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REVIEW 3 major objections 4 minor 28 references

Magnetic field induced arrested state and observation of spontaneous anomalous Hall effect in TbMn$_6$Sn$_6$

T0 review · 3 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Field cooling locks TbMn6Sn6's full magnetization until a half-kelvin collapse near 200 K.

desk verdict Believable measurements of large remanent magnetization and zero-field Hall in TbMn6Sn6, but the 'arrested state' framing is just ordinary hysteresis remanence until the interpretation is fixed. read the letter →

arxiv 2411.18950 v1 pith:5MCEJBC5 submitted 2024-11-28 cond-mat.mtrl-sci

Tamali Roy , Prasanta Chowdhury , Mohamad Numan , Saurav Giri , Subham Majumdar , Sanat Kumar Adhikari , Souvik Chatterjee This is my paper · ORCID
classification cond-mat.mtrl-sci
keywords thermo-remanentmagnetizationspontaneousanomalousHalleffectkagomeferrimagnetTbMn6Sn6field-cooledarrestedstatezero-fieldresistivityspinreorientationuniaxialanisotropy
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

The paper reports that cooling the kagome ferrimagnet TbMn6Sn6 in a moderate magnetic field (5 kOe) leaves it with a magnetization equal to its saturation value, and that this state survives on rewarming in fields as small as 20 Oe or even zero. The retained magnetization collapses within 0.5 K near 200 K, and exactly at that temperature an equally sharp step appears in the Hall resistivity measured in zero field. The paper interprets the two observations as one phenomenon: a field-induced arrested magnetic state whose large remanent moment drives a spontaneous anomalous Hall effect, both of which release together at a well-defined temperature. If correct, the compound gives a single material where a full magnetic polarization and its associated Berry-curvature Hall signal can be written by field cooling and read back with no applied field.

What carries the argument

The central object is the field-cooled arrested state: cooling in 5 kOe along the easy $c$ axis aligns the strongly anisotropic spins and freezes them into a configuration that stays at saturation when the field is removed. The named measurement objects are thermo-remanent magnetization ($M_{\text{tr}}$), the magnetization retained while heating in a small or zero field after field cooling, and thermo-remanent Hall resistivity ($\rho_{xy}^{\text{tr}}$), the zero-field Hall response of that same state. The argument that $\rho_{xy}^{\text{tr}}$ is a genuine spontaneous anomalous Hall effect is carried by the scaling relation $\rho_{xy} = S_H M \rho_{xx}^2(1+\alpha'/\rho_{xx})$, from Eq. (3) of the paper, which is fitted to the joint temperature dependence of $\rho_{xy}^{\text{tr}}/M_{\text{tr}}$ and $\rho_{xx}$ and traces the data well below 200 K; this ties the Hall signal directly to the retained magnetization rather than to an applied field. The sharp release near 200 K is attributed to cooperative de-arrest, supported by the strong intersite exchange ($J \sim -29$ meV) and by the onset of magnetic fluctuations in that temperature range.

What would settle it

After field cooling in 5 kOe, stop the zero-field heating at 150 K and monitor magnetization for several hours; if $M_{\text{tr}}$ relaxes toward the value expected from the hysteresis loop, or if pausing the heating at 150 K erases or weakens the subsequent 200 K jump, the arrested-state interpretation fails. A complementary check is to measure ac susceptibility or a field-stop memory protocol: a true glassy arrest produces aging and memory, whereas ordinary coercivity-driven remanence does not.

Watch

Extended reading notes

Core claim

Stated in the authors' terms: TbMn6Sn6, a collinear ferrimagnet with a kagome Mn lattice and a spin-reorientation transition near 310 K, is a topological magnet whose anomalous Hall conductivity comes from Berry curvature. When the crystal is cooled under $H_{\text{cool}} = 5$ kOe applied along the $c$ axis and then heated in 20–100 Oe or in zero field, the magnetization $M_{\text{tr}}$ stays pinned at the saturation value $M_{\text{sat}}$ up to about 200 K, then falls by more than an order of magnitude in a jump that occurs within 0.5 K. The zero-field Hall resistivity during the same protocol, called the thermo-remanent Hall effect $\rho_{xy}^{\text{tr}}$, matches the anomalous Hall resistivity extracted from hysteresis loops, both in magnitude and in its sharp collapse near 200 K; cooling in the opposite field produces the mirror-image response. The authors conclude that field cooling arrests the spin system in an energy minimum, that the arrest is broken only when the uniaxial anisotropy weakens or thermal fluctuations grow, and that the remanent magnetization itself is enough to produce a spontaneous anomalous Hall effect.

