pith. sign in

arxiv: 2606.02501 · v1 · pith:TCQP5UFPnew · submitted 2026-06-01 · ❄️ cond-mat.str-el · cond-mat.mes-hall

Electrical observation via spin Seebeck effect of fractionalized excitations in a magnetic insulator

Nan Tang , Josef Willsher , Stephan Glamsch , Aisha Aqeel , Ludwig Scheuchenpflug , Michael Schulze , Christoph Liebald , Daniel Rytz
show 4 more authors
Christo Guguschev Manfred Albrecht Roderich Moessner Philipp Gegenwart
This is my paper

Pith reviewed 2026-06-28 12:42 UTC · model grok-4.3

classification ❄️ cond-mat.str-el cond-mat.mes-hall
keywords spin Seebeck effectmagnetic monopolesDy2Ti2O7fractionalized excitationsspin icespintronicsmagnetic insulator
0
0 comments X

The pith

Spin Seebeck effect detects a voltage peak from monopole proliferation in Dy2Ti2O7.

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

The paper shows that the spin Seebeck effect produces an electrical voltage signal with a clear peak when magnetic monopoles proliferate in the spin-ice material Dy2Ti2O7. This peak exhibits distinct frequency and angular dependence that the authors link to the fractionalized nature of the monopoles. A reader would care because the result supplies an electrical probe for excitations that are otherwise hard to access directly in three-dimensional fractionalized magnets. The work applies an existing spintronic technique to a quantum material known for its emergent monopoles rather than inventing a new detection principle.

Core claim

In the non-collinear Ising magnet Dy2Ti2O7, the spin Seebeck effect voltage develops a pronounced peak at the temperature of monopole proliferation; this peak is accompanied by characteristic frequency and angular dependence that the measurements attribute to the fractionalized monopole excitations.

What carries the argument

The spin Seebeck effect, which converts thermally driven magnetic excitations into a measurable voltage across an adjacent metal layer.

If this is right

  • SSE supplies an electrical readout of monopole proliferation and transport in Dy2Ti2O7.
  • The frequency dependence can distinguish monopole contributions from other magnetic excitations.
  • Angular dependence reveals the directional character of monopole motion in the lattice.
  • Spintronic interfaces can access fractionalized excitations in other magnetic insulators.

Where Pith is reading between the lines

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

  • The same SSE setup might be tested on other spin-ice compounds or quantum spin liquids to check for analogous peaks.
  • If the voltage signal scales with calculated monopole density, it could become a quantitative probe of monopole concentration.
  • Combining SSE with applied fields could map how monopoles respond to external perturbations in real time.

Load-bearing premise

The observed SSE peak and its dependencies are produced specifically by the fractionalized monopoles rather than by conventional magnons or other thermal spin excitations in the same temperature range.

What would settle it

If the same peak with matching frequency and angular dependence appears in SSE measurements on a non-spin-ice magnetic insulator that lacks monopole excitations, the attribution to monopoles would be falsified.

read the original abstract

Fractionalized excitations are among the most striking signatures of emergence in quantum matter. While widely sought in frustrated magnets, their detection and characterization remain challenging, motivating the exploration of new probes. Meanwhile, Spintronics offers versatile tools for probing spin-related phenomena. In particular, the spin Seebeck effect (SSE) converts thermally driven magnetic excitations into a voltage in an adjacent metal, providing electrical access to the underlying dynamics and transport properties. Here we employ the SSE to probe emergent magnetic monopoles in the non-collinear Ising magnet Dy$_2$Ti$_2$O$_7$, a rare instance of a three-dimensional fractionalized magnet. We observe an SSE signal featuring a pronounced peak at monopole proliferation, accompanied by characteristic frequency and angular dependence. Our results broaden the scope of spintronic methods for detecting exotic excitations, provide new insights into magnetic insulators generally and monopole physics specifically, and suggest the potential of quantum materials as functional interfaces.

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 / 0 minor

Summary. The manuscript claims to employ the spin Seebeck effect (SSE) as an electrical probe of fractionalized monopole excitations in the three-dimensional spin ice Dy2Ti2O7. The central experimental observation is an SSE voltage signal exhibiting a pronounced peak coinciding with the temperature regime of monopole proliferation, together with distinctive frequency and angular dependence.

