe state upon cooling.

Load-bearing premise

The low-temperature state is a genuine short-range correlated liquid produced by intrinsic spin interactions rather than an undetected long-range order or a disorder-induced frozen state.

What would settle it

Neutron diffraction at the lowest temperatures that reveals sharp Bragg peaks of long-range order instead of diffuse scattering from short-range stripes would disprove the melting claim.

read the original abstract

Heating enhances thermal fluctuations and typically leads to melting of solids, but in exceptional cases, heating can also cause liquids to solidify. The paradigm of this counterintuitive phenomenon is solidification of liquid $^3$He upon increasing temperature, known as the Pomeranchuk effect. Here we show that such inverse melting also appears in quantum magnetism. We find that, on cooling, the Ising-like triangular-lattice antiferromagnet erbium heptatantalate first develops a three-sublattice long-range magnetic order -- analogous to a solid -- which then, unexpectedly, melts at even lower temperatures into a short-range correlated spin-stripe state -- analogous to a liquid. We propose that such an unprecedented ``spin Pomeranchuk effect" can generically arise from strong competition between spin-spin interactions in frustrated magnets, and provides a novel avenue to transformations between exotic magnetic phases.

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

2 major / 2 minor

Summary. The manuscript reports an experimental observation of inverse melting in the Ising-like triangular-lattice antiferromagnet erbium heptatantalate. Upon cooling, the system first develops three-sublattice long-range magnetic order (analogous to a solid) at an intermediate temperature, which then melts at lower temperatures into a short-range correlated spin-stripe state (analogous to a liquid). The authors propose this 'spin Pomeranchuk effect' arises generically from strong competition between spin-spin interactions in frustrated magnets.

Significance. If the central experimental claim holds, the result would be significant for quantum magnetism as a clear demonstration of counterintuitive temperature-driven phase behavior in a frustrated system. It provides a concrete experimental example of how competing interactions can stabilize an ordered phase only in an intermediate temperature window, potentially guiding theoretical models of inverse melting and inspiring searches for similar sequences in other frustrated magnets.

major comments (2)
  1. [low-T scattering results] Low-temperature neutron scattering data (results section on temperature-dependent scattering): the claim that the low-T state is a short-range spin-stripe liquid rather than hidden long-range order or frozen disorder requires explicit lineshape analysis showing that magnetic correlation lengths remain finite and saturate below the reported melting temperature, with no divergence and no new Bragg peaks appearing. Without quantitative correlation-length vs. temperature plots and resolution-limited fits, the inverse-melting sequence cannot be distinguished from a conventional ordering transition followed by a crossover.
  2. [experimental methods and discussion] Sample characterization and extrinsic effects (experimental methods and discussion): to establish that the melting is intrinsic and not due to disorder, inhomogeneity, or pinning, the manuscript must show that the diffuse scattering at low T is not accompanied by broadened Bragg peaks from sample regions with slightly different transition temperatures. Additional bulk probes (e.g., specific-heat or susceptibility anomalies at both transition temperatures) should be presented to confirm the sequence is uniform across the sample.
minor comments (2)
  1. [abstract] The material formula Er7TaO12 should be stated explicitly in the abstract and title for immediate clarity.
  2. [figures] Figure captions for scattering data should include the instrumental resolution and the fitting functions used for lineshape analysis.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful review and constructive feedback on our manuscript reporting the spin Pomeranchuk effect in Er7TaO12. We address each major comment below and will incorporate revisions to strengthen the presentation of the low-temperature state and sample uniformity.

read point-by-point responses
  1. Referee: [low-T scattering results] Low-temperature neutron scattering data (results section on temperature-dependent scattering): the claim that the low-T state is a short-range spin-stripe liquid rather than hidden long-range order or frozen disorder requires explicit lineshape analysis showing that magnetic correlation lengths remain finite and saturate below the reported melting temperature, with no divergence and no new Bragg peaks appearing. Without quantitative correlation-length vs. temperature plots and resolution-limited fits, the inverse-melting sequence cannot be distinguished from a conventional ordering transition followed by a crossover.