Load-bearing premise

The interpretation rests on the premise that the saturated magnetization retained after field cooling is a genuinely arrested magnetic state, rather than ordinary remanence from a wide hysteresis loop, because the paper relies on the sharp collapse to label the state exotic and does not include relaxation, aging, or memory measurements to separate the two.

Editorial extensions

If this is right

  • A field-cooled sample heated in 20 Oe or 100 Oe follows the 5 kOe cooling curve to about 200 K, so the remanent state carries the full saturation moment rather than a reduced fraction.
  • The zero-field Hall resistivity after field cooling matches the anomalous Hall resistivity from hysteresis loops, so the intrinsic Berry-curvature Hall signal can be read with no applied field.
  • The magnetization and the Hall signal both collapse within 0.5 K near 200 K, so the same event switches off the magnetic polarization and the spontaneous Hall voltage.
  • The effect is absent for fields perpendicular to the c axis and present for fields along the c axis, identifying the uniaxial anisotropy as the ingredient that makes the arrested state possible.
  • Fits of the thermo-remanent Hall to the anomalous Hall scaling relation indicate the intrinsic contribution dominates in the zero-field state as well.

Reading between the lines

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

  • Because the 200 K collapse coincides with the temperature where the hysteresis loop and coercivity nearly vanish, the 'arrested' state may be the high-coercivity branch of ordinary magnetization reversal; an aging or time-decay experiment would decide without invoking new physics.
  • The sign of the cooling field sets the sign of both the remanent magnetization and the zero-field Hall voltage, so field cooling could serve as a write step and zero-field Hall measurement as a read step; repeated cycling would test whether the write-read sequence is durable.
  • If the zero-field Hall signal faithfully reproduces the anomalous Hall effect, the field-cooling protocol gives a way to measure Berry-curvature Hall response without applying a field, which could simplify transport studies of kagome magnets at high temperatures.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper reports thermo-remanent magnetization (TRM) and zero-field Hall resistivity (TRH) measurements on single-crystal TbMn6Sn6 after field cooling in ±5 kOe. On heating in 20–100 Oe or zero field, the magnetization and Hall resistivity retain near-saturation values up to about 200 K and then collapse abruptly within roughly 0.5 K. The authors interpret this as evidence for an arrested, cluster-glass-like magnetic state induced by field cooling, and they describe the zero-field Hall signal as a spontaneous anomalous Hall effect. They also fit the TRH and TRM data to scaling relations (Eqs. 2 and 3) to argue that the two quantities vary conjointly and that the intrinsic contribution dominates.

Significance. The measurements are careful and reproducible across two independently grown batches (B1 and B2), and the observation that the zero-field Hall resistivity follows the remanent magnetization in the same temperature window is a useful confirmation of anomalous Hall scaling in a ferrimagnet. If the arrested-state interpretation were established, the sharp collapse near 200 K would be an interesting phenomenon. However, the central interpretation is not yet supported: the data are quantitatively consistent with ordinary ferromagnetic remanence controlled by the temperature-dependent coercivity, and no discriminating glass diagnostics (aging, memory, ac susceptibility, nonlinear susceptibility) are presented. The paper would be significantly strengthened either by adding such measurements or by reframing the claims as a study of remanence and its Hall signature.