Significance. If the attribution of the SSE feature specifically to monopoles is substantiated by controls and analysis, the work would constitute a meaningful extension of spintronic methods to emergent fractionalized quasiparticles in frustrated magnets, supplying new electrical transport data on monopole dynamics.

major comments (2)
  1. [Results section describing temperature, frequency, and angular dependence of the SSE signal] The central claim that the observed SSE peak arises from monopole proliferation rather than conventional magnon or thermal spin excitations rests on correlation with the known monopole density temperature scale, but the manuscript provides no control measurements (e.g., field regimes suppressing monopoles while retaining other spin degrees of freedom) or quantitative lineshape modeling to isolate the monopole contribution. This attribution is load-bearing for the interpretation.
  2. [Discussion or analysis of the SSE dependencies] No explicit comparison is made between the measured frequency and angular dependence and theoretical expectations for monopole transport versus phonon-drag or magnon mechanisms that could produce similar features at the same temperature.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the detailed review and valuable suggestions. We address each major comment below and outline revisions to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Results section describing temperature, frequency, and angular dependence of the SSE signal] The central claim that the observed SSE peak arises from monopole proliferation rather than conventional magnon or thermal spin excitations rests on correlation with the known monopole density temperature scale, but the manuscript provides no control measurements (e.g., field regimes suppressing monopoles while retaining other spin degrees of freedom) or quantitative lineshape modeling to isolate the monopole contribution. This attribution is load-bearing for the interpretation.

    Authors: We agree that the attribution of the SSE peak to monopoles is central and would benefit from stronger substantiation. The current manuscript correlates the peak with the monopole proliferation temperature and notes the unique frequency and angular dependencies. In the revised manuscript, we will incorporate a qualitative lineshape analysis based on available models and discuss why conventional mechanisms are less likely to produce the observed features. However, we cannot add new control measurements in applied magnetic fields without performing additional experiments, which are outside the scope of this revision. We will instead reference existing studies on field-suppressed regimes in Dy2Ti2O7 to support the interpretation. revision: partial

  2. Referee: [Discussion or analysis of the SSE dependencies] No explicit comparison is made between the measured frequency and angular dependence and theoretical expectations for monopole transport versus phonon-drag or magnon mechanisms that could produce similar features at the same temperature.

    Authors: We acknowledge the lack of explicit comparisons in the original manuscript. In the revised version, we will add a dedicated paragraph comparing the observed frequency dependence (e.g., the peak position and width) and angular anisotropy with theoretical expectations from magnon SSE, phonon-drag SSE, and emerging models for monopole transport in spin ice. This will include citations to relevant theoretical works on each mechanism to clarify the distinction. revision: yes

standing simulated objections not resolved
  • Control measurements in field regimes suppressing monopoles while retaining other spin degrees of freedom, as these require new experimental data not available in the current study.

Circularity Check

0 steps flagged

No circularity: experimental observation with no derivation chain or self-referential predictions

full rationale

The paper reports an experimental measurement of the spin Seebeck effect in Dy2Ti2O7, claiming observation of a peak in the SSE signal at temperatures linked to monopole proliferation along with frequency and angular dependence. No equations, model derivations, fitted parameters presented as predictions, or load-bearing self-citations that reduce the central claim to its own inputs are described in the abstract or reader-provided context. The result is framed as an empirical finding whose interpretation rests on external knowledge of the material rather than any internal derivation that is circular by construction. This is the expected non-finding for an observational study without theoretical modeling steps.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the standard assumption that Dy2Ti2O7 hosts deconfined magnetic monopoles as fractionalized excitations, plus the domain assumption that SSE voltage directly reports the spin current carried by those monopoles. No free parameters or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption Dy2Ti2O7 realizes a three-dimensional fractionalized magnet with emergent magnetic monopoles
    Invoked in the abstract as the physical system under study.
  • domain assumption SSE voltage is proportional to the spin current carried by the monopole excitations
    Implicit in the interpretation of the observed signal.

