Pith. sign in

REVIEW 4 major objections 4 minor 67 references

Curvature induced modifications of chirality and magnetic configuration in perpendicular magnetized films

T0 review · 4 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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

Pith's one-line read Bending a perpendicularly magnetized Co/Pd film over 50-nm nanowires generates a curvature-induced Dzyaloshinskii-Moriya interaction about one-third as strong as the film's intrinsic DMI.

desk verdict Impressive 3D magnetic imaging of a curved PMA film, but the headline curvature-induced DMI quantification is a parameter-fed estimate, not a direct measurement. read the letter →

arxiv 2506.05938 v2 pith:4SCPGEWZ submitted 2025-06-06 cond-mat.mtrl-sci

David Raftrey , Dhritiman Bhattacharya , Colin Langton , Bradley Fugetta , Subhashree Satapathy , Olha Bezsmertna , Andrea Sorrentino , Denys Makarov
show 3 more authors
Gen Yin Peter Fischer Kai Liu
This is my paper · ORCID
classification cond-mat.mtrl-sci
keywords 3DnanomagnetismmagneticX-raynanotomographyDzyaloshinskii-Moriyainteractioncurvature-inducedchiralityperpendicularanisotropydomainwallsnanowirenetworksCo/Pdmultilayers
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 reports direct experimental evidence that bending a perpendicularly magnetized film changes not only the direction of magnetization but also the handedness of its domain walls. Soft X-ray nanotomography of a Co/Pd multilayer grown on 50-nm copper nanowires produces a three-dimensional map of the magnetization, showing that over a curved wire the magnetization tilts toward the local surface normal and that domain walls become more uniformly right-handed Néel walls. The paper quantifies the curvature-induced Dzyaloshinskii-Moriya interaction (DMI) as roughly $0.8\ \mathrm{mJ/m^2}$, about one-third of the intrinsic DMI of the same Co/Pd stack, using the relation $D_c = 2A/R$ with wire radius $R=25\ \mathrm{nm}$. If correct, this makes curvature a practical design parameter for chiral spin textures in proposed three-dimensional spintronic devices such as racetrack memory and neuromorphic circuitry.

What carries the argument

The load-bearing relation is the curvature-induced DMI estimate $D_c = 2A\kappa$, where $\kappa = 1/R$ is the curvature of a cylindrical surface, $A$ is the exchange stiffness, and $R$ is the nanowire radius; with $A=10^{-11}\ \mathrm{J/m}$ and $R=25\ \mathrm{nm}$ it gives $0.8\ \mathrm{mJ/m^2}$. The experimental mechanism is three-dimensional vector magnetic nanotomography: circular-polarization soft X-ray images taken over two orthogonal tilt series are iteratively reconstructed into a full magnetization vector field at roughly 30-nm resolution. The paper uses histograms of the angle between the domain-wall magnetization and the wall normal to quantify chirality, defining a right-handed Néel wall as the case where that angle is near zero; the tighter histogram in the curved region is what carries the argument that curvature has modified the chiral interaction.

What would settle it

Perform a direct DMI measurement, such as asymmetric domain-wall propagation or Brillouin light scattering, on the same curved Co/Pd film and on a flat control sample; the curvature-DMI attribution fails if the curved sample shows no additional DMI near $0.8\ \mathrm{mJ/m^2}$, or if the enhancement does not scale as $1/R$ when the nanowire diameter is varied.

Watch

Extended reading notes

Core claim

The central claim is that geometric curvature of a perpendicularly magnetized Co/Pd film induces an additional Dzyaloshinskii-Moriya interaction, observed here for the first time in such a film, with strength $D_c = 2A\kappa \approx 0.8\ \mathrm{mJ/m^2}$ for a 50-nm-diameter wire (radius $R=25\ \mathrm{nm}$, exchange stiffness $A=10^{-11}\ \mathrm{J/m}$). In the curved regions, reconstructed magnetization fans toward the local surface normal, and chirality histograms show the fraction of right-handed Néel domain walls increases from 40.8% in planar regions to 53.9% in curved regions. Micromagnetic simulations reproduce both the domain reorientation along the nanowire and the enhanced right-handedness. The paper interprets the 13.1-percentage-point increase as the signature of curvature-induced DMI, comparable to one-third of the intrinsic interfacial DMI expected in Co/Pd multilayers.

Load-bearing premise

The size of the curvature-induced DMI is not measured directly; it is inferred by attributing a 13.1-percentage-point increase in right-handed wall fraction to a formula using assumed values of exchange stiffness and wire radius, while the paper also credits magnetostatic energy with the same alignment effect.

Editorial extensions

If this is right

  • If curvature adds a DMI of magnitude $D_c = 2A/R$, then reducing nanowire diameter or choosing materials with larger exchange stiffness enlarges the chiral contribution, giving a geometry-based knob for tuning total DMI without altering interfaces.
  • Right-handed Néel domain walls become more stable on curved sections, which should make chiral textures such as skyrmions more robust there, a stated route toward three-dimensional racetrack memory.
  • The shift from 40.8% to 53.9% right-handed Néel walls provides a quantitative experimental benchmark that future studies of curved magnetic films can compare against.
  • Because the same curvature also aligns domains parallel to the nanowire axis, a curved film offers a single platform for patterning both domain orientation and domain-wall chirality.
  • The reconstruction of full 3D magnetization vectors means the curvature-induced changes are captured spatially, not just averaged, enabling local comparison of chirality with local curvature.

