pith. sign in

arxiv: 2604.05454 · v1 · submitted 2026-04-07 · ❄️ cond-mat.mes-hall

Nonlinear thermal gradient induced magnetization in d^(prime), g^(prime) and i^(prime) altermagnets

Motohiko Ezawa This is my paper

Pith reviewed 2026-05-10 19:40 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords altermagnetsnonlinear thermal gradientinduced magnetizationd-wave altermagnetinversion symmetryhigh-temperature regimespin-split bands
0
0 comments X p. Extension

The pith

A second-order nonlinear temperature gradient induces magnetization in d', g' and i' altermagnets but not in the d, g and i versions.

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

The paper asks whether magnetization can be generated by a purely nonlinear temperature gradient with no linear component present. It finds that this occurs in the d'-wave, g'-wave and i'-wave altermagnets whose spin-split bands follow a cosine angular form, while the sine-form d-, g- and i-wave versions produce zero response. Because inversion symmetry forbids any linear thermal magnetization, the nonlinear term is the leading effect. Analytic formulas are given for the induced magnetization in the high-temperature regime, and the same nonlinear response is shown to be absent in odd-parity magnets.

Core claim

A finite magnetization is induced in the d′-wave, g′-wave, i′-wave altermagnets under a second-order nonlinear temperature gradient, whereas no such response occurs in the d-wave, g-wave, i-wave altermagnets. This constitutes the leading-order contribution because the linear response is forbidden by inversion symmetry. Analytic expressions for the induced magnetization are derived in the high-temperature regime. No analogous nonlinear thermal response appears in p-wave, f-wave, p′-wave and f′-wave odd-parity magnets.

What carries the argument

The distinction between k^{N_X} sin(N_X φ) spin-split bands (standard altermagnets) and k^{N_X} cos(N_X φ) bands (primed altermagnets) with N_X = 2,4,6; only the cosine form produces a nonzero nonlinear thermal magnetization.

If this is right

  • Magnetization appears only in the cosine-based altermagnets under nonlinear gradients.
  • Explicit analytic expressions exist for the size of the induced magnetization at high temperature.
  • No analogous response occurs in the sine-based altermagnets or in odd-parity magnets.
  • Linear thermal magnetization remains zero due to inversion symmetry.

Where Pith is reading between the lines

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

  • Thermal control of magnetization could be possible in altermagnetic films using engineered heat flows without external magnetic fields.
  • The same symmetry-based selection between sine and cosine forms may govern nonlinear responses to other gradients, such as electric or strain gradients.
  • Precise nanoscale temperature profiling would be needed to test the predicted quadratic dependence.

Load-bearing premise

The band structures are accurately described by the simple k^N times sine or cosine angular forms, and the system stays in the high-temperature regime where scattering and interaction corrections can be neglected.

What would settle it

An experiment that applies a pure second-order temperature gradient to a d'-wave altermagnet and measures zero induced magnetization, or finds equal response in both sine and cosine versions, would falsify the central claim.

Figures

Figures reproduced from arXiv: 2604.05454 by Motohiko Ezawa.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
read the original abstract

It is a highly nontrivial question whether a magnetization can be induced by applying a nonlinear temperature gradient in the absence of any linear component. In this work, we address this issue and provide explicit examples demonstrating that such a response can indeed arise. The spin-split band structures of $d$-wave, $g$-wave, $i$-wave altermagnets are characterized by $k^{N_{X}}\sin N_{X}\phi $, where $N_{X}=2,4$ and $6$, respectively. In contrast, the corresponding $d^{\prime }$-wave, $g^{\prime } $-wave, $i^{\prime }$-wave altermagnets are described by $k^{N_{X}}\cos N_{X}\phi $. We show that a finite magnetization is induced in the $d^{\prime }$-wave, $g^{\prime }$-wave, $i^{\prime }$-wave altermagnets under a second-order nonlinear temperature gradient, whereas no such response occurs in the $d$-wave, $g$-wave, $i$-wave altermagnets. This constitutes the leading-order contribution because the linear response is forbidden by inversion symmetry. Furthermore, we derive analytic expressions for the induced magnetization in the high-temperature regime. We also demonstrate that no analogous nonlinear thermal response appears in $p$-wave, $f$-wave, $p^{\prime }$-wave and $f^{\prime }$-wave odd-parity magnets.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The manuscript claims that a second-order nonlinear temperature gradient induces finite magnetization in d', g', and i' altermagnets whose spin-split bands follow k^{N_X} cos(N_X phi) forms (N_X = 2,4,6), while the effect vanishes for the corresponding d-, g-, and i-wave altermagnets with sin(N_X phi) dispersions. Linear response is symmetry-forbidden by inversion, making the quadratic term the leading contribution. Analytic expressions for the induced magnetization are derived in the high-temperature regime within the semiclassical Boltzmann framework, and no analogous nonlinear thermal response is found in odd-parity p-, f-, p', and f' magnets.