pith-pipeline@v0.9.1-grok · 5737 in / 1234 out tokens · 16573 ms · 2026-06-28T12:42:43.535443+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

62 extracted references · 59 canonical work pages

  1. [1]

    Representation in

    Giamarchi, T. Quantum Physics in One Dimension (Oxford University Press, 2003). URL https://doi.org/10.1093/acprof:oso/9780198525004.001.0001

    work page doi:10.1093/acprof:oso/9780198525004.001.0001 2003

  2. [2]

    Kish, L. L. et al. High-temperature quantum coherence of spinons in a rare-earth spin chain. Nat. Commun.16, 6594 (2025). URL https://doi.org/10.1038/s41467-025-61715-z

    work page doi:10.1038/s41467-025-61715-z 2025

  3. [3]

    Kitaev, A. Y . Fault-tolerant quantum computation by anyons. Ann. Phys.303, 2–30 (2003)

    2003

  4. [4]

    & Moore, J

    Moessner, R. & Moore, J. E. Topological Phases of Matter (Cambridge University Press, 2021). URLhttps://doi.org/10.1017/9781316226308

    work page doi:10.1017/9781316226308 2021

  5. [5]

    A., Cowley, R

    Tennant, D. A., Cowley, R. A., Nagler, S. E. & Tsvelik, A. M. Mea- surement of the spin-excitation continuum in one-dimensional KCuF 3 us- ing neutron scattering. Phys. Rev. B52, 13368–13380 (1995). URL https://link.aps.org/doi/10.1103/PhysRevB.52.13368

    work page doi:10.1103/physrevb.52.13368 1995

  6. [6]

    Hirobe, D. et al. One-dimensional spinon spin currents. Nat. Phys.13, 30–34 (2017). URL https://doi.org/10.1038/nphys3895

    work page doi:10.1038/nphys3895 2017

  7. [7]

    Castelnovo, R

    Castelnovo, C., Moessner, R. & Sondhi, S. L. Magnetic monopoles in spin ice. Nature451, 42–45 (2008). URLhttps://doi.org/10.1038/nature06433

    work page doi:10.1038/nature06433 2008

  8. [8]

    Morris, D. J. P. et al. Dirac strings and magnetic monopoles in the spin ice Dy 2Ti2O7. Science326, 411–414 (2009). URL https://www.science.org/doi/10.1126/science.1178868. 23

    work page doi:10.1126/science.1178868 2009

  9. [9]

    Fennell, T. et al. Magnetic coulomb phase in the spin ice Ho 2Ti2O7. Science326, 415–417 (2009). URLhttps://doi.org/10.1126/science.1177582

    work page doi:10.1126/science.1177582 2009

  10. [10]

    Snyder, J. et al. Quantum-classical reentrant relaxation crossover in Dy 2Ti2O7 spin ice. Phys. Rev. Lett.91, 107201 (2003). URL https://doi.org/10.1103/PhysRevLett.91.107201

    work page doi:10.1103/physrevlett.91.107201 2003

  11. [11]

    Matsuhira, K. et al. Spin dynamics at very low temperature in spin ice Dy 2Ti2O7. J. Phys. Soc. Jpn.80, 123711 (2011). URL https://doi.org/10.1143/JPSJ.80.123711

    work page doi:10.1143/jpsj.80.123711 2011

  12. [12]

    Yaraskavitch, L. R. et al. Spin dynamics in the frozen state of the dipo- lar spin ice material Dy 2Ti2O7. Phys. Rev. B85, 020410 (2012). URL https://link.aps.org/doi/10.1103/PhysRevB.85.020410

    work page doi:10.1103/physrevb.85.020410 2012

  13. [13]

    A., Prabhakaran, D., Aeppli, G

    Bovo, L., Bloxsom, J. A., Prabhakaran, D., Aeppli, G. & Bramwell, S. T. Brownian motion and quantum dynamics of magnetic monopoles in spin ice. Nat. Commun.4, 1535 (2013). URLhttps://doi.org/10.1038/ncomms2551

    work page doi:10.1038/ncomms2551 2013

  14. [14]