Reading between the lines

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

  • If the curvature-induced DMI is additive and scales linearly with curvature, varying nanowire diameter across one sample would provide a direct test and, if confirmed, a calibration curve for $D_c$ as a function of $1/R$.
  • The paper itself notes that magnetostatic energy also favors magnetization parallel to the nanowire axis, so disentangling the DMI contribution from the magnetostatic contribution would require curved samples with the same geometry but reversed intrinsic DMI sign.
  • A natural extension is to measure the same chirality statistics in films with in-plane anisotropy or with stronger exchange coupling, where the curvature-induced chiral term is predicted to behave differently relative to anisotropy-driven alignment.
  • Strain gradients and increased roughness on curved wires are mentioned as additional DMI-enhancement sources; depositing identical stacks on rigid versus flexible curved scaffolds could separate those mechanical contributions from the purely geometric $2A/R$ term.
Share X Bluesky LinkedIn Reddit HN

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 manuscript reports magnetic soft X-ray nanotomography of Co/Pd multilayer films deposited on Cu nanowire networks, reconstructing three-dimensional magnetization configurations at approximately 30 nm resolution. It claims that the curved geometry reorients the magnetic easy axis toward the local surface normal, aligns magnetic domains along the nanowire axis near the wires, and enhances the fraction of right-handed Néel domain walls. The central quantitative claim is that these observations constitute a direct experimental observation of a curvature-induced Dzyaloshinskii-Moriya interaction (DMI) with strength Dc = 0.8 mJ/m², approximately one-third of the intrinsic Co/Pd DMI, inferred from a 13.1% enhancement in the right-handed Néel wall fraction and the theoretical formula Dc = 2A × curvature.

Significance. If the quantitative DMI claim were adequately supported, this would be the first experimental quantification of curvature-induced DMI in a perpendicularly magnetized film and would strengthen the case for curvature as a design parameter for chiral spin textures. The qualitative 3D imaging results, including the observed easy-axis reorientation and curvature-driven domain alignment, are plausible and appear to be supported by the micromagnetic simulations. The paper is potentially significant for 3D nanomagnetism, but the quantitative DMI claim is not supported by the presented data and analysis.

major comments (4)
  1. [Impact of curvature on chirality of domain walls] The quantitative DMI estimate is not derived from a measurement. The 13.1% histogram shift (40.8% vs. 53.9% right-handed Néel wall fraction) is not connected by any model to a DMI strength; the value Dc = 0.8 mJ/m² is obtained directly from the formula Dc = 2A × curvature with assumed A = 10^-11 J/m and R = 25 nm. The abstract's phrase "direct experimental observation ... quantified" is therefore an overstatement. In addition, even if the formula is accepted, taking R = 25 nm ignores the 52-nm film thickness on a 50-nm-diameter wire, so the effective curvature at the film surface is not simply 1/25 nm⁻¹. Please either provide a quantitative model that links the measured wall-fraction change to Dc, or revise the claims so that Dc is presented as a theoretical estimate consistent with, rather than measured by, the data.
  2. [Impact of curvature on chirality of domain walls] The causal attribution of the 13.1% enhancement to curvature-induced DMI is confounded. The same paragraph states that the enhancement "can be attributed to the magnetostatic energy which favors alignment parallel to the long NW axis," which is an alternative mechanism that could explain the increased right-handed Néel wall fraction without any DMI contribution. The micromagnetic simulations shown in Fig. 2(n,o) address domain alignment, not the chirality histogram. Please include simulations with DMI on/off or with magnetostatic energy on/off that compare the distribution of wall angles, so that the DMI contribution can be isolated from the magnetostatic geometrical effect.
  3. [Impact of curvature on chirality of domain walls] The histogram statistics are not characterized: the 40.8% and 53.9% values come from a single 120 × 170 pixel region, with no error bars, no number of independent domain-wall segments, and no reproducibility check across different nanowires or tilt series. The binarization threshold |Mz| > 0.7 is arbitrary, and its effect on the extracted fraction is not reported. Without this statistical characterization, the 13.1% enhancement cannot be assigned significance, and the claim that curvature promotes Néel-type walls is not quantitatively established.
  4. [Impact of curvature on chirality of domain walls] The comparison of Dc to "one-third of the intrinsic DMI" is not robust because the intrinsic DMI is not measured in this sample. The text cites literature values ranging from ±0.3 mJ/m² up to 3 mJ/m² for Co/Pd systems, and the actual value in the measured film is not known. The comparison should be based on a measurement of the intrinsic DMI in a co-deposited planar region of the same film, or the one-third claim should be removed. As written, the ratio depends on which literature value is chosen and does not reflect an experimental determination.
minor comments (4)
  1. [Impact of curvature on chirality of domain walls] The definition of the angle between the domain-wall magnetization m and the domain-wall normal n is not fully specified; the sign convention, the reference direction for 0°, and the coordinate system should be stated explicitly, and the inset in Fig. 4(a) is too small to read.
  2. [Impact of curvature on chirality of domain walls] The formula for the fraction of right-handed Néel walls is garbled as typeset and is not a clear mathematical definition; please provide a clean expression with proper integration limits and a description of the histogram bins.
  3. [Curvature-induced variation in anisotropy direction] In Fig. 2, the x- and z-axes are not defined in any panel, which makes the discussion of alternating x-component contrast in the curved regions difficult to follow; adding a coordinate triad to the figure would help.
  4. [Influence of curvature on domain wall orientation] The threshold values for binarizing the curvature map (K1 > 0.4) and the magnetic map (|Mz| > 0.7) are stated, but the sensitivity of the extracted angles to these thresholds is not discussed; a brief sensitivity analysis would strengthen the quantitative domain-alignment claim.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the measured 3D chirality and domain-alignment observations are self-contained; the one-third DMI figure is an assumption-driven theoretical estimate, not a circular prediction.

full rationale

I find no circular reduction among the paper's derivation steps. The reconstructed magnetization vectors, the planar-vs-curved wall-chirality histograms (40.8% vs 53.9% right-handed Néel walls), and the domain-orientation statistics versus NW distance are direct experimental observables. The micromagnetic simulations use stated Co/Pd parameters and do not take the target curvature-induced DMI as a fit input. The quantitative DMI claim is the only load-bearing step that relies on external input: the paper computes Dc = 2A×curvature from Ref. 30 with assumed A = 10^-11 J/m and R = 25 nm to get 0.8 mJ/m², then compares this with a literature intrinsic DMI up to 3 mJ/m² to obtain 'roughly one-third'. That is an assumption-driven estimate, not a fitted parameter renamed as a prediction, and no model maps the 13.1% wall-fraction enhancement to a DMI magnitude. The text itself even attributes the enhancement to magnetostatic energy, so the causal attribution to DMI is an interpretive step rather than a self-referential one. Self-citations (Refs. 30, 38, 39, 41 include a co-author) provide theoretical context and do not define the measured quantities. The overclaim 'direct experimental observation/quantification' is an evidentiary weakness, not circularity; I therefore assign a low score of 2.

