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arxiv: 2509.10309 · v2 · submitted 2025-09-12 · ❄️ cond-mat.mes-hall · cond-mat.str-el

Spin-qubit Noise Spectroscopy of Magnetic Berezinskii-Kosterlitz-Thouless Physics

Mark Potts , Shu Zhang This is my paper

Pith reviewed 2026-05-18 17:42 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.str-el
keywords spin-qubit noise spectroscopyBKT transition2D XY magnetsnitrogen-vacancy centermagnetic noise spectral densityvortex conductivityalgebraic spin correlationsphase transition dynamics
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0 comments X

The pith

An NV center coupled to a 2D XY magnet detects the BKT transition through a temperature-dependent power law in its magnetic noise spectrum below the transition and vortex signatures above it.

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

The paper proposes using a nitrogen-vacancy center as a spin-qubit sensor to measure the magnetic noise spectral density of a two-dimensional XY magnet. In the quasi-long-range ordered phase, this spectrum follows a power law set by the algebraic decay of spin correlations, with the exponent changing with temperature. Above the transition, free vortices dominate the fluctuations and the spectrum encodes the vortex conductivity that governs their transport. These features appear in the sub-MHz to GHz window, a regime where conventional probes struggle to resolve mesoscopic dynamics. A reader would care because the method supplies a quantitative, local way to map the BKT transition and extract a key transport coefficient without requiring direct imaging of vortices.

Core claim

We propose using spin-qubit noise magnetometry to probe dynamical signatures of magnetic Berezinskii-Kosterlitz-Thouless (BKT) physics. For a nitrogen-vacancy (NV) center coupled to two-dimensional XY magnets, we predict distinctive features in the magnetic noise spectral density in the sub-MHz to GHz frequency range. In the quasi-long-range ordered phase, the spectrum exhibits a temperature-dependent power law characteristic of algebraic spin correlations. Above the transition, the noise reflects the proliferation of free vortices and enables quantitative extraction of the vortex conductivity, a key parameter of vortex transport.

What carries the argument

The magnetic noise spectral density sensed by the NV center, obtained by Fourier-transforming the two-time spin correlation functions of the 2D XY magnet.

If this is right

  • The spectrum in the ordered phase directly encodes the algebraic exponent of spin correlations through its temperature dependence.
  • Above the transition the spectrum supplies a quantitative value for vortex conductivity from the noise amplitude and frequency dependence.
  • The technique resolves magnetic dynamics in the mesoscopic length and low-frequency regime where other methods lose sensitivity.
  • The same NV-magnet coupling framework can be used to study other exotic 2D magnetic phase transitions that produce distinct fluctuation spectra.

Where Pith is reading between the lines

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

  • The approach could be extended to layered van der Waals magnets that realize XY-like behavior, allowing table-top tests of BKT physics without cryogenic scanning probes.
  • Because the NV operates at room temperature while the magnet can be cooled separately, the method opens a route to hybrid quantum sensors for mapping vortex motion in real time.
  • If the predicted conductivity extraction proves accurate, the same noise channel could be inverted to measure other transport coefficients such as spin diffusion in related 2D systems.

Load-bearing premise

The noise spectrum measured by the NV center is dominated by the intrinsic spin fluctuations of the 2D XY magnet, with no significant back-action or extra decoherence channels that would obscure the BKT features.

What would settle it

A measured noise spectrum that fails to show a temperature-dependent power law below the expected transition temperature or that lacks the predicted change associated with free-vortex proliferation above it would falsify the central predictions.

Figures

Figures reproduced from arXiv: 2509.10309 by Mark Potts, Shu Zhang.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) An NV center is placed at a distance [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. In-plane and out-of-plane spin correlation functions [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) The magnetic noise spectral density for a range [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
read the original abstract

We propose using spin-qubit noise magnetometry to probe dynamical signatures of magnetic Berezinskii-Kosterlitz-Thouless (BKT) physics. For a nitrogen-vacancy (NV) center coupled to two-dimensional XY magnets, we predict distinctive features in the magnetic noise spectral density in the sub-MHz to GHz frequency range. In the quasi-long-range ordered phase, the spectrum exhibits a temperature-dependent power law characteristic of algebraic spin correlations. Above the transition, the noise reflects the proliferation of free vortices and enables quantitative extraction of the vortex conductivity, a key parameter of vortex transport. These results highlight NV as a powerful spectroscopic method to resolve magnetic dynamics in the mesoscopic and low-frequency regimes and to probe exotic magnetic phase transitions.