    Kassner, E. R. et al. Supercooled spin liquid state in the frustrated py- rochlore Dy 2Ti2O7. Proc. Natl. Acad. Sci. U.S.A.112, 8549–8554 (2015). URL https://www.pnas.org/doi/abs/10.1073/pnas.1511006112

    work page doi:10.1073/pnas.1511006112 2015

  15. [15]

    Billington, D. et al. Power spectrum of magnetic relaxation in spin ice: Anoma- lous diffusion in a coulomb fluid. Phys. Rev. B112, L020503 (2025). URL https://doi.org/10.1103/9ttp-n3p5. 24

    work page doi:10.1103/9ttp-n3p5 2025

  16. [16]

    Dusad, R. et al. Magnetic monopole noise. Nature571, 234–239 (2019). URL https://doi.org/10.1038/s41586-019-1358-1

    work page doi:10.1038/s41586-019-1358-1 2019

  17. [17]

    Samarakoon, A. M. et al. Anomalous magnetic noise in an imperfectly flat landscape in the topological magnet Dy2Ti2O7. Proc. Natl. Acad. Sci. U.S.A.119, e2117453119 (2022). URL https://www.pnas.org/doi/abs/10.1073/pnas.2117453119

    work page doi:10.1073/pnas.2117453119 2022

  18. [18]

    Hsu, C.-C. et al. Dichotomous dynamics of magnetic monopole flu- ids. Proc. Natl. Acad. Sci. U.S.A.121, e2320384121 (2024). URL https://www.pnas.org/doi/abs/10.1073/pnas.2320384121

    work page doi:10.1073/pnas.2320384121 2024

  19. [19]

    & Lorenz, T

    Kolland, G., Valldor, M., Hiertz, M., Frielingsdorf, J. & Lorenz, T. Anisotropic heat transport via monopoles in the spin-ice compound Dy 2Ti2O7. Phys. Rev. B88, 054406 (2013). URL https://link.aps.org/doi/10.1103/PhysRevB.88.054406

    work page doi:10.1103/physrevb.88.054406 2013

  20. [20]

    Scharffe, S. et al. Heat transport of the spin-ice materialsHo 2Ti2O7 andDy 2Ti2O7. J. Magn. Magn. Mater.383, 83–87 (2015). URL https://www.sciencedirect.com/science/article/pii/S0304885314011238

    2015

  21. [21]

    Toews, W. H. et al. Disorder dependence of monopole dynamics inDy 2Ti2O7 probed via thermal transport measurements. Phys. Rev. B98, 134446 (2018). URL https://link.aps.org/doi/10.1103/PhysRevB.98.134446

    work page doi:10.1103/physrevb.98.134446 2018

  22. [22]

    Klemke, B. et al. Thermal relaxation and heat transport in the spin- ice materialDy 2Ti2O7. J. Low Temp. Phys.163, 345–369 (2011). URL https://doi.org/10.1007/s10909-011-0348-y. 25

    work page doi:10.1007/s10909-011-0348-y 2011

  23. [23]

    Li, S. J. et al. Low-temperature thermal conductivity ofDy 2Ti2O7 andYb 2Ti2O7 single crystals. Phys. Rev. B92, 094408 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.094408

    work page doi:10.1103/physrevb.92.094408 2015

  24. [24]

    Wu, S. et al. Charge-neutral electronic excitations in quantum insulators.Nature635, 301–310 (2024). URLhttps://doi.org/10.1038/s41586-024-08091-8

    work page doi:10.1038/s41586-024-08091-8 2024

  25. [25]

    C., Stormer, H

    Tsui, D. C., Stormer, H. L. & Gossard, A. C. Two-Dimensional Magnetotransport in the Extreme Quantum Limit. Phys. Rev. Lett48, 1559–1562 (1982)

    1982

  26. [26]

    Laughlin, R. B. Anomalous Quantum Hall Effect: An incompressible quantum fluid with fractionally charged excitations. Phys. Rev. Lett.50, 1395–1398 (1983). URL https://doi.org/10.1103/PhysRevLett.50.1395

    work page doi:10.1103/physrevlett.50.1395 1983

  27. [27]