Significance. If the symmetry analysis and explicit integrals hold, the work supplies a concrete, symmetry-selective mechanism for nonlinear thermal magnetization in altermagnets that distinguishes the primed (cos) from unprimed (sin) classes. The provision of closed-form high-T expressions strengthens falsifiability and offers a potential experimental handle on altermagnetic band structures beyond linear probes. The extension to odd-parity cases usefully delineates the scope of the effect.

minor comments (3)
  1. The abstract states that analytic expressions are derived but does not mention the high-T expansion or the semiclassical Boltzmann starting point; adding one sentence would improve immediate context for readers.
  2. Notation for the angular dependence (phi) and the precise definition of the temperature gradient components should be introduced consistently in the first section where the model Hamiltonians appear.
  3. A brief discussion of the range of validity of the high-T approximation (e.g., relative to the Fermi energy or scattering rate) would help readers assess applicability to real materials.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive evaluation of our work, including the clear summary of our main results, the assessment of its significance in providing a symmetry-selective mechanism for nonlinear thermal magnetization, and the recommendation for minor revision. We have reviewed the report carefully.

Circularity Check

0 steps flagged

Derivation is self-contained from symmetry and explicit Boltzmann transport

full rationale

The central result follows directly from the input model Hamiltonians whose spin-split dispersions are given as k^{N_X} sin(N_X phi) versus k^{N_X} cos(N_X phi). Inversion symmetry is invoked to set the linear response to zero, after which the quadratic term in the temperature gradient is computed via the standard semiclassical Boltzmann equation and high-T expansion of the Fermi-Dirac integrals. These steps are algebraic consequences of the stated dispersions and the transport framework; they do not reduce to fitted parameters, self-referential definitions, or load-bearing self-citations. The distinction between primed and unprimed altermagnets is therefore an output of the symmetry-allowed integrals rather than an input smuggled in by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the assumed functional form of the spin-split bands and the validity of the high-temperature expansion; no free parameters or new entities are introduced in the abstract.

axioms (2)
  • domain assumption Spin-split band structures of d/g/i altermagnets are given by k^{N_X} sin(N_X phi) and of d'/g'/i' by k^{N_X} cos(N_X phi) with N_X = 2,4,6.
    This is the defining characterization stated in the abstract and used to distinguish which family responds to the nonlinear gradient.
  • standard math Inversion symmetry forbids linear thermal response, making the second-order term the leading contribution.
    Symmetry argument invoked to establish that the reported effect is the lowest-order allowed response.

pith-pipeline@v0.9.0 · 5580 in / 1489 out tokens · 37046 ms · 2026-05-10T19:40:35.509738+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

60 extracted references · 60 canonical work pages

  1. [1]

    Y . Gao, S. A. Yang, and Q. Niu, Field induced positional shift of Bloch electrons and its dynamical implications, Phys. Rev. Lett. 112, 166601 (2014)

    work page 2014

  2. [2]

    H. Liu, J. Zhao, Y .-X. Huang, W. Wu, X.-L. Sheng, C. Xiao, and S. A. Yang, Intrinsic second-order anomalous Hall effect and its application in compensated antiferromagnets, Phys. Rev. Lett. 127, 277202 (2021)

    work page 2021

  3. [3]

    Michishita and N

    Y . Michishita and N. Nagaosa, Dissipation and geometry in nonlinear quantum transports of multiband electronic systems, Phys. Rev. B 106, 125114 (2022)

    work page 2022

  4. [4]