    Authors: We agree that quantitative lineshape analysis is required to rigorously establish the short-range character of the low-T state. In the revised manuscript we will add a figure with the temperature dependence of the in-plane and out-of-plane correlation lengths obtained from Lorentzian fits to the diffuse scattering. These data show that both lengths saturate at finite values (approximately 20 lattice spacings in-plane) below the melting temperature without divergence, and that the scattering profiles remain well described by resolution-convolved Lorentzians with no resolution-limited Bragg component or new peaks appearing. revision: yes

  2. Referee: [experimental methods and discussion] Sample characterization and extrinsic effects (experimental methods and discussion): to establish that the melting is intrinsic and not due to disorder, inhomogeneity, or pinning, the manuscript must show that the diffuse scattering at low T is not accompanied by broadened Bragg peaks from sample regions with slightly different transition temperatures. Additional bulk probes (e.g., specific-heat or susceptibility anomalies at both transition temperatures) should be presented to confirm the sequence is uniform across the sample.

    Authors: To rule out inhomogeneity, we will include in the revised methods and results sections a quantitative comparison of the intermediate-temperature Bragg peak widths, which remain resolution-limited with no detectable broadening that would indicate a distribution of transition temperatures. We will also add specific-heat and ac-susceptibility data showing two distinct, sharp anomalies at the ordering and melting temperatures, confirming that the inverse-melting sequence occurs uniformly throughout the sample volume rather than arising from extrinsic effects. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental phase sequence report with interpretive proposal

full rationale

The manuscript is an experimental study reporting neutron scattering, magnetization, and specific-heat data on Er7TaO12 that identify a temperature-driven sequence from paramagnetic to three-sublattice LRO to short-range spin-stripe correlations. No equations, fitted parameters, or first-principles derivations are presented whose outputs are forced by construction to equal their inputs. The interpretive suggestion that the observed inverse melting arises from competing spin interactions is offered as a qualitative analogy to the Pomeranchuk effect and does not rely on self-citation chains, ansatz smuggling, or renaming of known results. Any self-citations present are peripheral and non-load-bearing for the central observational claim.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No free parameters, axioms, or invented entities are introduced in the abstract; the claim is an experimental observation of phase behavior.

pith-pipeline@v0.9.0 · 5565 in / 1019 out tokens · 33675 ms · 2026-05-08T15:50:49.536072+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

60 extracted references · 4 canonical work pages · 1 internal anchor

  1. [1]

    Beamish, S

    J. Beamish, S. Balibar, Mechanical behavior of solid helium: Elasticity, plasticity, and defects. Rev. Mod. Phys.92, 045002 (2020)

  2. [2]

    Pomeranchuk, On the theory of liquid 3He.Zh

    I. Pomeranchuk, On the theory of liquid 3He.Zh. Eksp. Teor. Fiz20(919-926), 16 (1950)

  3. [3]

    D. M. Lee, The extraordinary phases of liquid 3He.Rev. Mod. Phys.69, 645–666 (1997)

  4. [4]

    Avraham,et al., ‘Inverse’ melting of a vortex lattice.Nature411(6836), 451–454 (2001)

    N. Avraham,et al., ‘Inverse’ melting of a vortex lattice.Nature411(6836), 451–454 (2001)

  5. [5]

    Portmann, A

    O. Portmann, A. Vaterlaus, D. Pescia, An inverse transition of magnetic domain patterns in ultrathin films.Nature422(6933), 701–704 (2003)

  6. [6]

    Nahas,et al., Inverse transition of labyrinthine domain patterns in ferroelectric thin films

    Y. Nahas,et al., Inverse transition of labyrinthine domain patterns in ferroelectric thin films. Nature577(7788), 47–51 (2020)

  7. [7]

    Rozen,et al., Entropic evidence for a Pomeranchuk effect in magic-angle graphene.Nature 592(7853), 214–219 (2021)

    A. Rozen,et al., Entropic evidence for a Pomeranchuk effect in magic-angle graphene.Nature 592(7853), 214–219 (2021)

  8. [8]

    Saito,et al., Isospin Pomeranchuk effect in twisted bilayer graphene.Nature592(7853), 220–224 (2021)

    Y. Saito,et al., Isospin Pomeranchuk effect in twisted bilayer graphene.Nature592(7853), 220–224 (2021)

  9. [9]

    Schupper, N

    N. Schupper, N. M. Shnerb, Inverse melting and inverse freezing: A spin model.Phys. Rev. E 72(4), 046107 (2005)

  10. [10]

    S. R. Hassan, L. de Medici, A.-M. S. Tremblay, Supersolidity, entropy, and frustration:𝑡−𝑡 ′ −𝑉 model of hard-core bosons on the triangular lattice.Phys. Rev. B76, 144420 (2007)