    Uchida, K. et al. Observation of the spin Seebeck effect. Nature455, 778–781 (2008). URL https://doi.org/10.1038/nature07321

    work page doi:10.1038/nature07321 2008

  28. [28]

    Bauer, G. E. W., Saitoh, E. & van Wees, B. J. Spin caloritronics. Nat. Mater.11, 391–399 (2012). URLhttps://doi.org/10.1038/nmat3301

    work page doi:10.1038/nmat3301 2012

  29. [29]

    Aqeel, A. et al. Electrical detection of spiral spin structures in Pt|cu2oseo3 heterostructures. Phys. Rev. B94, 134418 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.134418

    work page doi:10.1103/physrevb.94.134418 2016

  30. [30]

    & Saitoh, E

    Kikkawa, T. & Saitoh, E. Spin Seebeck effect: Sensitive probe for ele- mentary excitation, spin correlation, transport, magnetic order, and domains in solids. Annu. Rev. Condens. Matter Phys.14, 129–154 (2023). URL https://doi.org/10.1146/annurev-conmatphys-040721-014957. 26

    work page doi:10.1146/annurev-conmatphys-040721-014957 2023

  31. [31]

    Ryzhkin, I. A. Magnetic relaxation in rare-earth oxide pyrochlores. J. Exp. Theor. Phys.101, 481–486 (2005). URLhttps://doi.org/10.1134/1.2103216

    work page doi:10.1134/1.2103216 2005

  32. [32]

    Jaubert, L. D. C. & Holdsworth, P. C. W. Signature of magnetic monopole and Dirac string dynamics in spin ice. Nat. Phys.5, 258–261 (2009). URL https://doi.org/10.1038/nphys1227

    work page doi:10.1038/nphys1227 2009

  33. [33]

    & Sakakibara, T

    Matsuhira, K., Hiroi, Z., Tayama, T., Takagi, S. & Sakakibara, T. A new macroscopically degenerate ground state in the spin ice compound Dy 2Ti2O7 un- der a magnetic field. J. Phys.: Condens. Matter14, L559–L565 (2002). URL https://doi.org/10.1088/0953-8984/14/29/101

    work page doi:10.1088/0953-8984/14/29/101 2002

  34. [34]

    & Takagi, S

    Sakakibara, T., Tayama, T., Hiroi, Z., Matsuhira, K. & Takagi, S. Obser- vation of a liquid-gas-type transition in the pyrochlore spin ice compound Dy2Ti2O7 in a magnetic field. Phys. Rev. Lett.90, 207205 (2003). URL https://link.aps.org/doi/10.1103/PhysRevLett.90.207205

    work page doi:10.1103/physrevlett.90.207205 2003

  35. [35]

    & Sondhi, S

    Moessner, R. & Sondhi, S. L. Theory of the [111] magnetiza- tion plateau in spin ice. Phys. Rev. B68, 064411 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.064411

    work page doi:10.1103/physrevb.68.064411 2003

  36. [36]

    V ., Raman, K

    Isakov, S. V ., Raman, K. S., Moessner, R. & Sondhi, S. L. Magnetization curve of spin ice in a [111] magnetic field. Phys. Rev. B70, 104418 (2004). URL https://link.aps.org/doi/10.1103/PhysRevB.70.104418. 27

    work page doi:10.1103/physrevb.70.104418 2004

  37. [37]

    M., Pearson, J

    Wu, S. M., Pearson, J. E. & Bhattacharya, A. Paramagnetic spin Seebeck effect. Phys. Rev. Lett.114, 186602 (2015). URL https://link.aps.org/doi/10.1103/PhysRevLett.114.186602

    work page doi:10.1103/physrevlett.114.186602 2015

  38. [38]

    & Starykh, O

    Wang, R.-B., Nishad, N., Keselman, A., Balents, L. & Starykh, O. A. Spin Seebeck effect of interacting spinons. Phys. Rev. B112, L060402 (2025). URL https://doi.org/10.1103/ncdj-9f2t

    work page doi:10.1103/ncdj-9f2t 2025

  39. [39]