Assumptions & free parameters 8 free parameters · 5 assumptions · 0 invented entities

The central quantitative claim depends on multiple parameters taken from prior literature (Ms, Ku, Aex, R, intrinsic DMI), on the assumption that the theoretical formula Dc = 2A×curvature applies, and on the causal attribution of the measured histogram shift to curvature-induced DMI. The paper does not directly measure DMI strength, so the 'one-third' value is an estimate, not a measurement. No new entities are introduced.

free parameters (8)
  • Saturation magnetization Ms = 500 kA/m
    Assumed from Co/Pd literature (Refs. 53,60) for Mumax3 simulations; not measured for this film. Affects micromagnetic energy landscape and domain behavior.
  • Anisotropy constant Ku = 0.15 MJ/m3
    Assumed from Co/Pd literature (Refs. 53,60); not measured for this film. Controls easy-axis strength relative to demagnetization.
  • Exchange stiffness Aex = 10 pJ/m
    Assumed from Co/Pd literature (Refs. 53,60); used both in simulations and in the Dc = 2A×curvature estimate, so it directly sets the claimed DMI magnitude.
  • Nanowire radius R = 25 nm
    Nominal NW diameter is 50 nm; used in Dc = 2A/R, so it directly sets the claimed DMI magnitude.
  • Film thickness = 52 nm
    Nominal thickness of the Co/Pd multilayer stack; used as simulation input.
  • Domain binarization threshold = |Mz| > 0.7
    Hand-chosen threshold for segmenting magnetic domains in the tomography data; affects domain orientation statistics.
  • Curvature binarization threshold = K1 > 0.4
    Hand-chosen threshold on principal curvature for identifying structural features; affects NW-domain alignment statistics.
  • Intrinsic DMI value = up to 3 mJ/m2
    Taken from literature (Refs. 54,55) for Co/Pd multilayers with 20 bilayers; not measured for this stack. Used as the denominator in the 'one-third' comparison.
assumptions (5)
  • domain assumption Dc = 2A × curvature (Ref. 30) applies quantitatively to the experimental geometry of a film on a cylindrical nanowire.
    The paper uses this formula without derivation to compute Dc = 0.8 mJ/m2; if the formula is not quantitatively accurate for this geometry, the claimed DMI magnitude is invalid.
  • domain assumption The magnetic easy axis is locally normal to the curved film surface.
    This is an assumed modeling choice in the simulations (and inferred from experiment); the conclusion that curvature modifies anisotropy direction depends on it.
  • domain assumption The sign of the intrinsic DMI in the measured Co/Pd stack is positive.
    Inferred from the predominance of right-handed Néel walls in the planar region; if the sign were opposite, the interpretation of the curved-region enhancement would change.
  • ad hoc to paper The 13.1% enhancement in right-handed Néel wall fraction is caused by curvature-induced DMI rather than by magnetostatic, strain, or roughness effects.
    The text itself attributes the enhancement to magnetostatic energy in one sentence, so the causal attribution to DMI is not established.
  • domain assumption The iterative X-ray tomography solver recovers the 3D magnetization vector field faithfully at ~30 nm resolution.
    The paper relies on the reconstruction algorithm (Refs. 57,58) to provide the magnetization vectors used in all subsequent analyses; no independent validation is shown.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Curvature induced modifications of chirality and magnetic configuration in perpendicular magnetized films." pith.science (2026). https://pith.science/paper/4SCPGEWZ

@misc{pith2026250605938,
  author       = {Pith},
  title        = {Pith review of: Curvature induced modifications of chirality and magnetic configuration in perpendicular magnetized films},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4SCPGEWZ}},
  note         = {Machine review of arXiv:2506.05938}
}
read the original abstract

Designing curvature in three-dimensional (3D) magnetic nanostructures enables controlled manipulation of local energy landscapes, allowing for the modification of noncollinear spin textures relevant for next-generation spintronic devices. In this study, we experimentally investigate 3D magnetization textures in a Co/Pd multilayer film, exhibiting strong perpendicular magnetic anisotropy (PMA), deposited onto curved Cu nanowire meshes with diameters as small as 50nm and lengths of several microns. Utilizing magnetic soft X-ray nanotomography, we achieve reconstructions of 3D magnetic domain patterns at approximately 30nm spatial resolution. This approach provides detailed information on both the orientation and magnitude of magnetization within the film. Our results reveal that interfacial anisotropy in the Co/Pd multilayers drives the magnetization towards the local surface normal. In contrast to typical labyrinth domains observed in planar films, the presence of curved nanowires significantly alters the domain structure, with domains preferentially aligning along the nanowire axis in close proximity, while adopting random orientations farther away. We report direct experimental observation of a curvature-induced Dzyaloshinskii-Moriya interaction (DMI), which is quantified to be approximately one-third of the intrinsic DMI in Co/Pd stacks. The curvature induced DMI enhances stability of Neel-type domain walls. These experimental observations are further supported by micromagnetic simulations. Altogether, our findings demonstrate that introducing curvature into magnetic nanostructures provides a powerful strategy for tailoring complex magnetic behaviors, paving the way for the design of advanced 3D racetrack memory and neuromorphic computing devices.

