Pith. sign in

REVIEW 3 major objections 5 minor 48 references

Controllable thickness inhomogeneity and Berry-curvature-engineering of anomalous Hall effect in SrRuO3 ultrathin films

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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

Pith's one-line read In SrRuO3 ultrathin films, hump-like Hall anomalies can be produced by a controllable thickness inhomogeneity that creates two anomalous Hall channels of opposite sign, rather than by magnetic skyrmions.

desk verdict A well-executed growth and imaging study that makes a strong case for two-channel AHE as the cause of hump Hall features in inhomogeneous SrRuO3, but the quantitative superposition evidence in Fig. 4 is underdocumented. read the letter →

arxiv 1908.08211 v1 pith:FX6DXERB submitted 2019-08-22 cond-mat.mtrl-sci cond-mat.mes-hallcond-mat.str-el

Lingfei Wang , Qiyuan Feng , Han Gyeol Lee , Eun Kyo Ko , Qingyou Lu , Tae Won Noh This is my paper · ORCID
classification cond-mat.mtrl-scicond-mat.mes-hallcond-mat.str-el
keywords anomalousHalleffectSrRuO3Berrycurvaturethicknessinhomogeneitytopologicalmagneticforcemicroscopystep-flowgrowthtwo-channelAHE
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

This paper addresses a long-standing ambiguity in the interpretation of Hall-effect anomalies in SrRuO3 thin films. It argues that hump-like features previously read as evidence for magnetic skyrmions and the topological Hall effect can instead arise from a spatial distribution of momentum-space Berry curvature caused by one-unit-cell thickness variations. By growing films in step-flow mode and stopping growth between monolayers, the authors create stripe-shaped regions of 4.0 and 5.0 unit-cell thickness, which have opposite anomalous Hall signs and different coercive fields. The measured Hall loops of inhomogeneous films are reproduced as a linear superposition of the two uniform-thickness loops, and the associated two-step magnetic switching and stripe-like magnetic domains are directly imaged. If correct, the work provides a way to engineer and distinguish these transport signals, and it cautions against reading every hump in SrRuO3 as a skyrmion signature.

What carries the argument

The central object is the two-channel anomalous Hall effect: the total Hall resistance $R_{xy}=R_0H+R_{AHE}$ of an inhomogeneous film is modeled as a linear superposition of the anomalous Hall loops of its 4.0 and 5.0 unit-cell regions, which have opposite signs of the anomalous Hall coefficient and different coercive fields. The mechanism that creates these channels is the coupling between film thickness, ferromagnetism, and the momentum-space Berry curvature (a geometric property of the band structure that governs the intrinsic anomalous Hall effect), combined with step-flow growth that organizes the thickness difference into ordered stripes. The linear-superposition fit and the directly imaged two-step magnetic switching carry the argument.

What would settle it

Grow an SrRuO3 film with the same nominal 4.5 unit-cell thickness but with all terraces completed so the thickness is uniform: the two-channel model predicts no hump-like Hall anomaly and no two-step magnetic switching, while a skyrmion-based explanation would not require thickness stripes. Observing humps in such a uniform film would refute the two-channel attribution.

Watch

Extended reading notes

Core claim

The paper's central claim is that a deliberate one-unit-cell thickness inhomogeneity in SrRuO3 ultrathin films produces two independent anomalous Hall channels with opposite signs and distinct coercive fields, so their superposition generates hump-like Hall anomalies similar to the topological Hall effect. The authors show that the relative weight of the two channels, and hence the shape of the Hall loop, can be continuously tuned by sub-unit-cell control of the nominal film thickness. They further identify two-step magnetic switching in magnetization hysteresis and stripe-like ferromagnetic domains aligned with terrace edges as microscopic fingerprints that distinguish this two-channel anomalous Hall effect from a skyrmion-induced topological Hall effect.

Load-bearing premise

The total Hall resistance of an inhomogeneous film is exactly an areal-weighted linear superposition of the independent Hall loops of the 4.0 and 5.0 unit-cell regions, with no significant current shunting, longitudinal conductance differences, or interface coupling between them.