    Kikkawa, T. et al. Magnon polarons in the spin Seebeck effect. Phys. Rev. Lett.117(2016). URLhttps://link.aps.org/doi/10.1103/PhysRevLett.117.207203

    work page doi:10.1103/physrevlett.117.207203 2016

  40. [40]

    Ramos, R. et al. Room temperature and low-field resonant enhancement of spin See- beck effect in partially compensated magnets. Nat. Commun.10, 5162 (2019). URL https://doi.org/10.1038/s41467-019-13121-5

    work page doi:10.1038/s41467-019-13121-5 2019

  41. [41]

    Xing, W. et al. Facet-dependent magnon-polarons in epitaxial ferri- magneticFe 3O4 thin films. Phys. Rev. B102, 184416 (2020). URL https://link.aps.org/doi/10.1103/PhysRevB.102.184416

    work page doi:10.1103/physrevb.102.184416 2020

  42. [42]

    Li, J. et al. Observation of magnon polarons in a uniaxial anti- ferromagnetic insulator. Phys. Rev. Lett.125, 217201 (2020). URL https://link.aps.org/doi/10.1103/PhysRevLett.125.217201

    work page doi:10.1103/physrevlett.125.217201 2020

  43. [43]

    He, X. et al. Spin Seebeck in the weakly exchange-coupled van der Waals anti- ferromagnet across the spin-flip transition. Nat. Commun.16, 3037 (2025). URL https://doi.org/10.1038/s41467-025-58306-3. 28

    work page doi:10.1038/s41467-025-58306-3 2025

  44. [44]

    Kimling, J. et al. Picosecond spin Seebeck effect. Phys. Rev. Lett.118, 057201 (2017). URL https://link.aps.org/doi/10.1103/PhysRevLett.118.057201

    work page doi:10.1103/physrevlett.118.057201 2017

  45. [45]

    Seifert, T. S. et al. Femtosecond formation dynamics of the spin Seebeck ef- fect revealed by terahertz spectroscopy. Nat. Commun.9, 2899 (2018). URL https://doi.org/10.1038/s41467-018-05135-2

    work page doi:10.1038/s41467-018-05135-2 2018

  46. [46]

    Schreier, M. et al. Spin Seebeck effect at microwave frequencies. Phys. Rev. B93, 224430 (2016). URLhttps://link.aps.org/doi/10.1103/PhysRevB.93.224430

    work page doi:10.1103/physrevb.93.224430 2016

  47. [47]

    Aqeel, A. et al. Spin Hall magnetoresistance and spin Seebeck effect in Pt|CoCr2O4 heterostructures. Sci. Technol. Adv. Mater.26, 2457320 (2025). URL https://doi.org/10.1080/14686996.2025.2457320

    work page doi:10.1080/14686996.2025.2457320 2025

  48. [48]

    & Saitoh, E

    Oyanagi, K., Takahashi, S., Kikkawa, T. & Saitoh, E. Mechanism of para- magnetic spin Seebeck effect. Phys. Rev. B107, 014423 (2023). URL https://doi.org/10.1103/PhysRevB.107.014423

    work page doi:10.1103/physrevb.107.014423 2023

  49. [49]

    & Maekawa, S

    Adachi, H., Uchida, K.-i., Saitoh, E. & Maekawa, S. Theory of the spin Seebeck effect. Rep. Prog. Phys.76, 036501 (2013). URL https://doi.org/10.1088/0034-4885/76/3/036501

    work page doi:10.1088/0034-4885/76/3/036501 2013

  50. [50]

    & Sondhi, S

    Castelnovo, C., Moessner, R. & Sondhi, S. L. Debye-H ¨uckel theory for spin ice at low temperature. Phys. Rev. B84, 144435 (2011). URL https://doi.org/10.1103/PhysRevB.84.144435. 29

    work page doi:10.1103/physrevb.84.144435 2011

  51. [51]

    & Sondhi, S

    Mostame, S., Castelnovo, C., Moessner, R. & Sondhi, S. L. Tunable nonequilibrium dynamics of field quenches in spin ice. Proc. Natl. Acad. Sci. U. S. A.111, 640–645 (2014). URL https://doi.org/10.1073/pnas.1317631111

    work page doi:10.1073/pnas.1317631111 2014

  52. [52]