major comments (3)
  1. [Sec. 3 (TRM results, Fig. 2)] The claim that field cooling produces an 'arrested state' is not distinguished from conventional remanence. The paper's own hysteresis data in Fig. 1(b) show a rectangular loop at 50 K with coercivity 4.3 kOe, with the loop almost vanishing above about 200 K. Cooling in 5 kOe and then applying 20–100 Oe leaves the sample on the positive remanence branch of the hysteresis loop; the magnetization will remain near saturation until Hc(T) falls to the order of the applied (or demagnetizing) field, at which point the remanence collapses. The observed jump near 200 K is therefore exactly where coercivity vanishes, as the authors themselves note. No aging, memory, or ac-susceptibility measurements are presented that would distinguish cluster-glass arrest from ordinary domain-wall pinning. This is a load-bearing interpretive step and must either be supported by such experiments or substantially moderated.
  2. [Sec. 4 and Fig. 3(d)] The zero-field Hall resistivity that matches the H=0 intercept of isothermal Hall loops is the remanent anomalous Hall effect expected from Eq. (1), ρxy = R0H + 4πRsM, with H=0 and M equal to the remanent magnetization. The agreement in Fig. 3(d) confirms the AHE scaling but does not by itself require any exotic arrested state. Calling this a 'spontaneous anomalous Hall effect' is misleading unless the authors demonstrate that the remanence itself cannot be produced by ordinary hysteresis in the same temperature range. Please either provide such a demonstration or use more neutral terminology such as 'remanent anomalous Hall effect.'
  3. [Eq. (3) fit and Fig. 4] The conclusion that TRH and TRM 'vary conjointly' rests on a two-parameter fit of ρtr_xy/Mtr against ρxx using Eq. (3). Because Mtr appears in the denominator of the plotted quantity, the fit is a weak test: any smooth temperature dependence of Mtr can be absorbed by the two free parameters SH and α′. The manuscript does not report fit residuals, parameter uncertainties, or an independent check where the measured ρtr_xy is compared with the prediction computed from separately measured Mtr and ρxx. Please provide these; otherwise the 'conjointly' claim is not established beyond the visual overlap in Figs. 2 and 3.
minor comments (4)
  1. [Abstract and main text] The sentence 'The ultrasharp jump in magnetization is also get reflected in our Hall data' contains a grammatical error; it should read 'is also reflected.'
  2. [Fig. 3(c) caption] The antisymmetrization procedure used to obtain the green and orange curves is not fully described. Please specify how the data from positive and negative cooling fields were combined and whether the symmetrized curve includes both cooling and heating branches.
  3. [Sec. 3, Fig. 2(b) discussion] The statement that 'Mtr is as high as Msat' would benefit from a quantitative comparison with error bars, since the red triangles and the heating curve appear to overlap but no numerical difference or uncertainty is given.
  4. [Eq. (2) and Fig. 4 inset] The quality of the fit to Eq. (2) is not quantified. Please report the goodness-of-fit (e.g., R² or chi-square) and the temperature range used, and enlarge the inset so that the data and fit line are legible.

Circularity Check

1 steps flagged · score 2.0 of 10

Central TRM/TRH observations are direct measurements; only the Eq. (3) 'conjoint variation' claim is self-confirming by construction.

  1. self definitional [Fig. 4 and Eq. (3), section discussing 'the role of TRM on ρtr_xy']
    "We have plotted ρtr_xy/Mtr as a function of ρxx in Fig. 4 for T <200 K, the curve is fitted using eqn. 3. The fitted curve traces the experimental data reasonably well, and it indicates that TRH and TRM vary conjointly."

    Eq. (3) is ρxy = SH M ρxx^2 (1 + α′/ρxx), so M appears explicitly as a factor in the assumed relation. Plotting ρtr_xy/Mtr against ρxx and fitting the two free parameters SH and α′ to the same measured ρxy and M data cannot independently demonstrate that TRH and TRM 'vary conjointly': the fitted form already builds in proportionality between ρxy and M. The success of a two-parameter fit to smooth data is therefore largely a consistency check, not a test of the conjoint variation claim.

full rationale

The magnetization and Hall measurements are direct: TRM is read from a magnetometer and TRH from a voltmeter after field cooling, and the sharp jumps near 200 K appear in the raw data. The main comparisons are external benchmarks, not fits: TRM is compared to Msat extracted from M-H loops, and TRH is compared to the H=0 intercept of anomalous Hall hysteresis loops. Those comparisons do not reduce to fitted inputs. The one genuinely circular element is the Eq. (3) analysis, where the paper fits ρtr_xy/Mtr versus ρxx with free parameters SH and α′ and then states that the fit 'indicates that TRH and TRM vary conjointly'; because Eq. (3) already contains M as a factor, the claimed conjoint variation is partly built into the assumed relation. This is a minor circularity in an ancillary confirmation, not in the central observation of thermo-remanence and spontaneous zero-field Hall resistivity. The 'arrested state' / cluster-glass interpretation relies on an external prior study and on the paper's own observation that coercivity vanishes near 200 K; the absence of aging or memory measurements is a scientific-support concern, not a circularity. Overall the derivation chain is largely self-contained, so the circularity score is 2.