Figures

Figures reproduced from arXiv: 2506.05938 by the authors.

Figure 1
Figure 1. 3D magnetic X-ray nanotomography of a curved thin film. a) Schematic of experimental setup for MTXM, b) right circularly-polarized magnetic contrast ln (T+δ), c) left circularly-polarized magnetic contrast ln (T-δ), d) non-magnetic signal ln (T-δ)+ln (T+δ), e) magnetic signal ln (T-δ)-ln (T+δ) where positive contrast indicates magnetization pointing along the X-ray incidence direction, f) reconstructed density isosu… view at source ↗
Figure 2
Figure 2. Curvature induced anisotropy. Side and top view of (a, c) the z-component and (b, d) the x-component of the magnetization in the curved film, respectively. The dashed lines and rectangles highlight the domains in the curved region. The solid line in panel (d) marks ridge line of the NW. Scale bars are 100 nm. (e-g) Micromagnetic configuration of a 512 nm × 512 nm area and (h-j) corresponding energy densities across … view at source ↗
Figure 3
Figure 3. Curvature induced domain alignment. (a) Representative field of view of the map of principal curvature K1, its binarized image (thresholded at K1 > 0.4) and ellipse fitting of the binarized image. (b) Same region in magnetic domains, binary segmentation selecting greatest magnetic contrast and ellipse fitting of regions of greatest magnetic contrast, where the magnetic domains are selected as the region with |𝑀𝑀𝑧𝑧| … view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Curvature modified chirality of domain walls. [PITH_FULL_IMAGE:figures/full_fig_p012_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

67 extracted references · 67 canonical work pages

  1. [1]

    P., Three - dimensional nanomagnetism

    Fernández-Pacheco, A.; Streubel, R.; Fruchart, O.; Hertel, R.; Fischer, P.; Cowburn, R. P., Three - dimensional nanomagnetism. Nature Communications 2017, 8, 15756

    work page 2017

  2. [2]

    APL Materials 2020, 8 (1), 010701

    Fischer, P.; Sanz -Hernández, D.; Streubel, R.; Fernández -Pacheco, A., Launching a new dimension with 3D magnetic nanostructures. APL Materials 2020, 8 (1), 010701

    work page 2020

  3. [3]

    K.; Deniz, H.; Migliorini, A.; Zhang, W.; Parkin, S

    Gu, K.; Guan, Y.; Hazra, B. K.; Deniz, H.; Migliorini, A.; Zhang, W.; Parkin, S. S. P., Three - dimensional racetrack memory devices designed from freestanding magnetic heterostructures. Nature Nanotechnology 2022, 17 (10), 1065-1071

    work page 2022

  4. [4]

    M.; Ying, Z

    Gentile, P.; Cuoco, M.; Volkov, O. M.; Ying, Z. -J.; Vera -Marun, I. J.; Makarov, D.; Ortix, C., Electronic materials with nanoscale curved geometries. Nature Electronics 2022, 5 (9), 551-563

    work page 2022

  5. [5]

    M.; Kákay, A.; Pylypovskyi, O

    Makarov, D.; Volkov, O. M.; Kákay, A.; Pylypovskyi, O. V.; Budinská, B.; Dobrovolskiy, O. V., New Dimension in Magnetism and Superconductivity: 3D and Curvilinear Nanoarchitectures. Advanced Materials 2022, 34 (3), 2101758

    work page 2022

  6. [6]

    D.; Pylypovskyi, O

    Sheka, D. D.; Pylypovskyi, O. V.; Volkov, O. M.; Yershov, K. V.; Kravchuk, V. P.; Makarov, D., Fundamentals of Curvilinear Ferromagnetism: Statics and Dynamics of Geometrically Curved Wires and Narrow Ribbons. Small 2022, 18 (12), 2105219

    work page 2022

  7. [7]

    C.; Gilbert, D

    Burks, E. C.; Gilbert, D. A.; Murray, P. D.; Fl ores, C.; Felter, T. E.; Charnvanichborikarn, S.; Kucheyev, S. O.; Colvin, J. D.; Yin, G.; Liu, K., 3D Nanomagnetism in Low Density Interconnected Nanowire Networks. Nano Lett 2021, 21 (1), 716-722

    work page 2021

  8. [8]

    J.; Liu, C.; Burks, E

    Bhattacharya, D.; Chen, Z.; Jensen, C. J.; Liu, C.; Burks, E. C.; Gilbert, D. A.; Zhang, X.; Yin, G.; Liu, K., 3D Interconnected Magnetic Nanowire Networks as Potential Integrated Multistate Memristors. Nano Letters 2022, 22 (24), 10010-10017

    work page 2022

Show all 67 references
  1. [9]

    -W.; Wang, M., Formation of magnetic nanowire arrays by cooperative lateral growth

    Chen, F.; Yang, Z.; Li, J.- N.; Jia, F.; Wang, F.; Zhao, D.; Peng, R. -W.; Wang, M., Formation of magnetic nanowire arrays by cooperative lateral growth. Sci. Adv. 2022, 8 (4), eabk0180

    2022

  2. [10]

    H.; Kang, M.; Ko, J.; Cho, S.; Han, H.; Kang, K.; Park, J.; J eon, S.; Jeong, J.-H.; Park, I., Nanoscale three- dimensional fabrication based on mechanically guided assembly

    Ahn, J.; Ha, J.-H.; Jeong, Y.; Jung, Y.; Choi, J.; Gu, J.; Hwang, S. H.; Kang, M.; Ko, J.; Cho, S.; Han, H.; Kang, K.; Park, J.; J eon, S.; Jeong, J.-H.; Park, I., Nanoscale three- dimensional fabrication based on mechanically guided assembly. Nature Communications 2023, 14 (1), 833

    2023

  3. [11]