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 paper proposes using nitrogen-vacancy (NV) center spin qubits for noise magnetometry to probe dynamical signatures of the Berezinskii-Kosterlitz-Thouless (BKT) transition in two-dimensional XY magnets. It predicts distinctive features in the magnetic noise spectral density in the sub-MHz to GHz range: a temperature-dependent power law in the quasi-long-range ordered phase arising from algebraic spin correlations, and above the transition, signatures of free vortex proliferation that enable quantitative extraction of vortex conductivity.

Significance. If the central predictions hold, this would establish NV-based noise spectroscopy as a tool for resolving low-frequency magnetic dynamics and topological transitions in mesoscopic 2D magnets, with potential for quantitative vortex transport measurements that complement existing probes.

major comments (2)
  1. [Theory/derivation of noise spectrum] The derivation of the noise spectral density from the magnet's spin correlation functions (theory section): the central claim requires that the NV-magnet dipolar coupling remains weak enough to leave BKT vortex dynamics unperturbed, but no quantitative estimate or bound on back-action strength (e.g., effect on vortex mobility or conductivity) is provided, making it impossible to confirm the signatures would appear as calculated.
  2. [Results/predictions for noise spectral density] Predictions for the quasi-long-range ordered phase (results section): the temperature-dependent power law is stated to follow from algebraic correlations, but without an explicit first-principles calculation or reference to the precise form of the BKT correlation function used to obtain the noise spectrum S(ω), it is unclear whether the result is derived or assumed phenomenologically.
minor comments (2)
  1. [Abstract and introduction] The abstract and introduction should explicitly state the NV coherence time or sensing protocol that sets the sub-MHz to GHz window to make the frequency range choice transparent.
  2. [General notation] Notation for the noise spectral density and spin correlation functions should be defined consistently with standard references to avoid ambiguity in how the NV probe couples to the XY magnet.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive comments. We address each major comment below and have revised the manuscript to provide additional details and clarifications.

read point-by-point responses

  1. Referee: [Theory/derivation of noise spectrum] The derivation of the noise spectral density from the magnet's spin correlation functions (theory section): the central claim requires that the NV-magnet dipolar coupling remains weak enough to leave BKT vortex dynamics unperturbed, but no quantitative estimate or bound on back-action strength (e.g., effect on vortex mobility or conductivity) is provided, making it impossible to confirm the signatures would appear as calculated.

    Authors: We agree that a quantitative estimate of back-action would strengthen the central claim. In the revised manuscript we have added a dedicated paragraph in the theory section that estimates the NV dipolar field strength relative to the magnet's exchange energy for realistic NV-magnet distances (10–100 nm) and typical 2D XY parameters. The resulting perturbation to vortex mobility and conductivity is shown to be below 1 %, which justifies the unperturbed-dynamics approximation used for the noise spectra. revision: yes

  2. Referee: [Results/predictions for noise spectral density] Predictions for the quasi-long-range ordered phase (results section): the temperature-dependent power law is stated to follow from algebraic correlations, but without an explicit first-principles calculation or reference to the precise form of the BKT correlation function used to obtain the noise spectrum S(ω), it is unclear whether the result is derived or assumed phenomenologically.