    Watanabe and Y

    H. Watanabe and Y . Yanase, Nonlinear electric transport in odd- parity magnetic multipole systems: Application to Mn-based compounds, Phys. Rev. Res. 2, 043081 (2020)

    work page 2020

  5. [6]

    C. Wang, Y . Gao, and D. Xiao, Intrinsic nonlinear Hall effect in antiferromagnetic tetragonal cumnas, Phys. Rev. Lett. 127, 277201 (2021)

    work page 2021

  6. [7]

    Oiwa and H

    R. Oiwa and H. Kusunose, Systematic analysis method for non- linear response tensors, J. Phys. Soc. Jpn. 91, 014701 (2022)

    work page 2022

  7. [8]

    Gao, Y .-F

    A. Gao, Y .-F. Liu, J.-X. Qiu, B. Ghosh, T.V . Trevisan, Y . On- ishi, C. Hu, T. Qian, H.-J. Tien, S.-W. Chen et al., Quantum metric nonlinear Hall effect in a topological antiferromagnetic heterostructure, Science 381, eadf1506 (2023)

    work page 2023

  8. [9]

    N. Wang, D. Kaplan, Z. Zhang, T. Holder, N. Cao, A. Wang, X. Zhou, F. Zhou, Z. Jiang, C. Zhang et al., Quantum metric- induced nonlinear transport in a topological antiferromagnet, Nature (London) 621, 487 (2023)

    work page 2023

  9. [10]

    Kamal Das, Shibalik Lahiri, Rhonald Burgos Atencia, Dimitrie Culcer, and Amit Agarwal, Intrinsic nonlinear conductivities induced by the quantum metric, Phys. Rev. B 108, L201405 (2023)

    work page 2023

  10. [11]

    Daniel Kaplan, Tobias Holder and Binghai Yan, Unification of Nonlinear Anomalous Hall Effect and Nonreciprocal Magne- toresistance in Metals by the Quantum Geometry, Phys. Rev. Lett. 132, 026301 (2024)

    work page 2024

  11. [12]

    YuanDong Wang, ZhiFan Zhang, Zhen-Gang Zhu, and Gang Su, Intrinsic nonlinear Ohmic current, Phys. Rev. B 109, 085419 (2024)

    work page 2024

  12. [13]

    Longjun Xiang, Bin Wang, Yadong Wei, Zhenhua Qiao, and Jian Wang, Linear displacement current solely driven by the quantum metric, Phys. Rev. B 109, 115121 (2024)

    work page 2024

  13. [14]

    Ezawa, Intrinsic nonlinear conductivity induced by quantum geometry in altermagnets and measurement of the in-plane Neel vector, Phys

    M. Ezawa, Intrinsic nonlinear conductivity induced by quantum geometry in altermagnets and measurement of the in-plane Neel vector, Phys. Rev. B 110, L241405 (2024)

    work page 2024

  14. [15]

    Yuan Fang, Jennifer Cano, and Sayed Ali Akbar Ghorashi, Quantum Geometry Induced Nonlinear Transport in Altermag- nets, Phys. Rev. Lett. 133, 106701 (2024)

    work page 2024

  15. [16]

    Ezawa, Purely electrical detection of the Neel vector of p-wave magnets based on linear and nonlinear conductivities, Phys

    M. Ezawa, Purely electrical detection of the Neel vector of p-wave magnets based on linear and nonlinear conductivities, Phys. Rev. B 112, 125412 (2025)

    work page 2025

  16. [17]

    Keita Hamamoto, Motohiko Ezawa, Kun Woo Kim, Takahiro Morimoto, and Naoto Nagaosa, Nonlinear spin current gener- 5 ation in noncentrosymmetric spin-orbit coupled systems, Phys. Rev. B 95, 224430 (2017)

    work page 2017

  17. [18]

    Mai Kameda Daichi Hirobe, Shunsuke Daimon, Yuki Shiomi, Saburo Takahashi, Eiji Saitoh, Microscopic formulation of non- linear spin current induced by spin pumping, Journal of Mag- netism and Magnetic Materials 476, 459 (2019)

    work page 2019

  18. [19]