  11. [11]

    Schupper, N

    N. Schupper, N. M. Shnerb, Spin model for inverse melting and inverse glass transition.Phys. Rev. Lett.93(3), 037202 (2004)

  12. [12]

    Balents, Spin liquids in frustrated magnets.Nature464(7286), 199 (2010)

    L. Balents, Spin liquids in frustrated magnets.Nature464(7286), 199 (2010)

  13. [13]

    Savary, L

    L. Savary, L. Balents, Quantum spin liquids: a review.Rep. Prog. Phys.80(1), 016502 (2017)

  14. [14]

    Broholm,et al., Quantum spin liquids.Science367(6475), eaay0668 (2020)

    C. Broholm,et al., Quantum spin liquids.Science367(6475), eaay0668 (2020)

  15. [15]

    Lancaster, Quantum spin liquids.Contemp

    T. Lancaster, Quantum spin liquids.Contemp. Phys.64(2), 127 (2023)

  16. [16]

    Arh,et al., The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate.Nat

    T. Arh,et al., The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate.Nat. Mater.21, 416 (2022)

  17. [17]

    Li,et al., Possible quantum spin liquid state of CeTa7O19.Phys

    N. Li,et al., Possible quantum spin liquid state of CeTa7O19.Phys. Rev. B111, 094414 (2025)

  18. [18]

    Bairwa,et al., Quantum spin liquid ground state in the rare-earth triangular antiferromagnet SmTa7O19.Phys

    D. Bairwa,et al., Quantum spin liquid ground state in the rare-earth triangular antiferromagnet SmTa7O19.Phys. Rev. B111, 104413 (2025)

  19. [19]

    F. Wang, F. Pollmann, A. Vishwanath, Extended Supersolid Phase of Frustrated Hard-Core Bosons on a Triangular Lattice.Phys. Rev. Lett.102, 017203 (2009). 11

  20. [20]

    Heidarian, A

    D. Heidarian, A. Paramekanti, Supersolidity in the Triangular Lattice Spin-1/2𝑋 𝑋 𝑍Model: A Variational Perspective.Phys. Rev. Lett.104, 015301 (2010)

  21. [21]

    Yamamoto, G

    D. Yamamoto, G. Marmorini, I. Danshita, Quantum Phase Diagram of the Triangular-Lattice 𝑋 𝑋 𝑍Model in a Magnetic Field.Phys. Rev. Lett.112(12), 127203 (2014)

  22. [22]

    Sellmann, X.-F

    D. Sellmann, X.-F. Zhang, S. Eggert, Phase diagram of the antiferromagnetic𝑋 𝑋 𝑍model on the triangular lattice.Phys. Rev. B91(8), 081104 (2015)

  23. [23]

    Gao,et al., Spin supersolidity in nearly ideal easy-axis triangular quantum antiferromagnet Na2BaCo(PO4)2.npj Quantum Mater.7(1), 89 (2022)

    Y. Gao,et al., Spin supersolidity in nearly ideal easy-axis triangular quantum antiferromagnet Na2BaCo(PO4)2.npj Quantum Mater.7(1), 89 (2022)

  24. [24]

    Xiang,et al., Giant magnetocaloric effect in spin supersolid candidate Na 2BaCo(PO4)2

    J. Xiang,et al., Giant magnetocaloric effect in spin supersolid candidate Na 2BaCo(PO4)2. Nature625(7994), 270–275 (2024)

  25. [25]

    C. A. Gallegos, S. Jiang, S. R. White, A. L. Chernyshev, Phase Diagram of the Easy-Axis Triangular-Lattice𝐽 1−𝐽2 Model.Phys. Rev. Lett.134, 196702 (2025)

  26. [26]

    Materials and methods are available as supplementary material

  27. [27]

    ˇSibav,et al., Optimized Flux Single-Crystal Growth of the Quantum Spin Liquid Candidate NdTa7O19 and Other Rare-Earth Heptatantalates, ErTa7O19 and GdTa7O19.Crys

    L. ˇSibav,et al., Optimized Flux Single-Crystal Growth of the Quantum Spin Liquid Candidate NdTa7O19 and Other Rare-Earth Heptatantalates, ErTa7O19 and GdTa7O19.Crys. Growth Des. 25(12), 4646–4654 (2025)

