Pith. sign in

REVIEW 4 major objections 4 minor 45 references

Quantum Critical Scaling of Specific Heat in a Quasicrystal

T0 review · 4 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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

Pith's one-line read The electronic specific heat of the Yb-Au-Al quasicrystal collapses onto one field-temperature scaling curve, with critical exponents $\alpha_T = 0.54$ and $\alpha_B = 0.50$.

desk verdict The field-dependent specific heat scaling is a genuine new measurement, but the central exponent and collapse rest on a single unvalidated nuclear subtraction and a fit that builds in the crossover. read the letter →

arxiv 2412.06558 v1 pith:WJCIMZ4Q submitted 2024-12-09 cond-mat.str-el

A. Khansili , Y.-C. Huang , U. Häussermann , C. Pay Gomez , A. Rydh This is my paper · ORCID
classification cond-mat.str-el
keywords quasicrystalquantumcriticalpointspecificheatnon-FermiliquidYb-Au-Alaccalorimetryscalingcollapseheavyfermion
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

Using ac calorimetry from about 0.1 K to 10 K in magnetic fields up to 12 T, the paper measures the specific heat of the quantum critical quasicrystal Yb-Au-Al and argues that its electronic contribution obeys quantum critical scaling. The zero-field data follow $C_{el}/T \propto T^{-0.54}$, the high-field data follow $C_{el}/T \propto B^{-0.50}$, and all data with $0.3\text{ K} < T < 6\text{ K}$ collapse onto a single curve when plotted as $(C_{el}/T)T^{0.54}$ against $B/T^{1.08}$. This means magnetic field acts as a cutoff for the critical fluctuations, competing with temperature in the same way as in periodic quantum critical heavy-fermion metals. The significance would be that an aperiodic quasicrystal, with frustrated magnetic interactions and no translational symmetry, still shows the universal field-temperature competition expected of quantum criticality. The paper also reports two weak low-field anomalies at about 0.7 K and 2.1 K, whose origin it leaves open.

What carries the argument

The central object is the two-parameter rational scaling function $f(x) = (1 + c_1 x^p)/(1 + c_2 x^{p+\alpha_B})$ with $x = gB/T^{1+\beta}$, inserted into $C_{el}/T = \gamma_0 (T/T_0)^{-\alpha_T} f(x)$. This function is engineered so that $f(0) = 1$ gives the zero-field power law, $f(x) \sim x^{-\alpha_B}$ at large $x$ gives the high-field power law after imposing $\beta = (\alpha_T - \alpha_B)/\alpha_B$, and the maximum at $x = 1$ defines the crossover field $B^{*}(T)$ where temperature and field cutoffs balance. The machinery connects the two measured limiting regimes into a single universal collapse, while the total fit separates the nuclear contribution as an $a/T^3$ Schottky term and the phonon contribution as $bT^2$.

What would settle it

Re-measure the lowest-temperature specific heat on a sample where the $^{173}$Yb nuclear quadrupole contribution is removed (for example by $^{170}$Yb substitution) or measure the nuclear term independently on a nonmagnetic isostructural approximant, then recompute $C_{el}/T$; if the $T^{-0.54}$ divergence and the 0.7 K and 2.1 K anomalies change or vanish, the scaling collapse is an artifact of the assumed subtraction.

Watch

Extended reading notes

Core claim

The paper's central claim is that the electronic specific heat of Yb-Au-Al obeys the scaling form $C_{el}/T = \gamma_0 (T/T_0)^{-\alpha_T} f(x)$ with $x = gB/T^{1+\beta}$ and $\beta = (\alpha_T - \alpha_B)/\alpha_B$, where $f(0) = 1$ reproduces the zero-field divergence and $f(x) \sim x^{-\alpha_B}$ at large $x$ reproduces the high-field field-only power law. A global fit to the total heat capacity $C/T = a/T^3 + C_{el}/T + bT^2$ yields $\alpha_T = 0.54$, $\alpha_B = 0.50$, $\beta \approx 0.08$, $p = 2.37$, and the combined amplitude $\gamma_0 T_0^{\alpha_T} = 240\ (\text{mJ}/\text{mol-Yb K}^2)\text{K}^{\alpha_T}$. The authors take the near-equality $\alpha_T \approx \alpha_B$, hence $\beta \approx 0$, as confirmation that the magnetic energy $\mu_B B$ enters as a cutoff competing with $k_B T$, and the crossover between temperature-limited and field-limited quantum critical regions is marked by the maximum of $f(x)$ at $x = 1$. They interpret the low entropy at 10 K, below $R\ln 2$ for a Kramers doublet, as evidence of strong correlations, and they flag two small low-field anomalies at roughly 0.7 K and 2.1 K as features whose origin is not settled.