Editorial extensions

If this is right

  • Hump-like features in Hall-resistance curves alone cannot be taken as evidence of skyrmions in SrRuO3-based heterostructures, because thickness inhomogeneity can generate the same signature.
  • The amplitude and sign of the hump can be continuously engineered through sub-unit-cell control of nominal thickness, offering a practical tuning knob for anomalous Hall response.
  • Two-step magnetic switching in magnetization hysteresis and stripe-like ferromagnetic domains provide a concrete way to identify the two-channel anomalous Hall effect and separate it from the topological Hall effect.
  • Growth-induced disorder, such as that produced at high laser repetition rates, creates uncontrolled thickness inhomogeneity and spurious Hall humps, so careful growth control is a prerequisite for any topological Hall effect study.
  • The step-flow method for producing controlled thickness inhomogeneity should transfer to other epitaxial oxide systems, opening a route to harness correlated topological phases in devices.

Reading between the lines

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

  • If the two-channel picture is generic, earlier reports attributing hump-like Hall anomalies in SrRuO3 heterostructures solely to skyrmions may need to be revisited with thickness and terrace characterization, since even nominally uniform films can contain mixed 4.0 and 5.0 unit-cell regions.
  • One could design a deliberately patterned two-channel device with alternating 4.0 and 5.0 unit-cell stripes whose Hall response encodes the area ratio, turning the effect into a sensitive probe of thickness uniformity.
  • The same superposition logic should apply to other materials where the anomalous Hall sign reverses across a sharp thickness, doping, or strain threshold: any coexistence of the two regimes will produce hump-like anomalies.
  • A concrete test would be to grow a uniform 4.5-unit-cell-equivalent film by completing all terraces and verifying that the hump and two-step switching disappear, which would separate the two-channel mechanism from any residual intrinsic effect.
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

3 major / 5 minor

Summary. The manuscript investigates magnetotransport in SrRuO3 ultrathin films with controlled thickness inhomogeneity. The authors grow films with nominal thickness tSRO between 4.0 and 5.0 u.c. using step-flow growth, producing stripe-like regions of 4.0 and 5.0 u.c. thickness. They report that the anomalous Hall resistance (RAHE) of these inhomogeneous films exhibits hump-like features similar to those previously attributed to the topological Hall effect (THE), with the hump amplitude peaking at tSRO = 4.5 u.c. They show that the RAHE-H curves can be 'well reproduced' by linear superposition of the RAHE-H curves of uniform 4.0 and 5.0 u.c. films. They further observe two-step magnetic switching in M-H loops and stripe-like ferromagnetic domains in MFM images, with the stripe geometry matching the terrace structure. These observations are interpreted as evidence for a two-channel anomalous Hall effect (AHE) arising from two distinct k-space Berry curvature channels, and the authors propose the two-step M-H and MFM stripe domains as fingerprints to distinguish this scenario from skyrmion-induced THE.

Significance. If the central claim holds, this work would provide a controlled platform for engineering Berry-curvature-related transport via thickness inhomogeneity and would offer practical criteria for distinguishing two-channel AHE from skyrmion-induced THE in SrRuO3 heterostructures. The microscopic evidence — two-step magnetic switching and terrace-aligned stripe domains in MFM — is strong and largely independent of the transport model; these data support the existence of two distinct magnetic channels and link the hump in RAHE to their sequential switching. However, the quantitative superposition analysis in Fig. 4, which is central to the claim that the hump is quantitatively captured by the two-channel model, suffers from an unresolved weighting problem (detailed in Major Comment 1). The paper does not provide machine-checked proofs or code, but the experimental dataset is systematic across tSRO and temperature and the MFM imaging with pixel-by-pixel subtraction is a notable strength.