    Authors: The temperature-dependent power law follows directly from the standard BKT algebraic spin correlations. To make the derivation explicit we have added a new appendix that starts from the known correlation function G(r) ∼ r^{−η(T)} with η(T) = T/(2πJ), computes the space-time Fourier transform, and obtains the noise spectral density via the fluctuation-dissipation relation. We have also inserted the relevant references to the original BKT works and subsequent literature on spin correlations. revision: yes

Circularity Check

0 steps flagged

No significant circularity; predictions follow from standard BKT correlations and NV noise formulas

full rationale

The derivation combines established BKT theory (algebraic spin correlations below the transition and free-vortex proliferation above) with conventional expressions for the noise spectral density of an NV center coupled via dipolar interaction. No load-bearing step reduces a claimed prediction to a fitted parameter, self-citation, or ansatz internal to the paper; the results are obtained by applying externally known functional forms for the spin correlator to the NV probe geometry. The central claim therefore remains independent of the present work's own inputs and is self-contained against prior BKT literature and NV magnetometry techniques.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The proposal relies on standard BKT theory for 2D XY models and standard expressions for NV-center magnetic noise; no new free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption The magnetic noise spectral density of the NV center is linearly related to the Fourier transform of the spin-spin correlation function of the 2D magnet.
    Implicit in the statement that the spectrum exhibits features characteristic of algebraic correlations and vortex proliferation.

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Works this paper leans on

101 extracted references · 101 canonical work pages

  1. [1]

    conductivity

    We plot γ 2 N V S(ω ), in units of Hz, to facilitate direct comparison with experi- ments. The overall factor of γ 2f (θN V ) in Eq. ( 1) will be implicit in the text from now on. Focusing on the the low-frequency regime ω ≪ c/d , where c is the spin wave velocity of the XY magnet, we observe a clear change in spectral behavior above and below the BKT tra...

    work page

  2. [2]

    [ϵ(ω,k ) − 2πσ/ (iω − Dk2)]. (11) For temperatures modestly higher than Tc, a constant approximationϵ(ω,k ) ≈ ϵc works well, as the correlation length quickly approaches the scale of a0 as tempera- ture increases. Below, we use the ϵc in the formulas for brevity, while the frequency and momentum dependence is retained in the numerical computations. We ide...

    work page

  3. [3]

    For ω < Ω, the disper- sive transverse spin wave is predominately relaxational, ω T ≈ i ( c2 0/ 2πσ ) k2

    that plays the role of a plasma frequency: Ω = 2 πσ/ϵ c. For ω < Ω, the disper- sive transverse spin wave is predominately relaxational, ω T ≈ i ( c2 0/ 2πσ ) k2 . At long length scales, Ω also deter- mines the relaxation rates of the second transverse mode ω ′ T ≈ − iΩ and the longitudinal mode ω = − i ( Dk2 + Ω ) , which is overdamped due to vortex diffu...

    work page

  4. [4]

    For example, the anisotropy is estimated to be ∼ 1

    32 K, where the lattice constant a0 ∼ 6 ˚ A . For example, the anisotropy is estimated to be ∼ 1. 3 K for NiPS 3 [45] and ∼ 6. 3 K for TmMgGaO 4 [24]. Here, the bare spin wave velocity is c0 ∼ 1. 4 × 104 cm/s and the BKT transition temperature is Tc = 15. 54 K. The bare vortex chemical potential is set at µ 0 ∼ π 2J0 [3], and the vortex density is compute...

    work page

  5. [5]

    V. L. Berezinski ˇi, Soviet Journal of Experimental and Theoretical Physics 32, 493 (1971)

    work page 1971

  6. [6]

    V. L. Berezinski ˇi, Soviet Journal of Experimental and Theoretical Physics 34, 610 (1972)

    work page 1972

  7. [7]

    J. M. Kosterlitz and D. J. Thouless, Journal of Physics C: Solid State Physics 6, 1181 (1973)

    work page 1973

  8. [8]

    J. M. Kosterlitz, Journal of Physics C: Solid State Physics 7, 1046 (1974)

    work page 1974

  9. [9]

    N. D. Mermin and H. Wagner, Phys. Rev. Lett. 17, 1133 (1966)

    work page 1966

  10. [10]

    M. R. Beasley, J. E. Mooij, and T. P. Orlando, Phys. Rev. Lett. 42, 1165 (1979)

    work page 1979

  11. [11]