    Advanced Materials Technologies 2020, 5 (8), 2000093

    Wu, H.; Tian, Y.; Luo, H.; Zhu, H.; Duan, Y.; Huang, Y., Fabrication Techniques for Curved Electronics on Arbitrary Surfaces. Advanced Materials Technologies 2020, 5 (8), 2000093

    2020

  4. [12]

    M., Tuning shape, composition and magnetization of 3D cobalt nanowires grown by focused electron beam induced deposition (FEBID)

    Pablo-Navarro, J.; Sanz-Hernández, D.; Magén, C.; Fernández-Pacheco, A.; de Teresa, J. M., Tuning shape, composition and magnetization of 3D cobalt nanowires grown by focused electron beam induced deposition (FEBID). Journal of Physics D: Applied Physics 2017, 50 (18), 18LT01

    2017

  5. [13]

    Beilstein Journal of Nanotechnology 2012, 3, 597-619

    Huth, M.; Porrati, F.; Schwalb, C.; Winhold, M .; Sachser, R.; Dukic, M.; Adams, J.; Fantner, G., Focused electron beam induced deposition: A perspective. Beilstein Journal of Nanotechnology 2012, 3, 597-619

    2012

  6. [14]

    D.; Rack, P

    Winkler, R.; Fowlkes, J. D.; Rack, P. D.; Plank, H., 3D nanoprinting via focused electron beams. Journal of Applied Physics 2019, 125 (21), 210901

    2019

  7. [15]

    M.; Ferrer, S.; Fischer, P.; Fernández-Pacheco, A., Artificial Double-Helix for Geometrical Control of Magnetic Chirality

    Sanz-Hernández, D.; Hierro-Rodriguez, A.; Donnelly, C.; Pablo- Navarro, J.; Sorrentino, A.; Pereiro, E.; Magén, C.; McVitie, S.; de Teresa, J. M.; Ferrer, S.; Fischer, P.; Fernández-Pacheco, A., Artificial Double-Helix for Geometrical Control of Magnetic Chirality. ACS Nano 20...

    2020

  8. [16]

    C., Two- photon lithography for three -dimensional fabrication in micro/nanoscale regime: A comprehensive review

    Harinarayana, V.; Shin, Y. C., Two- photon lithography for three -dimensional fabrication in micro/nanoscale regime: A comprehensive review. Optics & Laser Technology 2021, 142, 107180

    2021

  9. [17]

    -H.; Peng, R

    Xiong, X.; Jiang, S.- C.; Hu, Y. -H.; Peng, R. -W.; Wang, M., Structured Metal Film as a Perfect Absorber. Adv. Mater. 2013, 25 (29), 3994-4000

    2013

  10. [18]

    Materials Horizons 2019, 6 (4), 642-683

    Huang, Y.; Wu, H.; Xiao, L.; Duan, Y.; Zhu, H.; Bian, J.; Ye, D.; Yin, Z., Assembly and applications of 3D conformal electronics on curvilinear surfaces. Materials Horizons 2019, 6 (4), 642-683

    2019

  11. [19]

    A.; Soldatov, I.; Wolf, D.; Lubk, A.; Schäfer, R.; Fischer, P.; Makarov, D., Magnetic Solitons in Hierarchical 3D Magnetic Nanoarchitectures of Nanoflower Shape

    Bezsmertna, O.; Xu, R.; Pylypovskyi, O.; Raftrey, D.; Sor rentino, A.; Fernandez -Roldan, J. A.; Soldatov, I.; Wolf, D.; Lubk, A.; Schäfer, R.; Fischer, P.; Makarov, D., Magnetic Solitons in Hierarchical 3D Magnetic Nanoarchitectures of Nanoflower Shape. Nano Letters 2024, 24 ...

    2024

  12. [20]

    Phatak C, L. Y. G. E. B. S. D. S. E.; Petford- Long, A., Magnetic structure of 3D sculpted cobalt nanoparticles. Nano Lett. 2014, 14, 759

    2014

  13. [21]

    Nano Letters 2025, 25 (13), 5148-5155

    Fullerton, J.; Phatak, C., Design and Control of Three-Dimensional Topological Magnetic Fields Using Interwoven Helical Nanostructures. Nano Letters 2025, 25 (13), 5148-5155

    2025

  14. [22]

    K.; Kovács, A.; Schmidt, M.; Dunin- Borkowski, R

    Wolf, D.; Schneider, S.; Rößler, U. K.; Kovács, A.; Schmidt, M.; Dunin- Borkowski, R. E.; Büchner, B.; Rellinghaus, B.; Lubk, A., Unveiling the three -dimensional magnetic texture of skyrmion tubes. Nature Nanotechnology 2022, 17 (3), 250-255

    2022

  15. [23]

    M.; Wolf, D.; Pylypovskyi, O

    Volkov, O. M.; Wolf, D.; Pylypovskyi, O. V.; Kákay, A.; Sheka, D. D.; Büchner, B.; Fassbender, J.; Lubk, A.; Makarov, D., Chirality coupling in topological magnetic textures with multiple magnetochiral parameters. Nature Communications 2023, 14 (1), 1491

    2023

  16. [24]

    S.; Rybakov, F

    Zheng, F.; Kiselev, N. S.; Rybakov, F. N.; Yang, L.; Shi, W.; Blügel, S.; Dunin- Borkowski, R. E., Hopfion rings in a cubic chiral magnet. Nature 2023, 623 (7988), 718-723

    2023

  17. [25]

    V.; Dhuey, S.; Bayaraa, T.; Ashby, P.; Raabe, J.; Santos, T.; Griffin, S.; Fischer, P., Quantifying the topology of magnetic skyrmions in three dimensions

    Raftrey, D.; Finizio, S.; Chopdekar, R. V.; Dhuey, S.; Bayaraa, T.; Ashby, P.; Raabe, J.; Santos, T.; Griffin, S.; Fischer, P., Quantifying the topology of magnetic skyrmions in three dimensions. Science Advances 2024, 10 (40), eadp8615