Load-bearing premise

The extraction of $C_{el}/T$ assumes that the entire nuclear contribution is a single field-independent $a/T^3$ term, and the anomalies at 0.7 K and 2.1 K as well as the $T^{-0.54}$ divergence sit in the temperature range where that subtraction dominates, with no independent measurement or error analysis of the subtraction given.

Editorial extensions

If this is right

  • The quasicrystal Yb-Au-Al is intrinsically quantum critical: its zero-field electronic specific heat diverges as $T^{-0.54}$, consistent with the previously reported susceptibility exponent $T^{-0.51}$ and specific-heat exponent $T^{-0.66}$.
  • Magnetic field cuts off the critical fluctuations, and the temperature-to-field crossover is set by $x = gB/T^{1+\beta}$ with $\beta \approx 0.08$, so the crossover field tracks $\mu_B B^*/k_B T \approx \text{const}$.
  • The universal collapse $(C_{el}/T)T^{0.54}$ versus $B/T^{1.08}$ holds from 0.3 K to 6 K in fields up to 12 T, meaning the scaling is a property of the aperiodic lattice rather than of a particular sample-dependent tuning.
  • Two weak anomalies at about 0.7 K and 2.1 K appear only at low fields and are not reflected in published susceptibility; the authors suggest local antiferromagnetic-type ordering but leave the question open.
  • At high fields the effective mass enhancement is suppressed as $C_{el}/T \propto B^{-0.50}$, the field analog of the zero-field divergence, supporting the picture of magnetic field as a cutoff.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the scaling is generic, the same $f(x)$ collapse should apply to other physical quantities in Yb-Au-Al: re-plotting the published ac susceptibility against $B/T^{1+\beta}$ and checking whether the same exponents appear would be a direct test.
  • Because $\alpha_T$ and $\alpha_B$ both land near 1/2, the scaling may realize a simple quantum critical fixed point; extracting further exponents from resistivity or NMR relaxation would test whether the exponents obey standard scaling relations in an aperiodic system.
  • The assumed field independence of the $a/T^3$ nuclear term is not measured independently; verifying it by isotope substitution or by comparison with an approximant crystal would either harden the 0.54 exponent or reveal a subtraction artifact.
  • If the 0.7 K and 2.1 K anomalies are intrinsic, they suggest local ordering degrees of freedom coexisting with quantum criticality; muon spin rotation or inelastic neutron scattering could detect static or slowly fluctuating moments that susceptibility misses.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The paper reports specific-heat measurements of the quantum-critical quasicrystal Yb-Au-Al in fields up to 12 T and temperatures from about 0.1 to 10 K. The authors propose a scaling form for the electronic specific heat, C_el/T = γ0 (T/T0)^{-α_T} f(g B / T^{1+β}), with f(x) chosen to reproduce a power-law divergence at zero field, a power-law suppression at high field, and a maximum at the crossover field B*(T). From a global fit to Eq. (14) they obtain α_T = 0.54 and α_B = 0.50, and show a collapse of (C_el/T)T^{0.54} versus B/T^{1.08}. They also report two weak anomalies at 0.7 K and 2.1 K. The central claim is that magnetic field acts as a cutoff for critical fluctuations in an aperiodic system, in the same way as in periodic quantum-critical metals.