    A. F. Hebard and A. T. Fiory, Phys. Rev. Lett. 44, 291 (1980)

    work page 1980

  12. [12]

    Epstein, A

    K. Epstein, A. M. Goldman, and A. M. Kadin, Phys. Rev. Lett. 47, 534 (1981)

    work page 1981

  13. [13]

    Rudnick, Phys

    I. Rudnick, Phys. Rev. Lett. 40, 1454 (1978)

    work page 1978

  14. [14]

    D. J. Bishop and J. D. Reppy, Phys. Rev. Lett. 40, 1727 (1978)

    work page 1978

  15. [15]

    D. J. Resnick, J. C. Garland, J. T. Boyd, S. Shoemaker, and R. S. Newrock, Phys. Rev. Lett. 47, 1542 (1981)

    work page 1981

  16. [16]

    Hadzibabic, P

    Z. Hadzibabic, P. Kr¨ uger, M. Cheneau, B. Battelier, and J. Dalibard, Nature 441, 1118 (2006)

    work page 2006

  17. [17]

    Kr¨ uger, Z

    P. Kr¨ uger, Z. Hadzibabic, and J. Dalibard, Phys. Rev. Lett. 99, 040402 (2007)

    work page 2007

  18. [18]

    Clad´ e, C

    P. Clad´ e, C. Ryu, A. Ramanathan, K. Helmerson, and W. D. Phillips, Phys. Rev. Lett. 102, 170401 (2009)

    work page 2009

  19. [19]

    Ding, Phys

    H.-Q. Ding, Phys. Rev. Lett. 68, 1927 (1992)

    work page 1927

  20. [20]

    Majlis, S

    N. Majlis, S. Selzer, and G. C. Strinati, Phys. Rev. B 45, 7872 (1992)

    work page 1992

  21. [21]

    Majlis, S

    N. Majlis, S. Selzer, and G. C. Strinati, Phys. Rev. B 48, 957 (1993)

    work page 1993

  22. [22]

    B. J. Suh, F. Borsa, L. L. Miller, M. Corti, D. C. Johnston, and D. R. Torgeson, Phys. Rev. Lett. 75, 2212 (1995)

    work page 1995

  23. [23]

    Heinrich, H.-A

    M. Heinrich, H.-A. Krug von Nidda, A. Loidl, N. Rogado, and R. J. Cava, Phys. Rev. Lett. 91, 137601 (2003)

    work page 2003

  24. [24]

    Cuccoli, T

    A. Cuccoli, T. Roscilde, R. Vaia, and P. Verrucchi, Phys. Rev. Lett. 90, 167205 (2003)

    work page 2003

  25. [25]

    Carretta, M

    P. Carretta, M. Filibian, R. Nath, C. Geibel, and P. J. C. King, Phys. Rev. B 79, 224432 (2009)

    work page 2009

  26. [26]

    Tutsch, B

    U. Tutsch, B. Wolf, S. Wessel, L. Postulka, Y. Tsui, H. Jeschke, I. Opahle, T. Saha-Dasgupta, R. Valent ´ ı, A. Br¨ uhl,et al. , Nature communications 5, 5169 (2014)

    work page 2014

  27. [27]

    Kumar, T

    R. Kumar, T. Dey, P. M. Ette, K. Ramesha, A. Chakraborty, I. Dasgupta, R. Eremina, S. T´ oth, A. Sha- hee, S. Kundu, M. Prinz-Zwick, A. A. Gippius, H. A. K. von Nidda, N. B¨ uttgen, P. Gegenwart, and A. V. Maha- jan, Phys. Rev. B 99, 144429 (2019)

    work page 2019

  28. [28]

    Z. Hu, Z. Ma, Y.-D. Liao, H. Li, C. Ma, Y. Cui, Y. Shang- guan, Z. Huang, Y. Qi, W. Li, Z. Y. Meng, J. Wen, and W. Yu, Nature Communications 11, 5631 (2020)

    work page 2020

  29. [29]