    2024

  18. [26]

    J., Three-dimensional magnetization structures revealed with X-ray vector nanotomography

    Donnelly, C.; Guizar -Sicairos, M.; Scagnoli, V.; G liga, S.; Holler, M.; Raabe, J.; Heyderman, L. J., Three-dimensional magnetization structures revealed with X-ray vector nanotomography. Nature 2017, 547, 328

    2017

  19. [27]

    L.; Scagnoli, V.; Guizar-Sicairos, M.; Holler, M.; Bingham, N

    Donnelly, C.; Metlov, K. L.; Scagnoli, V.; Guizar-Sicairos, M.; Holler, M.; Bingham, N. S.; Raabe, J.; Heyderman, L. J.; Cooper, N. R.; Gliga, S., Experimental observation of vortex rings in a bulk magnet. Nature Physics 2021, 17 (3), 316-321

    2021

  20. [28]

    APL Materials 2024, 12 (2), 021116

    Harding, E.; Araki, T.; Askey, J.; Hunt, M.; Van Den Berg, A.; Raftrey, D.; Aballe, L.; Kaulich, B.; MacDonald, E.; Fischer, P.; Ladak, S., Imaging the magnetic nanowire cross section and magnetic ordering within a suspended 3D artificial spin-ice. APL Materials 2024, 12 (2), 021116

    2024

  21. [29]

    P.; Sheka, D

    Gaididei, Y.; Kravchuk, V. P.; Sheka, D. D., Curvature Effects in T hin Magnetic Shells. Physical Review Letters 2014, 112 (25), 257203

    2014

  22. [30]

    D.; Pylypovskyi, O

    Sheka, D. D.; Pylypovskyi, O. V.; Landeros, P.; Gaididei, Y.; Kákay, A.; Makarov, D., Nonlocal chiral symmetry breaking in curvilinear magnetic shells. Communications Physics 2020, 3 (1), 128

    2020

  23. [31]

    G.; Makarov, D., Retrieving spin textures on curved magnetic thin films with full-field soft X-ray microscopies

    Streubel, R.; Kronast, F.; Fischer, P.; Parkinson, D.; Schmidt, O. G.; Makarov, D., Retrieving spin textures on curved magnetic thin films with full-field soft X-ray microscopies. Nature Communications 2015, 6 (1), 7612

    2015

  24. [32]

    F.; Mühl, T.; Wolter, A

    Streubel, R.; Kronast, F.; Reiche, C. F.; Mühl, T.; Wolter, A. U. B.; Schmidt, O. G.; Makarov, D., Vortex circulation and polarity patterns in closely packed cap arrays. Applied Physics Letters 2016, 108 (4), 042407

    2016

  25. [33]

    C.; Bran, C.; Makarov, D.; Hellwig, O.; Risner-Jamtgaard, J

    Ulbrich, T. C.; Bran, C.; Makarov, D.; Hellwig, O.; Risner-Jamtgaard, J. D.; Yaney, D.; Rohrmann, H.; Neu, V.; Albrecht, M., Effect of magnetic coupling on the magnetization reversal in arrays of magnetic nanocaps. Physical Review B 2010, 81 (5), 054421

    2010

  26. [34]

    L.; Boneberg, J.; Schift, H.; Gobrecht, J.; Schatz, G.; Leiderer, P.; Albrecht, M., Arrays of magnetic nanoindentations with perpendicular anisotropy

    Makarov, D.; Baraban, L.; Guhr, I. L.; Boneberg, J.; Schift, H.; Gobrecht, J.; Schatz, G.; Leiderer, P.; Albrecht, M., Arrays of magnetic nanoindentations with perpendicular anisotropy. Applied Physics Letters 2007, 90 (9), 093117

    2007

  27. [35]

    C.; Makarov, D.; Hu, G.; Guhr, I

    Ulbrich, T. C.; Makarov, D.; Hu, G.; Guhr, I. L.; Suess, D.; Schrefl, T.; Albrecht, M., Magnetization Reversal in a Novel Gradient Nanomaterial. Physical Review Letters 2006, 96 (7), 077202

    2006

  28. [36]

    Physical Review E 2008, 77 (3), 031407

    Baraban, L.; Makarov, D.; Albrecht, M.; Rivier, N.; Leiderer, P.; Erbe, A., Frust ration-induced magic number clusters of colloidal magnetic particles. Physical Review E 2008, 77 (3), 031407

    2008

  29. [37]

    A.; Ganss, F.; Senn, T.; Liu, K.; Albrecht, M.; Schmidt, H., Size-dependent magnetization switching characteristics and spin wave modes of FePt nanostructures

    Brandt, R.; Ruumlckriem, R.; Gilbert, D. A.; Ganss, F.; Senn, T.; Liu, K.; Albrecht, M.; Schmidt, H., Size-dependent magnetization switching characteristics and spin wave modes of FePt nanostructures. J. Appl. Phys. 2013, 113 (20), 203910

    2013

  30. [38]

    M.; Sheka, D

    Volkov, O. M.; Sheka, D. D.; Gaididei, Y.; Kravchuk, V. P.; Rößler, U. K.; Fassbender, J.; Makarov, D., Mesoscale Dzyaloshinskii -Moriya interaction: geometrical tailoring of the magnetochirality. Scientific Reports 2018, 8 (1), 866. 19

    2018

  31. [39]

    P.; Rößler, U

    Kravchuk, V. P.; Rößler, U. K.; Volkov, O. M.; Sheka, D. D.; van den Brink, J.; Makarov, D.; Fuchs, H.; Fangohr, H.; Gaididei, Y., Topologically stable magnetization states on a spherical shell: Curvature- stabilized skyrmions. Physical Review B 2016, 94 (14), 144402

    2016

  32. [40]