major comments (3)
  1. [Results, 'Tunable AHE in SRO films with inhomogeneous tSRO'] The central quantitative claim that the RAHE-H curves in Fig. 4B–F are 'well reproduced by linear superposition' is not substantiated because the weights of the two components are unspecified. The text does not state whether the grey fits use the nominal area fractions (w4 = 5 - tSRO, w5 = tSRO - 4) or whether the weights were floated. In the Hall-bar geometry, the current flows along the terrace edges, so the 4.0 and 5.0 u.c. stripes act as parallel conductors. The measured Hall resistance should then be a sheet-conductance-weighted average, R_AHE,eff = (g4 R_AHE,4 + g5 R_AHE,5)/(g4 + g5), with g_i proportional to the sheet conductance of each stripe, not an area-weighted average. Fig. S2B explicitly shows that the longitudinal resistance follows a parallel-resistor combination, indicating different sheet conductances for the two thicknesses. If the weights were fixed to area fractions, the model is likely quantitatively incorrect wherever the conductivities differ; if the weights were free, the reproduction is a two-parameter fit and the agreement is partly a consistency check. The authors need to state the weights and, ideally, redo the fits with conductance weighting.
  2. [Fig. 4 caption] The caption does not provide the superposition weights or the procedure used to obtain the grey curves. Without this information, the reader cannot assess whether the 'continuous engineering' of the hump with tSRO is a genuine prediction of the two-channel model or an interpolation with adjustable parameters. Please provide the weights and an error estimate for the fits.
  3. [Results, 'Identifying the magnetic inhomogeneity in SRO films'] The two-step M-H curves in Fig. 5C are qualitatively consistent with the two-channel model, but the paper does not quantitatively compare the plateau magnetization with the area-weighted or conductance-weighted sum of the individual 4.0 and 5.0 u.c. M-H curves. Such a comparison would directly test whether the magnetic inhomogeneity matches the nominal thickness fractions and would strengthen the link between the M-H fingerprint and the transport model.
minor comments (5)
  1. [Abstract and title] The phrase 'Berry-curvature-engineering' is ambitious given that no direct measurement of Berry curvature is presented; the evidence is indirect. Consider softening the claim, e.g., 'Berry-curvature-sensitive engineering'.
  2. [Discussion] There is a typo: 'It pave s experimental routes' should read 'It paves experimental routes'.
  3. [Fig. S3] The STEM measurement is performed on a 15 u.c. film to infer the interface structure of thinner films. This approximation should be acknowledged, as the interface structure may be thickness-dependent.
  4. [Fig. 4] The light grey fitting curves in Fig. 4B–F are difficult to distinguish from the data; using a different color or dashed style would improve readability.
  5. [References] Reference 39 is an arXiv preprint; if a peer-reviewed version exists, it should be cited instead.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the two-channel AHE superposition is a model-data consistency check supported by independent two-step M-H and MFM fingerprints, not a prediction forced by its inputs.

full rationale

The paper does not claim to derive the hump-like Hall anomaly from first principles; it models the inhomogeneous films as a linear superposition of the measured uniform 4.0 and 5.0 u.c. RAHE loops and compares that superposition with independently measured curves. The weights are tied to nominal thickness fractions (e.g., tSRO = 4.3 u.c. gives 70% 4.0 u.c. and 30% 5.0 u.c. area), so the comparison is parameter-free in its central form. The two-step M-H switching and stripe-like MFM domains are experimental outcomes not used to construct the transport model and therefore provide independent support. The skyrmion comparison uses prior work by the same authors (ref. 34) as empirical benchmark data, not as an unverified theorem; the AHE sign-reversal mechanism is explicitly left for future ARPES/DFT work, so no result is imported by self-citation. The possible objection that parallel stripes should be conductance-weighted rather than area-weighted is a quantitative validity concern, not a circularity: it does not make the model's output equal to its input by construction. No fitted parameter is relabeled as a prediction, and the paper itself calls the grey curves 'fitting curves' rather than independent predictions. The central evidence for distinguishing the two-channel AHE from skyrmion-induced THE rests on the M-H and MFM fingerprints, which are not derived from the RAHE data being explained.