    Ashoka, K

    A. Ashoka, K. S. Bhagyashree, and S. V. Bhat, Phys. Rev. B 102, 024429 (2020)

    work page 2020

  30. [30]

    N. Caci, L. Weber, and S. Wessel, Phys. Rev. B 104, 155139 (2021)

    work page 2021

  31. [31]

    E. S. Klyushina, J. Reuther, L. Weber, A. T. M. N. Islam, J. S. Lord, B. Klemke, M. M ˚ ansson, S. Wessel, and B. Lake, Phys. Rev. B 104, 064402 (2021)

    work page 2021

  32. [32]

    Opherden, M

    D. Opherden, M. S. J. Tepaske, F. B¨ artl, M. Weber, M. M. Turnbull, T. Lancaster, S. J. Blundell, M. Baenitz, J. Wosnitza, C. P. Landee, R. Moessner, D. J. Luitz, and H. K¨ uhne,Phys. Rev. Lett. 130, 086704 (2023)

    work page 2023

  33. [33]

    Zhang, Y

    D. Zhang, Y. Zhu, G. Zheng, K.-W. Chen, Q. Huang, L. Zhou, Y. Liu, K. Jenkins, A. Chan, H. Zhou, and L. Li, arXiv preprint arXiv:2411.04755 (2024)

    work page arXiv 2024

  34. [34]

    Nakagawa, M

    K. Nakagawa, M. Kanega, T. Yokouchi, M. Sato, and Y. Shiomi, Phys. Rev. Mater. 9, L011401 (2025)

    work page 2025

  35. [35]

    R. E. Troncoso, A. Brataas, and A. Sudbø, Phys. Rev. Lett. 125, 237204 (2020)

    work page 2020

  36. [36]

    S. K. Kim and S. B. Chung, SciPost Phys. 10, 068 (2021)

    work page 2021

  37. [37]

    Flebus, Phys

    B. Flebus, Phys. Rev. B 104, L020408 (2021)

    work page 2021

  38. [38]

    U. F. P. Seifert, M. Ye, and L. Balents, Phys. Rev. B 105, 155138 (2022)

    work page 2022

  39. [39]

    H. Li, S. Ruan, and Y.-J. Zeng, Advanced Materials 31, 1900065 (2019)

    work page 2019

  40. [40]

    Kurebayashi, J

    H. Kurebayashi, J. H. Garcia, S. Khan, J. Sinova, and S. Roche, Nature Reviews Physics 4, 150 (2022)

    work page 2022

  41. [41]

    J.-G. Park, K. Zhang, H. Cheong, J. H. Kim, C. Belvin, D. Hsieh, H. Ning, and N. Gedik, arXiv preprint arXiv:2505.02355 (2025)

    work page arXiv 2025

  42. [42]

    Zhang, Q

    W.-B. Zhang, Q. Qu, P. Zhu, and C.-H. Lam, Journal of Materials Chemistry C 3, 12457 (2015)

    work page 2015

  43. [43]

    M. A. McGuire, H. Dixit, V. R. Cooper, and B. C. Sales, Chemistry of Materials 27, 612 (2015)

    work page 2015

  44. [44]

    Huang, G

    B. Huang, G. Clark, E. Navarro-Moratalla, D. R. Klein, R. Cheng, K. L. Seyler, D. Zhong, E. Schmidgall, M. A. McGuire, D. H. Cobden, et al. , Nature 546, 270 (2017)

    work page 2017

  45. [45]

    M. A. McGuire, G. Clark, S. Kc, W. M. Chance, G. E. Jellison Jr, V. R. Cooper, X. Xu, and B. C. Sales, Physical Review Materials 1, 014001 (2017)

    work page 2017

  46. [46]

    P. A. Joy and S. Vasudevan, Phys. Rev. B 46, 5425 (1992)

    work page 1992

  47. [47]

    A. R. Wildes, V. Simonet, E. Ressouche, G. J. McIn- tyre, M. Avdeev, E. Suard, S. A. J. Kimber, D. Lan¸ con, G. Pepe, B. Moubaraki, and T. J. Hicks, Phys. Rev. B 92, 224408 (2015)

    work page 2015

  48. [48]