Significance. If the scaling claim is correct, this is an important result: it would extend the phenomenology of quantum-critical scaling, usually developed for periodic heavy-fermion systems, to a quasicrystal, and it would establish that field-temperature competition survives aperiodicity. The paper reports a genuinely large dataset (0-12 T, 0.1-10 K) and makes an explicit, falsifiable scaling ansatz, which is a strength. The authors also performed a TISP check showing that nuclear spins are thermalized on the time scale of the ac measurement, which addresses one common experimental concern. However, the central result currently rests on a single fitted nuclear-subtraction term, on a scaling function whose maximum is fixed at x=1 by construction, and on fits that are presented without uncertainties. Because the collapse in Fig. 2(d) uses the same data that determined the exponents, the paper does not yet provide a quantitative test that would distinguish the proposed scaling from other low-order phenomenological descriptions. The potential significance justifies a major revision, but the evidence as presented is not yet fully convincing.

major comments (4)
  1. [Results & Discussion, Eq. (14) and Table I] The extraction of C_el/T depends entirely on the nuclear subtraction a/T^3. The paper asserts that the nuclear contribution is field-independent and dominated by the zero-field quadrupole term, but no independent measurement, no error estimate, and no sensitivity analysis is provided. The TISP result (T1 < 1 ms) demonstrates that the nuclear spins thermalize on a fast time scale, but it does not establish the functional form or magnitude of the nuclear Schottky term. Because the lowest-temperature points, where the anomalies at 0.7 K and 2.1 K and the zero-field exponent 0.54 are most influential, are precisely where a/T^3 dominates, a misestimate of a can trade off directly against α_T. I ask for a sensitivity analysis: vary a within a plausible range (e.g., using known quadrupole moments and hyperfine parameters), include a field-dependent or multi-level nuclear term, and show how α_T, α_B, and the collapse in Fig. 2(d) change.
  2. [Results & Discussion, Eqs. (7)-(8) and (13)] The crossover field B*(T) is imposed by construction rather than derived from the data. Equation (8) is chosen specifically so that f(x) has its maximum at x=1, and Eq. (13) defines x so that x=1 corresponds to B = B*(T). Consequently, the observation that C/T exhibits a maximum at the crossover field does not confirm the field-as-cutoff picture; it is built into the ansatz. The text around Eq. (13) and in the Conclusions states that the data 'confirm' the assumption that magnetic field is a cutoff. That statement overreaches. I recommend rephrasing this as a consistency check and, more importantly, providing tests of the ansatz that are not built in, such as whether the collapse holds when the exponents are fixed by independent data sets or when f(x) is replaced by a different functional form.
  3. [Abstract and Introduction] The abstract claims that the zero-field exponent α_T = 0.54 'aligns' with the previous specific-heat measurement reported in Ref. [2], but Ref. [2] reported C/T ∝ T^{-0.66}. A difference of 0.12 in the exponent is not an alignment, and the paper never discusses possible reasons for the discrepancy (different temperature range, different fitting procedure, sample composition, or nuclear subtraction). This is a direct conflict between the stated claim and the cited literature. At minimum, the paper must address this explicitly and, if the difference is real, explain it; if the difference reflects the subtraction, that strengthens the concern raised above about Eq. (14).
  4. [Results & Discussion, Fig. 2(e)-(f) and Table I] The paper presents no uncertainties on any of the fitted parameters in Table I and no residuals or confidence contours from the χ² maps in Figs. 2(e) and 2(f). The scaling collapse in Fig. 2(d) is visually plausible, but it is obtained using the same dataset that was used to optimize α_T and α_B, so a visual collapse is expected to some degree even if the model is only approximately correct. The paper should report residuals, a bootstrap or leave-one-out procedure, or a holdout analysis, and should give confidence intervals for α_T, α_B, p, and the other parameters. Without this, the claim that the data 'confirm' the scaling function is not quantitatively falsifiable.
minor comments (4)
  1. [Figure 2(d) caption and Eq. (13)] The x-axis in Fig. 2(d) is labeled B/T^{1.08}, whereas the scaling variable in Eq. (13) is x = g B / T^{1+β} with g = 1.09. Please state explicitly whether g has been set to 1 for plotting or whether the plotted axis already includes g.
  2. [Figure 1(a) caption] The caption for Fig. 1(a) appears garbled: 'TE DOD ICS IDH RTH DF' and 'Non- RE site' are not meaningful as printed. The caption should be rewritten to clearly define the cluster shells and the labeling of the Yb sites.
  3. [Eq. (8)] The condition c1 > c2 is stated without explanation, and the denominator p - α_B c2 could vanish for certain parameter combinations. Please specify the domain of parameters used in the fit and whether the positivity of c1 imposes constraints on c2 and p.
  4. [Table I] The units given for g, '(K/T) K^β', are awkward though dimensionally plausible. Consider writing g in units of K^{1+β}/T or stating that β = 0.08 so the units are approximately K^{1.08}/T.