    Satoru Hayami, Megumi Yatsushiro, and Hiroaki Kusunose, Nonlinear spin Hall effect in PT -symmetric collinear magnets, Phys. Rev. B 106, 024405 (2022)

    work page 2022

  19. [20]

    Satoru Hayami, Linear and nonlinear spin-current generation in polar collinear antiferromagnets without relativistic spin-orbit coupling, Phys. Rev. B 109, 214431 (2024)

    work page 2024

  20. [21]

    Ezawa, Third-order and fifth-order nonlinear spin-current generation in g-wave and i-wave altermagnets and perfect spin- current diode based on f-wave magnets Phys

    M. Ezawa, Third-order and fifth-order nonlinear spin-current generation in g-wave and i-wave altermagnets and perfect spin- current diode based on f-wave magnets Phys. Rev. B 111, 125420 (2025)

    work page 2025

  21. [22]

    Ezawa, Fourth-order and six-order nonlinear spin cur- rent diode in h-wave and j-wave odd-parity magnets arXiv:2603.23915

    M. Ezawa, Fourth-order and six-order nonlinear spin cur- rent diode in h-wave and j-wave odd-parity magnets arXiv:2603.23915

    work page arXiv

  22. [23]

    Xiao-Qin Yu, Zhen-Gang Zhu, Jhih-Shih You, Tony Low, and Gang Su, Topological nonlinear anomalous Nernst effect in strained transition metal dichalcogenides Phys. Rev. B 99, 201410(R) (2019)

    work page 2019

  23. [24]

    D. B. Karki and Mikhail N. Kiselev, Nonlinear Seebeck effect of SU(2) Kondo impurity, Phys. Rev. B 100, 125426 (2019)

    work page 2019

  24. [25]

    Taraphder, and Sumanta Tewari, Nonlinear Nernst effect in bilayer WTe2 Phys

    Chuanchang Zeng, Snehasish Nandy, A. Taraphder, and Sumanta Tewari, Nonlinear Nernst effect in bilayer WTe2 Phys. Rev. B 100, 245102 (2019)

    work page 2019

  25. [26]

    Marchegiani, A

    G. Marchegiani, A. Braggio, and F. Giazotto, Nonlinear Ther- moelectricity with Electron-Hole Symmetric Systems, Phys. Rev. Lett. 124, 106801 (2020)

    work page 2020

  26. [27]

    Observation of nonlinear thermoelectric effect in MoGe/Y3Fe5O12 Hiroki Arisawa, Yuto Fujimoto, Takashi Kikkawa and Eiji Saitoh Nature Communications 15, 6912 (2024)

    work page 2024

  27. [28]

    Hirata, T

    Y . Hirata, T. Kikkawa, H. Arisawa, E. SaitohNonlinear Seebeck effect in at room temperature, Appl. Phys. Lett. 126, 252408 (2025)

    work page 2025

  28. [29]

    Harsh Varshney, Amit Agarwal, Intrinsic nonlinear Nernst and Seebeck effect, New J. Phys. 27, 083506 (2025)

    work page 2025

  29. [30]

    Harsh Varshney, Amit Agarwal, Asymmetric Scatter- ing Drives Large Nonlinear Nernst and Seebeck Effects, arXiv:2601.17775

    work page arXiv

  30. [31]

    Ying-Fei Zhang, Zhi-Fan Zhang, Hua Jiang, Zhen-Gang Zhu, Gang Su, Fundamental Relations as the Leading Order in Non- linear Thermoelectric Responses with Time-Reversal Symme- try, arXiv:2601.19625

    work page arXiv

  31. [32]

    Ezawa, Nonlinear spin-Seebeck diode in f-wave magnets, third-order spin-Nernst effects in g-wave magnets and spin- Nernst effects in i-wave altermagnets arXiv:2602.19034

    M. Ezawa, Nonlinear spin-Seebeck diode in f-wave magnets, third-order spin-Nernst effects in g-wave magnets and spin- Nernst effects in i-wave altermagnets arXiv:2602.19034

    work page arXiv

  32. [33]

    Haowei Xu, Jian Zhou, Hua Wang, and Ju Li, Light-induced static magnetization: Nonlinear Edelstein effect, Phys. Rev. B 103, 205417(2021)

    work page 2021

  33. [34]