    K. Kim, S. Y. Lim, J.-U. Lee, S. Lee, T. Y. Kim, K. Park, G. S. Jeon, C.-H. Park, J.-G. Park, and H. Cheong, Nature communications 10, 345 (2019)

    work page 2019

  49. [49]

    Hu, H.-X

    L. Hu, H.-X. Wang, Y. Chen, K. Xu, M.-R. Li, H. Liu, P. Gu, Y. Wang, M. Zhang, H. Yao, and Q. Xiong, Phys. Rev. B 107, L220407 (2023)

    work page 2023

  50. [50]

    J. V. Jos´ e, L. P. Kadanoff, S. Kirkpatrick, and D. R. Nelson, Phys. Rev. B 16, 1217 (1977)

    work page 1977

  51. [51]

    Rondin, J.-P

    L. Rondin, J.-P. Tetienne, T. Hingant, J.-F. Roch, P. Maletinsky, and V. Jacques, Reports on progress in physics 77, 056503 (2014)

    work page 2014

  52. [52]

    Casola, T

    F. Casola, T. van der Sar, and A. Yacoby, Nat. Rev. Mater. 3, 17088 (2018)

    work page 2018

  53. [53]

    Y. Xu, W. Zhang, and C. Tian, Photonics Research 11, 393 (2023)

    work page 2023

  54. [54]

    Rovny, S

    J. Rovny, S. Gopalakrishnan, A. C. B. Jayich, P. Maletinsky, E. Demler, and N. P. de Leon, Nature Reviews Physics , 1 (2024)

    work page 2024

  55. [55]

    Kolkowitz, A

    S. Kolkowitz, A. Safira, A. High, R. Devlin, S. Choi, Q. Un- terreithmeier, D. Patterson, A. Zibrov, V. Manucharyan, H. Park, et al. , Science 347, 1129 (2015)

    work page 2015

  56. [56]

    Ariyaratne, D

    A. Ariyaratne, D. Bluvstein, B. A. Myers, and A. C. B. Jayich, Nature communications 9, 2406 (2018)

    work page 2018

  57. [57]

    Flebus and Y

    B. Flebus and Y. Tserkovnyak, Phys. Rev. Lett. 121, 187204 (2018)

    work page 2018

  58. [58]

    J. F. Rodriguez-Nieva, K. Agarwal, T. Giamarchi, B. I. Halperin, M. D. Lukin, and E. Demler, Phys. Rev. B 98, 7 195433 (2018)

    work page 2018

  59. [59]

    H. Wang, S. Zhang, N. J. McLaughlin, B. Flebus, M. Huang, Y. Xiao, C. Liu, M. Wu, E. E. Fullerton, Y. Tserkovnyak, et al. , Science advances 8, eabg8562 (2022)

    work page 2022

  60. [60]

    H. Fang, S. Zhang, and Y. Tserkovnyak, Phys. Rev. B 105, 184406 (2022)

    work page 2022

  61. [61]

    Zhang and Y

    S. Zhang and Y. Tserkovnyak, Phys. Rev. B 106, L081122 (2022)

    work page 2022

  62. [62]

    J. F. Rodriguez-Nieva, D. Podolsky, and E. Demler, Phys. Rev. B 105, 174412 (2022)

    work page 2022

  63. [63]

    Signatures of magnon hydrodynamics in an atomically-thin ferromag- net,

    R. Xue, N. Maksimovic, P. E. Dolgirev, L.-Q. Xia, R. Kita- gawa, A. M¨ uller, F. Machado, D. R. Klein, D. Mac- Neill, K. Watanabe, T. Taniguchi, P. Jarillo-Herrero, M. D. Lukin, E. Demler, and A. Yacoby, “Signatures of magnon hydrodynamics in an atomically-thin ferromag- net,” (2024), arXiv:2403.01057 [cond-mat.mes-hall]

    work page arXiv 2024

  64. [64]