Circularity Check

2 steps flagged · score 6.0 of 10

The crossover line and the zero-field power law are partly imposed by the fitted scaling function; the data collapse is a real fit outcome but not an independent confirmation of the quantum-critical assumptions.

  1. self definitional [Eqs. (7)-(8), (13); Fig. 3(b)]
    "We fix the relation between c1 and c2 so that f (x) in Eq. (7) has its maximum at x = 1, where c1 = c2(p + αB)/(p − αBc2) ... The location of B∗(T ) of Eq. (5), given by x = 1 and Eq. (13), is marked by the solid line."

    The maximum of f(x) is imposed to occur at x = 1 by Eq. (8), and then x = 1 is used to define the crossover field B*(T). The solid line in Fig. 3(b) is therefore a contour of the same fitted function (through fitted g and β), not an independent prediction of where the temperature-limited and field-limited regions meet. Its agreement with the measured markers is a consistency check on the fitted ansatz, not a verification that magnetic field acts as a cutoff.

  2. fitted input called prediction [Eq. (14); Table I; Fig. 3(a)]
    "After subtracting the nuclear contribution to C/T in Fig. 1b, the remaining Cel/T closely follows Eq. (3). ... The data of Fig. 1b,c were used to fit an expression for the total specific heat capacity, C/T|total = a/T^3 + Cel/T + bT^2, where Cel/T is given by Eq. (6), the parameter a describes the high-temperature Schottky tail of the nuclear specific heat, and b gives the low-temperature phonon contribution."

    Cel/T is not independently measured: the nuclear Schottky coefficient a and Cel/T are determined by the same global fit in Eq. (14). At zero field, Eq. (6) already enforces Cel/T = γ0(T/T0)^−αT f(0) = γ0(T/T0)^−αT because f(0)=1, so the statement that the residual 'closely follows' Eq. (3) is a restatement of the fitting function. The exponent 0.54 and the two small anomalies are outputs of this same subtraction-plus-fit procedure, so they cannot serve as an independent check on the nuclear subtraction or on the scaling hypothesis.

full rationale

The paper's central collapse in Fig. 2(d) does have genuine empirical content: obtaining a single scaling curve for C/T data over 0.3-6 K and 0-12 T is not guaranteed merely by fitting. Nevertheless, two load-bearing parts of the claimed derivation reduce to the fitted ansatz. First, Eq. (8) forces f(x) to have its maximum at x=1, and x=1 then defines B*(T); hence the crossover line in Fig. 3(b) is a contour of the fitted function rather than a predicted boundary. Second, the zero-field electronic specific heat is not a directly measured quantity: Eq. (14) fits a, b, and Cel/T simultaneously, with Cel/T defined by Eq. (6); the observation that the residual 'closely follows' T^{-0.54} is therefore built into the fit, not an independent confirmation. The scaling exponents are legitimate fit outputs, and the collapse is a nontrivial characterization, but the paper's statements that the data 'confirm' the field-cutoff assumption and that the zero-field law aligns with prior measurements go beyond what the same-data fit can establish. No load-bearing self-citation chain was found; the TISP citation supports experimental thermalization and is not circular.

Assumptions & free parameters 9 free parameters · 5 assumptions · 0 invented entities

The central scaling claims rest on nine fitted parameters and several assumptions about the scaling function and the nuclear subtraction. No first-principles derivation is offered, so the ledger is dominated by fitting choices rather than independently grounded inputs.