Assumptions & free parameters 1 free parameters · 3 assumptions · 0 invented entities

No new physical entities are postulated. The central phenomenological input is the empirical sign reversal of the anomalous Hall coefficient between 4.0 and 5.0 u.c. films, and the two-channel superposition model is the quantitative bridge to the measured humps.

free parameters (1)
  • superposition weights w4, w5 = not stated in paper; nominal tSRO implies w4 = 0.7 and w5 = 0.3 for 4.3 u.c., 0.5 and 0.5 for 4.5 u.c.
    The grey curves in Fig. 4B-F are described as 'fitting curves' with 'simple linear superpositions'. If the weights were adjusted to optimize agreement rather than fixed by nominal areal fractions, the hump amplitude is partly fitted to the target data.
assumptions (3)
  • domain assumption The film consists of two laterally separated regions with uniform thicknesses of 4.0 and 5.0 u.c., with area fractions equal to the fractional part (and complement) of the nominal tSRO.
    Used to interpret RHEED intensities, AFM terraces, and to define non-integer tSRO; the authors support this with AFM (Fig. 4I) and Rxx parallel-resistor fitting (Fig. S2B).
  • ad hoc to paper The total transverse Hall resistance of the inhomogeneous film is the areal-weighted linear superposition of the individual uniform film Hall resistances.
    Invoked in Results ('Both features can be well reproduced by linear superposition...') without a derivation of parallel-channel Hall combination; this is the main load-bearing modeling premise.
  • domain assumption The AHE of SrRuO3 is dominated by intrinsic k-space Berry curvature, so sign reversal with thickness reflects band-structure changes.
    Used to interpret the thickness-driven sign reversal as Berry curvature engineering (Section 3, Fig. 3E). The authors state the mechanism is 'elusive' and requires further ARPES/DFT, so this is an interpretive assumption rather than an established fact.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Controllable thickness inhomogeneity and Berry-curvature-engineering of anomalous Hall effect in SrRuO3 ultrathin films." pith.science (2026). https://pith.science/paper/FX6DXERB

@misc{pith2026190808211,
  author       = {Pith},
  title        = {Pith review of: Controllable thickness inhomogeneity and Berry-curvature-engineering of anomalous Hall effect in SrRuO3 ultrathin films},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FX6DXERB}},
  note         = {Machine review of arXiv:1908.08211}
}
read the original abstract

In quantum matters hosting electron-electron correlation and spin-orbit coupling, spatial inhomogeneities, arising from competing ground states, can be essential for determining and understanding topological properties. A prominent example is Hall anomalies observed in SrRuO3 films, which were interpreted in terms of either magnetic skyrmion-induced topological Hall effect (THE) or inhomogeneous anomalous Hall effect (AHE). To clarify this ambiguity, we systematically investigated the AHE of SrRuO3 ultrathin films with controllable inhomogeneities in film thickness (tSRO). By harnessing the step-flow growth of SrRuO3 films, we induced microscopically-ordered stripes with one-unit-cell differences in tSRO. The resultant spatial distribution of momentum-space Berry curvatures enables a two-channel AHE, which shows hump-like anomalies similar to the THE and can be continuously engineered via sub-unit-cell control of tSRO. In these inhomogeneous SRO films, we microscopically identified a two-step magnetic switching and stripe-like ferromagnetic domains. These features are fingerprints for distinguishing the two-channel AHE from the skyrmion-induced THE.

Figures

Figures reproduced from arXiv: 1908.08211 by the authors.

Figure 1
Figure 1. Two-channel anomalous Hall effect and magnetic skyrmion-induced topological Hall effect. (A) Schematic illustration of topological Hall effect (THE), which originates from the real-space Berry curvature acquired by the spin-polarized electron when it passes through a magnetic skyrmion. The corresponding magnetic-field-dependent Hall resistance (Rxy-H) curve (B) consists of both the anomalous Hall effect (AHE) and TH… view at source ↗
Figure 2
Figure 2. Growth of SrRuO3 films with controlled thickness inhomogeneity. (A) Time-dependent reflection high-energy electron diffraction (RHEED) intensity profile of the specular spot during the growth of SrRuO3 (SRO) thin films with various nominal thickness tSRO. All of the RHEED intensity profiles clearly show two oscillations and then saturate, signifying a surface termination conversion and a growth mode transition from … view at source ↗
Figure 3
Figure 3. Evolution of anomalous Hall effect with various t [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Two-channel anomalous Hall effect of SRO films with thickness inhomogeneity. [PITH_FULL_IMAGE:figures/full_fig_p018_4.png]
Figure 5
Figure 5. Figure 5: Two-step magnetic switching in the SRO films with inhomogeneous tSRO. (A) H-dependent magnetization (M‒H) curves measured from the 4.0 and 5.0 u.c. SRO films at 10 K. (B) Schematic RAHE‒H and M‒H curves of the SRO film with nominal tSRO = 4.3 u.c., which can be seen as…
Figure 6
Figure 6. Figure 6: Magnetic force microscopy on the ferromagnetic domain structure and switching behavior of the 4.5 u.c. SRO film. (A) AFM topographic image measured from a 4.5 u.c. SRO film in a preselected region. (B) Magnetic force microscopy (MFM) image acquired after zero-field coo…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