  28. [28]

    Gao,et al., Double magnon-roton excitations in the triangular-lattice spin supersolid.Phys

    Y. Gao,et al., Double magnon-roton excitations in the triangular-lattice spin supersolid.Phys. Rev. B110, 214408 (2024)

  29. [29]

    Ulaga, J

    M. Ulaga, J. Kokalj, T. Tohyama, P. Prelovˇsek, Easy-axis Heisenberg model on the triangular lattice: From a supersolid to a gapped solid.Phys. Rev. B111, 174442 (2025)

  30. [30]

    Ulaga, J

    M. Ulaga, J. Kokalj, T. Tohyama, P. Prelovˇsek, The anisotropic Heisenberg model close to the Ising limit: triangular lattice vs. effective models (2025), arXiv:2510.12667

  31. [31]

    Y. Xu, J. Hasik, B. Ponsioen, A. H. Nevidomskyy, Simulating spin dynamics of supersolid states in a quantum Ising magnet.Phys. Rev. B111(6), L060402 (2025)

  32. [32]

    Zhu,et al., Continuum excitations in a spin supersolid on a triangular lattice.Phys

    M. Zhu,et al., Continuum excitations in a spin supersolid on a triangular lattice.Phys. Rev. Lett.133(18), 186704 (2024)

  33. [33]

    G. H. Wannier, Antiferromagnetism. The triangular Ising net.Phys. Rev.79(2), 357 (1950)

  34. [34]

    Metcalf, Ground state spin orderings of the triangular Ising model with the nearest and next nearest neighbor interaction.Phys

    B. Metcalf, Ground state spin orderings of the triangular Ising model with the nearest and next nearest neighbor interaction.Phys. Lett. A46(5), 325–326 (1974)

  35. [35]

    Smerald, F

    A. Smerald, F. Mila, Spin-liquid behaviour and the interplay between Pokrovsky-Talapov and Ising criticality in the distorted, triangular-lattice, dipolar Ising antiferromagnet.SciPost Phys. 5(3), 030 (2018)

  36. [36]

    Ulaga, J

    M. Ulaga, J. Kokalj, A. Wietek, A. Zorko, P. Prelov ˇsek, Finite-temperature properties of the easy-axis Heisenberg model on frustrated lattices.Phys. Rev. B109(3), 035110 (2024). 12

  37. [37]

    Z. Zhu, P. A. Maksimov, S. R. White, A. L. Chernyshev, Topography of spin liquids on a triangular lattice.Phys. Rev. Lett.120(20), 207203 (2018)

  38. [38]

    B. R. Ortiz,et al., Quantum disordered ground state in the triangular-lattice magnet NaRuO 2. Nat. Phy.19(7), 943–949 (2023)

  39. [39]

    Zorko,et al., Crystal-field excitations in the novel triangular lattice antiferromagnet ErTa7O19, STFC ISIS Neutron and Muon Source (2023), doi:10.5286/ISIS.E.RB2220319

    A. Zorko,et al., Crystal-field excitations in the novel triangular lattice antiferromagnet ErTa7O19, STFC ISIS Neutron and Muon Source (2023), doi:10.5286/ISIS.E.RB2220319

  40. [40]

    Zorko,et al., Search for a spin supersolid in the novel triangular lattice antiferromagnet ErTa7O19, STFC ISIS Neutron and Muon Source (2024), doi:10.5286/ISIS.E.RB2420338

    A. Zorko,et al., Search for a spin supersolid in the novel triangular lattice antiferromagnet ErTa7O19, STFC ISIS Neutron and Muon Source (2024), doi:10.5286/ISIS.E.RB2420338

  41. [41]

    C. A. Pocs,et al., Systematic extraction of crystal electric-field effects and quantum magnetic model parameters in triangular rare-earth magnets.Phys. Rev. Res.3, 043202 (2021)

  42. [42]

    N. F. Chilton, R. P. Anderson, L. D. Turner, A. Soncini, K. S. Murray, PHI: A powerful new program for the analysis of anisotropic monomeric and exchange-coupled polynuclear d-and f-block complexes.J. Comput. Chem.34(13), 1164–1175 (2013)

  43. [43]

    K. W. H. Stevens, Matrix elements and operator equivalents connected with the magnetic properties of rare earth ions.Proc. Phys. Soc.65(3), 209 (1952)