    Farinha, A. M. A.; Yang, S.- H.; Yoon, J.; Pal, B.; Parkin, S. S. P., Interplay of geometrical and spin chiralities in 3D twisted magnetic ribbons. Nature 2025, 639 (8053), 67-72

    2025

  33. [41]

    M.; Kákay, A.; Kronast, F.; Mönch, I.; Mawass, M.-A.; Fassbender, J.; Makarov, D., Experimental Observation of Exchange -Driven Chiral Effects in Curvilinear Magnetism

    Volkov, O. M.; Kákay, A.; Kronast, F.; Mönch, I.; Mawass, M.-A.; Fassbender, J.; Makarov, D., Experimental Observation of Exchange -Driven Chiral Effects in Curvilinear Magnetism. Physical Review Letters 2019, 123 (7), 077201

    2019

  34. [42]

    P.; Sheka, D

    Kravchuk, V. P.; Sheka, D. D.; Kákay, A.; Volkov, O. M.; Rößler, U. K.; van den Brink, J.; Makarov, D.; Gaididei, Y., Multiplet of Skyrmion States on a Curvilinear Defect: Reconfigurable Skyrmion Lattices. Physical Review Letters 2018, 120 (6), 067201

    2018

  35. [43]

    V.; Makarov, D.; Kravchuk, V

    Pylypovskyi, O. V.; Makarov, D.; Kravchuk, V. P.; Gaididei, Y.; Saxena, A.; Sheka, D. D., Chiral Skyrmion and Skyrmionium States Engineered by the Gradient of Curvature. Physical Review Applied 2018, 10 (6), 064057

    2018

  36. [44]

    M.; Hamoir, G.; Ferain, E.; Piraux, L., Artificially modified magnetic anisotropy in interconnected nanowire networks

    Araujo, E.; Encinas, A.; Velázquez-Galván, Y.; Martínez-Huerta, J. M.; Hamoir, G.; Ferain, E.; Piraux, L., Artificially modified magnetic anisotropy in interconnected nanowire networks. Nanoscale 2015, 7 (4), 1485-1490

    2015

  37. [45]

    M.; Marlowe, E.; Chen, Z.; Al Misba, W.; Atulasimha, J.; Zhang, X.; Yin, G.; Liu, K., Self -assembled 3D Inter connected Magnetic Nanowire Networks for Neuromorphic Computing

    Bhattacharya, D.; Langton, C.; Rajib, M. M.; Marlowe, E.; Chen, Z.; Al Misba, W.; Atulasimha, J.; Zhang, X.; Yin, G.; Liu, K., Self -assembled 3D Inter connected Magnetic Nanowire Networks for Neuromorphic Computing. ACS Appl. Mater. Interfaces 2025, 17, 20087-20095

    2025

  38. [46]

    C.; Chien, C

    Liu, K.; Nagodawithana, K.; Searson, P. C.; Chien, C. L., Perpendicular giant magnetoresistance of multilayered Co/Cu nanowires. Phys. Rev. B 1995, 51 (11), 7381

    1995

  39. [47]

    Y.; Liu, K.; Reich, D

    Hong, K.; Yang, F. Y.; Liu, K.; Reich, D. H.; Searson, P. C.; Chien, C. L.; Balakirev, F. F.; Boebinger, G. S., Giant positive magnetoresistance of Bi nanowire arrays in high magnetic fields. J. Appl. Phys. 1999, 85, 6184

    1999

  40. [48]

    J.; Liu, K., Efficient and Robust Metallic Nanowire Foams for Deep Submicrometer Particulate Filtration

    Malloy, J.; Quintana, A.; Jensen, C. J.; Liu, K., Efficient and Robust Metallic Nanowire Foams for Deep Submicrometer Particulate Filtration. Nano Lett. 2021, 21 (7), 2968-2974

    2021

  41. [49]

    A.; Maranville, B

    Gilbert, D. A.; Maranville, B. B.; Balk, A. L.; Kirby, B. J.; Fischer, P .; Pierce, D. T.; Unguris, J.; Borchers, J. A.; Liu, K., Realization of Ground State Artificial Skyrmion Lattices at Room Temperature. Nat. Commun. 2015, 6, 8462

    2015

  42. [50]

    E.; Hellwig, O.; Fullerton, E

    Davies, J. E.; Hellwig, O.; Fullerton, E. E.; Denbeaux, G.; Kortright, J. B.; Liu, K., Ma gnetization reversal of Co/Pt multilayers: Microscopic origin of high -field magnetic irreversibility. Phys. Rev. B 2004, 70 (22), 224434

    2004

  43. [51]

    K.; Liu, K., Ultrasensitive Sub-monolayer Palladium Induced Chirality Switching and Topological Evolution of Skyrmions

    Chen, G.; Ophus, C.; Lo Conte, R.; Wiesendanger, R.; Yin, G.; Schmid, A. K.; Liu, K., Ultrasensitive Sub-monolayer Palladium Induced Chirality Switching and Topological Evolution of Skyrmions. Nano Lett. 2022, 22, 6678-6684

    2022

  44. [52]

    L.; Hoffmann, M.; González Barrio, M

    Chen, G.; Mascaraque, A.; Jia, H.; Zimmermann, B.; Robertson, M.; Conte, R. L.; Hoffmann, M.; González Barrio, M. A.; Ding, H.; Wiesendanger, R.; Michel, E. G.; Blügel, S.; Schmid, A. K.; Liu, K., Large Dzyaloshinskii -Moriya Interaction Induced by Chemisor bed Oxygen on a Fer...