free parameters (9)
  • a = 1.26 mJ K/mol-Yb
    Amplitude of the nuclear Schottky tail a/T^3 in Eq. 14; fitted to the total specific heat.
  • b = 2.83 mJ/mol-Yb K^4
    Low-temperature phonon coefficient in the bT^2 term of Eq. 14; fitted.
  • gamma0_T0_combined = 240 (mJ/mol-Yb K^2) K^0.54
    Combined scaling prefactor gamma0 T0^alphaT; the fit cannot separate gamma0 from T0.
  • alphaT = 0.54
    Zero-field critical exponent in Eq. 3 and Eq. 6; optimized by stepping through values in Fig. 2e.
  • alphaB = 0.50
    High-field critical exponent in Eq. 4; optimized by stepping through values in Fig. 2e.
  • c1 = 1.73
    Numerator constant in f(x), Eq. 7; constrained by Eq. 8 to place the maximum at x = 1.
  • c2 = 1.10
    Denominator constant in f(x), Eq. 7; fitted.
  • p = 2.37
    Exponent in f(x) controlling the crossover shape; fitted, with intensity plot in Fig. 2f.
  • g = 1.09 (K/T) K^beta
    Conversion factor in x = g B/T^(1+beta), Eq. 13; fitted.
assumptions (5)
  • domain assumption The Yb 4f state is effectively a spin-1/2 Kramers doublet below about 50 K due to crystal field splitting.
    Taken from prior susceptibility work (Ref. 2) and used in the introduction to motivate quantum criticality in this material.
  • domain assumption Hertz-Millis quantum critical scaling applies to this quasicrystal, with temperature and magnetic field entering as cutoffs for critical fluctuations.
    The entire analysis adopts the standard quantum critical framework of Refs. 41-42 without testing whether quasicrystalline disorder requires a different description.
  • ad hoc to paper The scaling function f(x) in Eq. 7 has the specific rational form with a maximum at x = 1.
    This form is constructed, not derived, to interpolate between the T^(-0.54) and B^(-0.50) limits and to place the crossover at x = 1.
  • ad hoc to paper High-field C/T is independent of T, which forces beta = (alphaT - alphaB)/alphaB in Eq. 11.
    This is an imposed constraint rather than a measured or derived relation, used to cancel temperature dependence in the high-field limit.
  • ad hoc to paper The crossover field B*(T) is defined by g B/T^(1+beta) = 1.
    Combines Eq. 5 and Eq. 13; the observed maximum in C/T versus B is matched by construction through the c1 constraint.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Quantum Critical Scaling of Specific Heat in a Quasicrystal." pith.science (2026). https://pith.science/paper/WJCIMZ4Q

@misc{pith2026241206558,
  author       = {Pith},
  title        = {Pith review of: Quantum Critical Scaling of Specific Heat in a Quasicrystal},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WJCIMZ4Q}},
  note         = {Machine review of arXiv:2412.06558}
}
abstract

In strongly correlated systems, interactions give rise to critical fluctuations surrounding the quantum critical point (QCP) of a quantum phase transition. Quasicrystals allow the study of quantum critical phenomena in aperiodic systems with frustrated magnetic interactions. Here, we study the magnetic field and temperature scaling of the low-temperature specific heat for the quantum critical Yb-Au-Al quasicrystal. We devise a scaling function that encapsulates the limiting behaviors as well as the area where the system goes from a temperature-limited to a field-limited quantum critical region, where magnetic field acts as a cutoff for critical fluctuations. The zero-field electronic specific heat is described by a power-law divergence, ${C_{el}/T \propto T^{-0.54}}$, aligning with previously observed ac-susceptibility and specific heat measurements. The field dependence of the electronic specific heat at high magnetic fields shows a similar power-law ${C_{el}/T \propto B^{-0.50}}$. In the zero-field and low-field region, we observe two small but distinct anomalies in the specific heat, located at 0.7 K and 2.1 K.

Figures

Figures reproduced from arXiv: 2412.06558 by the authors.