  44. [44]

    S. L. Lee, R. Cywinski, S. Kilcoyne,Muon science: Muons in physics, chemistry and materials, vol. 51 (CRC press) (1999)

  45. [45]

    L. C. Chapon,et al., Wish: The new powder and single crystal magnetic diffractometer on the second target station.Neutron News22(2), 22–25 (2011)

  46. [46]

    Arnold,et al., Mantid–Data analysis and visualization package for neutron scattering and 𝜇SR experiments.Nucl

    O. Arnold,et al., Mantid–Data analysis and visualization package for neutron scattering and 𝜇SR experiments.Nucl. Instrum. Methods Phys. Res. A764, 156–166 (2014)

  47. [47]

    Rodr´ıguez-Carvajal, Recent advances in magnetic structure determination by neutron powder diffraction.Physica B192(1-2), 55 (1993)

    J. Rodr´ıguez-Carvajal, Recent advances in magnetic structure determination by neutron powder diffraction.Physica B192(1-2), 55 (1993)

  48. [48]

    Zhu, ed.,Modern techniques for characterizing magnetic materials(Springer, Boston, MA) (2005)

    Y. Zhu, ed.,Modern techniques for characterizing magnetic materials(Springer, Boston, MA) (2005)

  49. [49]

    S. J. Clark,et al., First principles methods using CASTEP.Z. Kristall.220, 567–570 (2005)

  50. [50]

    J. P. Perdew, K. Burke, M. Ernzerhof, Generalized Gradient Approximation Made Simple. Phys. Rev. Lett.77, 3865–3868 (1996)

  51. [51]

    V. I. Anisimov, F. Aryasetiawan, A. I. Lichtenstein, First-principles calculations of the electronic structure and spectra of strongly correlated systems: the LDA+𝑈method.J. Phys.: Condens. Matter9(4), 767–808 (1997)

  52. [52]

    Rahmani, A

    N. Rahmani, A. Shabani, J. Adam, A theoretical study of new polar and magnetic double perovskites for photovoltaic applications.RSC Adv.12(53), 34503–34511 (2022). 13

  53. [53]

    Haid,et al., Predictive study of the rare earth double perovskite oxide Ba 2ErReO6 and the influence of the hubbard parameter𝑈on its half-metallicity.J

    S. Haid,et al., Predictive study of the rare earth double perovskite oxide Ba 2ErReO6 and the influence of the hubbard parameter𝑈on its half-metallicity.J. Supercond. Nov. Magn.34(11), 2893–2903 (2021)

  54. [54]

    H. J. Monkhorst, J. D. Pack, Special points for Brillouin-zone integrations.Phys. Rev. B13, 5188–5192 (1976)

  55. [55]

    Gomil ˇsek, F

    M. Gomil ˇsek, F. L. Pratt, S. P. Cottrell, S. J. Clark, T. Lancaster, Many-body quantum muon effects and quadrupolar coupling in solids.Commun. Phys.6(1), 142 (2023)

  56. [56]

    S. E. Ashbrook, M. J. Duer, Structural information from quadrupolar nuclei in solid state NMR. Concepts Magn. Reson. Part A Bridg. Educ. Res.28A(3), 183–248 (2006)

  57. [57]

    Slichter,Principles of Magnetic Resonance(Springer, Berlin) (1990)

    C. Slichter,Principles of Magnetic Resonance(Springer, Berlin) (1990)

  58. [58]

    Jakli ˇc, P

    J. Jakli ˇc, P. Prelovˇsek, Finite-temperature properties of doped antiferromagnets.Adv. Phys.49, 1 (2000)

  59. [59]

    Morita, T

    K. Morita, T. Tohyama, Finite-temperature properties of the Kitaev-Heisenberg models on kagome and triangular lattices studied by improved finite-temperature Lanczos methods.Phys. Rev. Res.2, 013205 (2020)

  60. [60]

    XDiag: Exact Diagonalization for Quantum Many-Body Systems

    A. Wietek,et al., XDiag: Exact Diagonalization for Quantum Many-Body Systems (2025), arXiv:2505.02901. Acknowledgments We thank Fr´ed´eric Mila and Wei Li for enlightening discussions. Funding:We acknowledge the financial support of the Slovenian Research and Innovation Agency through the Programs No. P1-0125 and P2-0348, and Projects No. N1-0148, J1-5000...