48 extracted references · 46 canonical work pages

  1. [1]

    Witczak-Krempa, G

    W. Witczak-Krempa, G. Chen, Y. B. Kim, L. Balents, Annu. Rev. Condens. Matter Phys. 5, 57-82 (2013)

    work page 2013

  2. [2]

    Schaffer, E

    R. Schaffer, E. Kin-Ho Lee, B. J. Yang, Y. B. Kim, Reports Prog. Phys. 79, 094504 (2016)

    work page 2016

  3. [3]

    B. J. Kim et al., Phys. Rev. Lett. 101, 076402 (2008)

    work page 2008

  4. [4]

    B. J. Kim, H. Ohsumi, T. Komesu, S. Sakai, T. Morita, H. Takagi, Science 323, 1329–1332 (2009)

    work page 2009

  5. [5]

    X. Wan, A. M. Turner, A. Vishwanath, S. Y. Savrasov, Phys. Rev. B. 83, 205101 (2011)

    work page 2011

  6. [6]

    Kuroda et al., Nat

    K. Kuroda et al., Nat. Mater. 16, 1090–1095 (2017)

    work page 2017

  7. [7]

    Mazin et al., Nat

    I. Mazin et al., Nat. Commun. 5, 4261 (2014)

    work page 2014

  8. [8]

    Ye et al., Nature

    L. Ye et al., Nature. 555, 638–642 (2018)

    work page 2018

Show all 48 references
  1. [9]

    Tokura, K

    Y. Tokura, K. Yasuda, A. Tsukazaki, Nat. Rev. Phys. 1, 126–143 (2019)

    2019

  2. [10]

    Y. Ando, J. Phys. Soc. Japan. 82, 102001 (2013)

    2013

  3. [11]

    M. Z. Hasan, J. E. Moore, Annu. Rev. Condens. Matter Phys. 2, 55–78 (2010)

    2010

  4. [12]

    Dagotto, Science 309, 257–262 (2005)

    E. Dagotto, Science 309, 257–262 (2005)

    2005

  5. [13]

    Mathur, P

    N. Mathur, P. Littlewood Phys. Today. 56, 25–30 (2003)

    2003

  6. [14]

    Wang et al., Nat

    W. Wang et al., Nat. Phys. 14, 791–795 (2018)

    2018

  7. [15]

    E. Y. Ma et al., Science 538, 538–542 (2015)

    2015

  8. [16]

    M. V. Berry, Proc. R. Soc. L. 392, 45–57 (1984)

    1984

  9. [17]

    D. Xiao, M. C. Chang, Q. Niu, Rev. Mod. Phys. 82, 1959–2007 (2010)

    2010

  10. [18]

    Nagaosa, J

    N. Nagaosa, J. Sinova, S. Onoda, A. H. MacDonald, N. P. Ong, Rev. Mod. Phys. 82, 1539–1592 (2010)

    2010

  11. [19]

    Manna, Y

    K. Manna, Y. Sun, L. Muechler, J. Kübler, C. Felser, Nat. Rev. Mater. 3, 244–256 (2018)

    2018

  12. [20]

    Yao et al., Phys

    Y. Yao et al., Phys. Rev. Lett. 92, 037204 (2004)

    2004

  13. [21]

    Taguchi, Y

    Y. Taguchi, Y. Oohara, H. Yoshizawa, N. Nagaosa, Y. Tokura, Science 291, 2573–2576 (2001)

    2001

  14. [22]