    2020

  45. [53]

    D.; Garlow, J

    Pollard, S. D.; Garlow, J. A.; Yu, J.; Wang, Z.; Zhu, Y.; Yang, H., Observation of stable Néel skyrmions in cobalt/palladium multilayers with Lorentz transmission electron microscopy. Nature Communications 2017, 8 (1), 14761

    2017

  46. [54]

    V.; Kozlov, A

    Davydenko, A. V.; Kozlov, A. G.; Stebliy, M. E.; Kolesnikov, A. G.; Sarnavskiy, N. I.; Iliushin, I. G.; Golikov, A. P., Dzyaloshinskii -Moriya interaction and chiral damping effect in symmetric epitaxial Pd/Co/Pd(111) trilayers. Physical Review B 2021, 103 (9), 094435

    2021

  47. [55]

    V.; Kozlov, A

    Davydenko, A. V.; Kozlov, A. G.; Kolesnikov, A. G.; Stebliy, M. E.; Suslin, G. S.; Vekovshinin, Y. E.; Sadovnikov, A. V.; Nikitov, S. A., Dzyaloshinskii -Moriya interaction in symmetric epita xial [Co/Pd(111)] N superlattices with different numbers of Co/Pd bilayers. Physical ...

    2019

  48. [56]

    Sorrentino, A.; Nicolas, J.; Valcarcel, R.; Chichon, F. J.; Rosanes, M.; Avila, J.; Tkachuk, A.; Irwin, J.; Ferrer, S.; Pereiro, E., MIST RAL: a transmission soft X -ray microscopy beamline for cryo nano- tomography of biological samples and magnetic domains imaging. Journal o...

    2015

  49. [57]

    J.; Guizar -Sicairos, M., Tomographic reconstruction of a three-dimensional magnetization vector field

    Donnelly, C.; Gliga, S.; Scagnoli, V.; Holler, M.; Raabe, J.; Heyderman, L. J.; Guizar -Sicairos, M., Tomographic reconstruction of a three-dimensional magnetization vector field. New Journal of Physics 2018, 20 (8), 083009

    2018

  50. [58]

    A.; M ajor, B.; Avery, P.; Ercius, P.; Ayachit, U.; Geveci, B.; Muller, D

    Schwartz, J.; Harris, C.; Pietryga, J.; Zheng, H.; Kumar, P.; Visheratina, A.; Kotov, N. A.; M ajor, B.; Avery, P.; Ercius, P.; Ayachit, U.; Geveci, B.; Muller, D. A.; Genova, A.; Jiang, Y.; Hanwell, M.; Hovden, R., Real-time 3D analysis during electron tomography using tomviz...

    2022

  51. [59]

    AIP Advances 2014, 4 (10), 107133

    Vansteenkiste, A.; Leliaert, J.; Dvornik, M.; Helsen, M.; Garcia -Sanchez, F.; Van Waeyenberge, B., The design and verification of MuMax3. AIP Advances 2014, 4 (10), 107133

    2014

  52. [60]

    K.; Kirby, B

    Greene, P. K.; Kirby, B. J.; Lau, J. W.; Borchers, J. A.; Fitzsimmons, M. R.; Liu, K., Deposition order dependent magnetization reversal in pressure graded Co/Pd films. Applied Physics Letters 2014, 104 (15), 152401

    2014

  53. [61]

    W.; Wang, M., Periodic spin configura tion in single -crystalline cobalt filaments

    Chen, F.; Wang, F.; Jia, F.; Li, J.; Liu, K.; Huang, S.; Luan, Z.; Wu, D.; Chen, Y.; Zhu, J.; Peng, R. W.; Wang, M., Periodic spin configura tion in single -crystalline cobalt filaments. Phys. Rev. B 2016, 93, 054405

    2016

  54. [62]

    J.; Makarov, D.; Sanchez, S.; Fomin, V

    Smith, E. J.; Makarov, D.; Sanchez, S.; Fomin, V. M.; Schmidt, O. G., Magnetic Microhelix Coil Structures. Physical Review Letters 2011, 107 (9), 097204

    2011

  55. [63]

    1 ed.; Springer Cham: 2016; p VIII, 366

    Tapp, K., Differential Geometry of Curves and Surfaces. 1 ed.; Springer Cham: 2016; p VIII, 366

    2016

  56. [64]

    Physical Review Letters 2021, 127 (11), 117204

    Zhang, Y.; Liu, J.; Dong, Y.; Wu, S.; Zhang, J.; Wang, J.; Lu, J.; Rückriegel, A.; Wang, H.; Duine, R.; Yu, H.; Luo, Z.; Shen, K.; Zhang, J., Strain- Driven Dzyaloshinskii -Moriya Interaction for Room - Temperature Magnetic Skyrmions. Physical Review Letters 2021, 127 (11), 117204

    2021

  57. [65]

    V.; Kozlov, A

    Davydenko, A. V.; Kozlov, A. G.; Chernousov, N. N.; Turpak, A. A.; Ermakov, K. S.; Stebliy, M. E.; Letushev, M. E.; Sadovnikov, A. V.; Golikov, A. P.; Ognev, A. V.; Shiota, Y.; Ono, T.; Samardak, A. S., Giant Asymmetry of Domain Walls Propagation in Pd/Co/Pd(111) Epitaxial Str...

    2024

  58. [66]

    S.; Davydenko, A

    Samardak, A. S.; Davydenko, A. V.; Kolesnikov, A. G.; Samardak, A. Y.; Kozlov, A. G.; Pal, B.; Ognev, A. V.; Sadovnikov, A. V.; Nikitov, S. A.; Gerasimenko, A. V.; Cha, I. H.; Kim, Y. J.; Kim, G. W.; Tretiakov, O. A.; Kim, Y. K., Enhancement of perpendicular magnetic anisotrop...

    2020

  59. [67]

    G.; Davydenko, A

    Kozlov, A. G.; Davydenko, A. V.; Afremov, L. L.; Iliushin, I. G.; Kharitonov, V. N.; Mushtuk, P. S.; Tarasov, E. V.; Turpak, A. A.; Shishelov, A. F.; Chernousov, N. N.; Letushev, M. E.; Sadovnikov, A. V.; Khutieva, A. B.; Ognev, A. V.; Samardak, A. S., Effects of Interfacial N...

    2024

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.