Figure 1
Figure 1. FIG. 1. Measured specific heat as a function of temperature and magnetic field. (a) The polyhedron cluster shells that make the [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Analysis of scaling behavior. (a) Scaling function [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a) Temperature dependence of electronic spe [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

45 extracted references · 42 canonical work pages

  1. [2]

    Watanuki, S

    T. Watanuki, S. Kashimoto, D. Kawana, T. Yamazaki, A. Machida, Y. Tanaka, and T. J. Sato, Physical Review B 86, 094201 (2012)

    work page 2012

  2. [1]

    Deguchi, S

    K. Deguchi, S. Matsukawa, N. K. Sato, T. Hattori, K. Ishida, H. Takakura, and T. Ishimasa, Nature Mate- rials 11, 1013 (2012)

    work page 2012

  3. [3]

    Stewart, Reviews of Modern Physics 73, 797 (2001)

    G. Stewart, Reviews of Modern Physics 73, 797 (2001)

    2001

  4. [4]

    H. v. L¨ ohneysen, A. Rosch, M. Vojta, and P. W¨ olfle, Reviews of Modern Physics 79, 1015 (2007)

    work page 2007

  5. [5]

    Gegenwart, Q

    P. Gegenwart, Q. Si, and F. Steglich, Nature Physics 4, 186 (2008)

    work page 2008

  6. [6]

    M. Y. Amusia, K. G. Popov, V. R. Shaginyan, and V. A. Stephanovich, Springer Series in Solid-State Sci- ences 182, 33 (2014)

    work page 2014

  7. [7]

    A. J. Schofield, Contemporary Physics 40, 95 (1999)

    1999

  8. [8]

    Armitage, P

    N. Armitage, P. Fournier, and R. Greene, Reviews of Modern Physics 82, 2421 (2010)

    work page 2010

Show all 45 references
  1. [9]

    Abrahams and Q

    E. Abrahams and Q. Si, Journal of Physics: Condensed Matter 23, 223201 (2011)

    2011

  2. [10]

    C. M. Varma, Reviews of Modern Physics 92, 031001 (2020)

    2020

  3. [11]

    Khansili, Y.-C

    A. Khansili, Y.-C. Huang, U. H¨ aussermann, C. Gomez, and A. Rydh, arXiv preprint arXiv: 2409.04279 (2024)

    2024 arXiv

  4. [12]

    M. B. Stone, C. Broholm, D. Reich, O. Tchernyshyov, P. Vorderwisch, and N. Harrison, Physical Review Let- ters 96, 257203 (2006)

    2006

  5. [13]

    Dressel, Journal of Physics: Condensed Matter 23, 293201 (2011)

    M. Dressel, Journal of Physics: Condensed Matter 23, 293201 (2011)

    2011

  6. [14]

    Furukawa, K

    T. Furukawa, K. Miyagawa, H. Taniguchi, R. Kato, and K. Kanoda, Nature Physics 11, 221 (2015)

    2015

  7. [15]

    Shechtman, I

    D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, Physical Review Letters 53, 1951 (1984)

    1984

  8. [16]

    Wessel, A

    S. Wessel, A. Jagannathan, and S. Haas, Physical Re- view Letters 90, 177205 (2003)

    2003

  9. [17]

    A. I. Goldman, T. Kong, A. Kreyssig, A. Jesche, M. Ra- mazanoglu, K. W. Dennis, S. L. Bud’ko, and P. C. Can- field, Nature Materials 12, 714 (2013)

    2013

  10. [18]

    A. I. Goldman, Science and Technology of Advanced Ma- terials 15, 044801 (2014)

    2014

  11. [19]

    Thiem and J

    S. Thiem and J. Chalker, Physical Review B 92, 224409 (2015)

    2015

  12. [20]

    Kamiya, T

    K. Kamiya, T. Takeuchi, N. Kabeya, N. Wada, T. Ishi- masa, A. Ochiai, K. Deguchi, K. Imura, and N. Sato, Nature Communications 9, 154 (2018)

    2018

  13. [21]

    Tamura, A

    R. Tamura, A. Ishikawa, S. Suzuki, T. Kotajima, Y. Tanaka, T. Seki, N. Shibata, T. Yamada, T. Fujii, C.-W. Wang, et al., Journal of the American Chemical Society 143, 19938 (2021)

    2021

  14. [22]

    N. K. Sato, T. Ishimasa, K. Deguchi, and K. Imura, Journal of the Physical Society of Japan 91, 072001 (2022)

    2022

  15. [23]

    Takeuchi, F

    R. Takeuchi, F. Labib, T. Tsugawa, Y. Akai, A. Ishikawa, S. Suzuki, T. Fujii, and R. Tamura, Physical Review Letters 130, 176701 (2023)