    Matthews, M. J. et al. High-temperature onset of field-induced transitions in the spin-ice compoundDy 2Ti2O7. Phys. Rev. B86, 214419 (2012). URL https://doi.org/10.1103/PhysRevB.86.214419

    work page doi:10.1103/physrevb.86.214419 2012

  53. [53]

    & Quintanilla, J

    Tomasello, B., Castelnovo, C., Moessner, R. & Quintanilla, J. Correlated quantum tunneling of monopoles in spin ice. Phys. Rev. Lett.123, 067204 (2019). URL https://link.aps.org/doi/10.1103/PhysRevLett.123.067204

    work page doi:10.1103/physrevlett.123.067204 2019

  54. [54]

    N., Grigera, S

    Hall ´en, J. N., Grigera, S. A., Tennant, D. A., Castelnovo, C. & Moessner, R. Dynamical fractal and anomalous noise in a clean magnetic crystal. Science378, 1218–1221 (2022). URLhttps://www.science.org/doi/abs/10.1126/science.add1644

    work page doi:10.1126/science.add1644 2022

  55. [55]

    Snyder, J. et al. Low-temperature spin freezing in the Dy2Ti2O7 spin ice. Phys. Rev. B69, 064414 (2004). URL https://link.aps.org/doi/10.1103/PhysRevB.69.064414

    work page doi:10.1103/physrevb.69.064414 2004

  56. [56]

    Eyvazov, A. B. et al. Common glass-forming spin-liquid state in the pyrochlore magnets Dy 2Ti2O7 and Ho 2Ti2O7. Phys. Rev. B98, 214430 (2018). URL https://link.aps.org/doi/10.1103/PhysRevB.98.214430

    work page doi:10.1103/physrevb.98.214430 2018

  57. [57]

    Rezende, S. M. et al. Magnon spin-current theory for the longitu- dinal spin-Seebeck effect. Phys. Rev. B89, 014416 (2014). URL https://link.aps.org/doi/10.1103/PhysRevB.89.014416. 30

    work page doi:10.1103/physrevb.89.014416 2014

  58. [58]

    Agrawal, M. et al. Role of bulk-magnon transport in the temporal evolution of the longitudinal spin-Seebeck effect. Phys. Rev. B89, 224414 (2014). URL https://link.aps.org/doi/10.1103/PhysRevB.89.224414

    work page doi:10.1103/physrevb.89.224414 2014

  59. [59]

    Guo, E.-J. et al. Influence of thickness and interface on the low-temperature enhance- ment of the spin Seebeck effect in YIG films. Phys. Rev. X6, 031012 (2016). URL https://link.aps.org/doi/10.1103/PhysRevX.6.031012

    work page doi:10.1103/physrevx.6.031012 2016

  60. [60]

    & Rau, J

    Sutcliffe, R. & Rau, J. G. Thermal conductivity of square ice. Phys. Rev. B105, 104405 (2022). URLhttps://doi.org/10.1103/PhysRevB.105.104405

    work page doi:10.1103/physrevb.105.104405 2022

  61. [61]

    Vlietstra, N. et al. Simultaneous detection of the spin-Hall magnetoresistance and the spin- Seebeck effect in platinum and tantalum on yttrium iron garnet. Phys. Rev. B90, 174436 (2014). URLhttps://link.aps.org/doi/10.1103/PhysRevB.90.174436

    work page doi:10.1103/physrevb.90.174436 2014

  62. [62]

    Kikkawa, T. et al. Observation of nuclear-spin Seebeck effect.Nat. Commun.12, 4356 (2021). URLhttps://doi.org/10.1038/s41467-021-24623-6. 31 Methods Sample preparation A single crystal of Dy2Ti2O7 with the dimensions of 6 mm diameter and 44 mm length was grown in a Crystal Systems Corporation (CSC) optical floating zone furnace. Small rectangular pieces a...

    work page doi:10.1038/s41467-021-24623-6 2021