Assumptions & free parameters 4 free parameters · 3 assumptions · 0 invented entities

The central observation requires no invented entities. The main burden is the assumed applicability of the standard Hall decompositions and the assumed cluster-glass landscape; the fitted parameters are data-reduction parameters, not independent physical quantities.

free parameters (4)
  • alpha (skew-scattering coefficient in Eqn 2) = 8.6 x 10^-4
    Fitted to rho_xy^tr versus rho_xx using Eqn 2; used to argue that the intrinsic contribution dominates in the thermoremanent Hall signal.
  • beta (side-jump and intrinsic coefficient in Eqn 2) = 1.37 x 10^-4 (micro-ohm-cm)^-1
    Fitted in the same procedure; compared with literature values to identify the intrinsic AHE contribution.
  • SH (Hall coefficient in Eqn 3) = 0.056 V^-1
    Fitted to rho_xy^tr/Mtr versus rho_xx; used to claim that TRH and TRM vary conjointly.
  • alpha-prime (parameter in Eqn 3) = 2.13 x 10^-7 ohm-m
    Fitted in the same procedure; not independently verified against external predictions.
assumptions (3)
  • domain assumption The Hall resistivity separates as rho_xy = R0 H + 4 pi Rs M (Eqn 1), and linear high-field extrapolation to H = 0 gives the anomalous Hall contribution.
    Standard two-channel Hall decomposition is assumed; any multiband or topological contribution would bias the extracted rho_A^xy.
  • domain assumption TbMn6Sn6 is in a cluster-glass-like magnetic state based on Ref 14, providing multiple energy minima for field cooling.
    The 'arrested' explanation assumes glassy or cluster-glass dynamics; the paper does not directly measure aging, memory, or ac susceptibility.
  • domain assumption The relations rho_A = alpha rho_xx + beta rho_xx^2 (Eqn 2) and Eqn 3 from Ref 21 apply to the thermoremanent Hall data.
    These are fitting forms assumed valid; fitted parameters are then used to discuss scattering mechanisms.

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Pith. "Pith review of Magnetic field induced arrested state and observation of spontaneous anomalous Hall effect in TbMn$_6$Sn$_6$." pith.science (2026). https://pith.science/paper/5MCEJBC5

@misc{pith2026241118950,
  author       = {Pith},
  title        = {Pith review of: Magnetic field induced arrested state and observation of spontaneous anomalous Hall effect in TbMn$_6$Sn$_6$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5MCEJBC5}},
  note         = {Machine review of arXiv:2411.18950}
}
abstract

The quasi two-dimensional kagome ferrimagnet TbMn$_6$Sn$_6$ is investigated for thermo-remanent magnetization and Hall effects. On cooling under a moderate magnetic field, the sample attains a magnetization value close to the saturation magnetization. Upon heating in a very small magnetic field, the sample continues to maintain the large value of magnetization, which eventually diminishes distinctly at around 200 K manifesting an ultrasharp jump. A similar feature is also observed in the Hall resistivity, which holds its saturation value when heated back in zero field after being field-cooled. The ultrasharp jump in magnetization is also get reflected in our Hall data. The observed data is exotic and can be rooted to the large anisotropy and the strong exchange interaction.

Figures

Figures reproduced from arXiv: 2411.18950 by the authors.

Figure 2
Figure 2. FIG. 2. Temperature dependence of magnetization while cool [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 1
Figure 1. FIG. 1. (a) Temperature dependence of magnetization along [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a) Field dependence of Hall resistivity ( [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Temperature dependence of magnetization is shown [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]
Figure 5
Figure 5. Figure 5: FIG. 5. (a) XRD pattern of a single crystal piece (from batch [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]
Figure 7
Figure 7. Figure 7: FIG. 7. (a) Temperature dependence of magnetization with [PITH_FULL_IMAGE:figures/full_fig_p006_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. (a) The longitudinal resistivity ( [PITH_FULL_IMAGE:figures/full_fig_p006_8.png]

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