    Everschor-Sitte, M

    K. Everschor-Sitte, M. Sitte, J. Appl. Phys. 115, 172602 (2014)

    2014

  15. [23]

    Neubauer et al., Phys

    A. Neubauer et al., Phys. Rev. Lett. 102, 186602 (2009)

    2009

  16. [24]

    Soumyanarayanan et al., Nat

    A. Soumyanarayanan et al., Nat. Mater. 16, 898–904 (2017)

    2017

  17. [25]

    Sürgers, G

    C. Sürgers, G. Fischer, P. Winkel, H. v. Löhneysen, Nat. Commun. 5, 3400 (2014)

    2014

  18. [26]

    Nakatsuji, N

    S. Nakatsuji, N. Kiyohara, T. Higo, Nature. 527, 212–215 (2015)

    2015

  19. [27]

    A. K. Nayak et al., Sci. Adv. 2, e1501870 (2016)

    2016

  20. [28]

    P. K. Rout, P. V. P. Madduri, S. K. Manna, A. K. Nayak, Phys. Rev. B. 99, 094430 (2019). 14

    2019

  21. [29]

    Ahadi, L

    K. Ahadi, L. Galletti, S. Stemmer, Appl. Phys. Lett. 111, 172403 (2017)

    2017

  22. [30]

    K. S. Takahashi et al., Sci. Adv. 4, eaar7880 (2018)

    2018

  23. [31]

    Koster et al., Rev

    G. Koster et al., Rev. Mod. Phys. 84, 253–298 (2012)

    2012

  24. [32]

    Matsuno et al., Sci

    J. Matsuno et al., Sci. Adv. 2, e1600304 (2016)

    2016

  25. [33]

    Ohuchi et al., Nat

    Y. Ohuchi et al., Nat. Commun. 9, 213 (2018)

    2018

  26. [34]

    Wang et al., Nat

    L. Wang et al., Nat. Mater. 17, 1087–1094 (2018)

    2018

  27. [35]

    K. Y. Meng et al., Nano Lett. 19, 3169–3175 (2019)

    2019

  28. [36]

    Qin et al., Adv

    Q. Qin et al., Adv. Mater. 31, 1807008 (2019)

    2019

  29. [37]

    D. Kan, T. Moriyama, K. Kobayashi, Y. Shimakawa, Phys. Rev. B. 98, 180408 (2018)

    2018

  30. [38]

    Gerber, Phys

    A. Gerber, Phys. Rev. B. 98, 214440 (2018)

    2018

  31. [39]

    D. J. Groenendijk et al., arXiv:1810.05619

    arXiv

  32. [40]

    Fang et al., Science

    Z. Fang et al., Science. 302, 92–96 (2003)

    2003

  33. [41]

    Mathieu et al., Phys

    R. Mathieu et al., Phys. Rev. Lett. 93, 016602 (2004)

    2004

  34. [42]

    Rijnders, D

    G. Rijnders, D. H. A. Blank, J. Choi, C. -B. Eom, Appl. Phys. Lett. 84, 505–507 (2004)

    2004

  35. [43]

    J. Choi, C. -B. Eom, G. Rijnders, H. Rogalla, D. H. A. Blank, Appl. Phys. Lett. 79, 1447–1449 (2001)

    2001

  36. [44]

    Hong et al., Phys

    W. Hong et al., Phys. Rev. Lett. 95, 095501 (2005)

    2005

  37. [45]

    Y. J. Chang et al., Phys. Rev. Lett. 103, 057201 (2009)

    2009

  38. [46]

    L. Si, Z. Zhong, J. M. Tomczak, K. Held, Phys. Rev. B 92, 041108 (2015)

    2015

  39. [47]

    Kang et al., Phys

    S. Kang et al., Phys. Rev. B. 99, 045113 (2019)

    2019

  40. [48]

    Kurenkov et al., Adv

    A. Kurenkov et al., Adv. Mater. 31, 1900636 (2019). 15 Fig. 1. Two-channel anomalous Hall effect and magnetic skyrmion-induced topological Hall effect. (A) Schematic illustration of topological Hall effect (THE), which originates from the real-space Berry curvature acquired by...

    2019

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.