    Dussaux, P

    A. Dussaux, P. Sch¨ onherr, K. Koumpouras, J. Chico, K. Chang, L. Lorenzelli, N. Kanazawa, Y. Tokura, M. Garst, A. Bergman, et al. , Nature Communications 7, 12430 (2016)

    work page 2016

  65. [65]

    Flebus, H

    B. Flebus, H. Ochoa, P. Upadhyaya, and Y. Tserkovnyak, Phys. Rev. B 98, 180409 (2018)

    work page 2018

  66. [66]

    Jenkins, M

    A. Jenkins, M. Pelliccione, G. Yu, X. Ma, X. Li, K. L. Wang, and A. C. B. Jayich, Phys. Rev. Mater. 3, 083801 (2019)

    work page 2019

  67. [67]

    D. M. Juraschek, Q. N. Meier, M. Trassin, S. E. Trolier- McKinstry, C. L. Degen, and N. A. Spaldin, Phys. Rev. Lett. 123, 127601 (2019)

    work page 2019

  68. [68]

    N. J. McLaughlin, C. Hu, M. Huang, S. Zhang, H. Lu, G. Q. Yan, H. Wang, Y. Tserkovnyak, N. Ni, and C. R. Du, Nano Letters 22, 5810 (2022)

    work page 2022

  69. [69]

    Rable, J

    J. Rable, J. Dwivedi, and N. Samarth, npj Spintronics 1, 2 (2023)

    work page 2023

  70. [70]

    N. J. McLaughlin, S. Li, J. A. Brock, S. Zhang, H. Lu, M. Huang, Y. Xiao, J. Zhou, Y. Tserkovnyak, E. E. Fuller- ton, et al. , ACS nano 17, 25689 (2023)

    work page 2023

  71. [71]

    Schlussel, T

    Y. Schlussel, T. Lenz, D. Rohner, Y. Bar-Haim, L. Bougas, D. Groswasser, M. Kieschnick, E. Rozenberg, L. Thiel, A. Waxman, J. Meijer, P. Maletinsky, D. Budker, and R. Folman, Phys. Rev. Appl. 10, 034032 (2018)

    work page 2018

  72. [72]

    Chatterjee, J

    S. Chatterjee, J. F. Rodriguez-Nieva, and E. Demler, Phys. Rev. B 99, 104425 (2019)

    work page 2019

  73. [73]

    E. J. K¨ onig, P. Coleman, and A. M. Tsvelik, Phys. Rev. B 102, 104514 (2020)

    work page 2020

  74. [74]

    Chatterjee, P

    S. Chatterjee, P. E. Dolgirev, I. Esterlis, A. A. Zibrov, M. D. Lukin, N. Y. Yao, and E. Demler, Phys. Rev. Res. 4, L012001 (2022)

    work page 2022

  75. [75]

    P. E. Dolgirev, I. Esterlis, A. A. Zibrov, M. D. Lukin, T. Giamarchi, and E. Demler, Phys. Rev. Lett. 132, 246504 (2024)

    work page 2024

  76. [76]

    J. B. Curtis, N. Maksimovic, N. R. Poniatowski, A. Ya- coby, B. Halperin, P. Narang, and E. Demler, Phys. Rev. B 110, 144518 (2024)

    work page 2024

  77. [77]

    Z. Liu, R. Gong, J. Kim, O. K. Diessel, Q. Xu, Z. Rehfuss, X. Du, G. He, A. Singh, Y. S. Eo, et al. , arXiv preprint arXiv 2502 (2025)

    work page 2025

  78. [78]

    Ambegaokar, B

    V. Ambegaokar, B. I. Halperin, D. R. Nelson, and E. D. Siggia, Phys. Rev. B 21, 1806 (1980)

    work page 1980

  79. [79]

    Ct´ e and A

    R. Ct´ e and A. Griffin, Phys. Rev. B 34, 6240 (1986)

    work page 1986

  80. [80]

    Dasgupta, S

    S. Dasgupta, S. Zhang, I. Bah, and O. Tchernyshyov, Phys. Rev. Lett. 124, 157203 (2020)

    work page 2020

Showing first 80 references.