    2023

  16. [24]

    Lopez-Bezanilla and C

    A. Lopez-Bezanilla and C. Nisoli, Science Advances 9, eadf6631 (2023)

    2023

  17. [25]

    Terashima, Y

    T. Terashima, Y. Tokumoto, K. Hamano, T. Konoike, N. Kikugawa, and K. Edagawa, npj Quantum Materials 9, 56 (2024)

    2024

  18. [26]

    Charrier, B

    B. Charrier, B. Ouladdiaf, and D. Schmitt, Physical Re- view Letters 78, 4637 (1997)

    1997

  19. [27]

    L. Pham, T. Park, S. Maquilon, J. Thompson, and Z. Fisk, Physical Review Letters 97, 056404 (2006)

    2006

  20. [28]

    Belitz, T

    D. Belitz, T. Kirkpatrick, and T. Vojta, Reviews of Mod- ern Physics 77, 579 (2005)

    2005

  21. [29]

    Ishimasa, Y

    T. Ishimasa, Y. Tanaka, and S. Kashimoto, Philosophi- cal Magazine 91, 4218 (2011)

    2011

  22. [30]

    Tagliati, V

    S. Tagliati, V. M. Krasnov, and A. Rydh, Review of Scientific Instruments 83, 055107 (2012)

    2012

  23. [31]

    Willa, Z

    K. Willa, Z. Diao, D. Campanini, U. Welp, R. Divan, M. Hudl, Z. Islam, W.-K. Kwok, and A. Rydh, Review of Scientific Instruments 88, 125108 (2017)

    2017

  24. [32]

    Khansili, A

    A. Khansili, A. Bangura, R. D. Mcdonald, B. J. Ramshaw, A. Rydh, and A. Shekhter, Physical Review B 107, 195145 (2023)

    2023

  25. [33]

    A.-P. Tsai, J. Guo, E. Abe, H. Takakura, and T. J. Sato, Nature 408, 537 (2000)

    2000

  26. [34]

    Takakura, C

    H. Takakura, C. P. Gomez, A. Yamamoto, M. De Boissieu, and A. P. Tsai, Nature Materials 6, 58 (2007)

    2007

  27. [35]

    Coleman and A

    P. Coleman and A. H. Nevidomskyy, Journal of Low Tem- perature Physics 161, 182 (2010)

    2010

  28. [36]

    Coleman, Physica Status Solidi (b) 247, 506 (2010)

    P. Coleman, Physica Status Solidi (b) 247, 506 (2010)

    2010

  29. [37]

    Gegenwart, F

    P. Gegenwart, F. Steglich, C. Geibel, and M. Brando, The European Physical Journal Special Topics 224, 975 (2015)

    2015

  30. [38]

    Stone, Atomic Data and Nuclear Data Tables 111, 1 (2016)

    N. Stone, Atomic Data and Nuclear Data Tables 111, 1 (2016)

    2016

  31. [39]

    H. v. L¨ ohneysen, C. Pfleiderer, T. Pietrus, O. Stockert, and B. Will, Physical Review B 63, 134411 (2001)

    2001

  32. [40]

    Khansili, A

    A. Khansili, A. Bangura, R. McDonald, B. Ramshaw, A. Rydh, and A. Shekhter, arXiv preprint arXiv: 2311.11914 (2023)

    2023

  33. [41]

    J. A. Hertz, Physical Review B 14, 1165 (1976)

    1976

  34. [42]

    Millis, Physical Review B 48, 7183 (1993)

    A. Millis, Physical Review B 48, 7183 (1993)

    1993

  35. [43]

    Shaginyan, M

    V. Shaginyan, M. Y. Amusia, A. Msezane, and K. Popov, Physics Reports 492, 31 (2010)

    2010

  36. [44]

    Shaginyan, A

    V. Shaginyan, A. Msezane, K. Popov, G. Japaridze, and V. Khodel, Physical Review B 87, 245122 (2013)

    2013

  37. [45]

    Shaginyan, A

    V. Shaginyan, A. Msezane, G. Japaridze, K. Popov, and V. Khodel, Frontiers of Physics 11, 1 (2016)

    2016

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.