    Insu Baek, Seungyun Han, SuikCheon and Hyun-Woo Lee, Nonlinearorbital and spin Edelstein effect in centrosymmetric metals, npj spintronics 2, 33 (2024)

    work page 2024

  34. [35]

    Facio, Alfonso Maiellaro, Francesco Romeo, Roberta Citro, Jeroen van den Brink, Non-linear anomalous Edelstein re- sponse at altermagnetic interfaces, Phys

    Mattia Trama, Irene Gaiardoni, Claudio Guarcello, Jorge I. Facio, Alfonso Maiellaro, Francesco Romeo, Roberta Citro, Jeroen van den Brink, Non-linear anomalous Edelstein re- sponse at altermagnetic interfaces, Phys. Rev. B 112, 184404 (2025)

    work page 2025

  35. [36]

    Jinxiong Jia, Longjun Xiang, Zhenhua Qiao, Jian Wang, Non- linear Magnetoelectric Edelstein Effect, arXiv:2507.23415

    work page arXiv

  36. [37]

    Smejkal, J

    L. Smejkal, J. Sinova, and T. Jungwirth, Beyond Conventional Ferromagnetism and Antiferromagnetism: A Phase with Non- relativistic Spin and Crystal Rotation Symmetry, Phys. Rev. X, 12, 031042 (2022)

    work page 2022

  37. [38]

    Libor Šmejkal, Jairo Sinova, and Tomas Jungwirth, Emerg- ing Research Landscape of Altermagnetism, Phys. Rev. X 12, 040501 (2022)

    work page 2022

  38. [39]

    Hayami, Y

    S. Hayami, Y . Yanagi, and H. Kusunose, Momentum- Dependent Spin Splitting by Collinear Antiferromagnetic Or- dering, J. Phys. Soc. Jpn. 88, 123702 (2019)

    work page 2019

  39. [40]

    Anna Birk Hellenes, Tomas Jungwirth, Jairo Sinova, Libor Šmejkal, Unconventional p-wave magnets, arXiv:2309.01607

    work page Pith review arXiv

  40. [41]

    Jungwirth, R

    T. Jungwirth, R. M. Fernandes, E. Fradkin, A. H. MacDon- ald, J. Sinova, L. Smejkal, From supefluid 3He to altermagnets, arXiv:2411.00717

    work page arXiv

  41. [42]

    Xun-Jiang Luo, Jin-Xin Hu, Meng-Li Hu, K. T. Law, Spin Group Symmetry Criteria for Odd-parity Magnets, arXiv:2510.05512

    work page arXiv

  42. [43]

    Motohiko Ezawa, Quantum geometry and X-wave magnets with X=p,d,f,g,i, Appl. Phys. Express 19 030101 (2026)

    work page 2026

  43. [44]

    Ezawa, Almost half-quantized planar Hall effects in X-wave magnets with X=p,d,f,g,i, Phys

    M. Ezawa, Almost half-quantized planar Hall effects in X-wave magnets with X=p,d,f,g,i, Phys. Rev. B 112, 235307 (2025)

    work page 2025

  44. [45]

    Ezawa, Tunneling magnetoresistance in a junction made of X-wave magnets with X = p, d, f, g, i, Phys

    M. Ezawa, Tunneling magnetoresistance in a junction made of X-wave magnets with X = p, d, f, g, i, Phys. Rev. B 113, 155303 (2026)

    work page 2026

  45. [46]

    Smejkal, A

    L. Smejkal, A. H. MacDonald, J. Sinova, S. Nakatsuji and T. Jungwirth, Anomalous Hall antiferromagnets, Nat. Rev. Mater. 7, 482 (2022)

    work page 2022

  46. [47]

    Di Zhu, Zheng-Yang Zhuang, Zhigang Wu, and Zhongbo Yan, Topological superconductivity in two-dimensional altermag- netic metals, Phys. Rev. B 108, 184505 (2023)

    work page 2023

  47. [48]

    Hughes, Jennifer Cano, Altermagnetic Routes to Majorana Modes in Zero Net Magne- tization, Phys

    Sayed Ali Akbar Ghorashi, Taylor L. Hughes, Jennifer Cano, Altermagnetic Routes to Majorana Modes in Zero Net Magne- tization, Phys. Rev. Lett. 133, 106601 (2024)

    work page 2024

  48. [49]

    Yu-Xuan Li and Cheng-Cheng Liu, Majorana corner modes and tunable patterns in an altermagnet heterostructure, Phys. Rev. B 108, 205410 (2023)

    work page 2023

  49. [50]

    M. Ezawa. Detecting the Neel vector of altermagnets in het- erostructures with a topological insulator and a crystalline valley-edge insulator, Physical Review B 109 (24), 245306 (2024)

    work page 2024

  50. [51]

    Edelstein, Spin polarization of conduction electrons in- duced by electric current in two-dimensional asymmetric elec- tron systems, Solid State Communications 73 (3): 233 (1990)

    V .M. Edelstein, Spin polarization of conduction electrons in- duced by electric current in two-dimensional asymmetric elec- tron systems, Solid State Communications 73 (3): 233 (1990)

    work page 1990

  51. [52]

    Gambardella and I

    P. Gambardella and I. M. Miron, Current-induced spin-orbit torques, Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. 369, 3175 (2011)

    work page 2011

  52. [53]

    Cercellier, C

    H. Cercellier, C. Didiot, Y . Fagot-Revurat, B. Kierren, L. Moreau, and D. Malterre, Interplay between structural, chemi- cal, and spectroscopic properties of Ag/Au 111 epitaxial ultra- thin films: A way to tune the Rashba coupling, Phys. Rev. B 73, 195413 (2006)

    work page 2006

  53. [54]

    Junsaku Nitta, Tatsushi Akazaki, and Hideaki Takayanagi, Takatomo Enoki, Gate Control of Spin-Orbit Interaction in an Inverted InGaAs/InAs Heterostructure Phys. Rev. Lett. 78, 1335 (1997)

    work page 1997

  54. [55]

    LaShell, B.A

    S. LaShell, B.A. McDougall, and E. Jensen, Spin Splitting of an Au(111) Surface State Band Observed with Angle Resolved Photoelectron Spectroscopy, Phys. Rev. Lett. 77, 3419 (1996)

    work page 1996

  55. [56]

    Vergniory, Spin Hall and Edelstein Ef- fects in Novel Chiral Noncollinear Altermagnets, Nat

    Mengli Hu, Oleg Janson, Claudia Felser, Paul McClarty, Jeroen van den Brink, Maia G. Vergniory, Spin Hall and Edelstein Ef- fects in Novel Chiral Noncollinear Altermagnets, Nat. Com. 16, 8529 (2025)

    work page 2025

  56. [57]

    Oppeneer, Spin polar- 6 ization engineering in d-wave altermagnets, Phys

    Mohsen Yarmohammadi, Marco Berritta, Marin Bukov, Libor Smejkal, Jacob Linder, and Peter M. Oppeneer, Spin polar- 6 ization engineering in d-wave altermagnets, Phys. Rev. B 113, L060403 (2026)

    work page 2026

  57. [58]

    Iguchi, K

    Dazhi Hou, Zhiyong Qiu, R. Iguchi, K. Sato, E.K. Vehst- edt, K. Uchida, G.E.W. Bauer and E. Saitoh, Observation of temperature-gradient-induced magnetization, Nat. Com. 7, 12265 (2016)

    work page 2016

  58. [59]

    Buchner, K

    M. Buchner, K. Hofler, B. Henne, V . Ney; A. Ney, Tutorial: Ba- sic principles, limits of detection, and pitfalls of highly sensi- tive SQUID magnetometry for nanomagnetism and spintronics, J. Appl. Phys. 124, 161101 (2018)

    work page 2018

  59. [60]

    Jefferson Ferraz Damasceno Felix Araujo, Helio Ricardo Car- valho, Sonia Renaux Wanderley Louro, Paulo Edmundo de Leers Costa Ribeiro, Antonio Carlos Oliveira Bruno, SQUID and Hall Effect Magnetometers for Detecting and Characteriz- ing Nanoparticles Used in Biomedical Applications, Brazilian Journal of Physics 52, 46 (2022)

    work page 2022

  60. [61]

    Hassinger, F

    E. Hassinger, F. Arnold, T. Lumann, A. Mackenzie, M. Naumann, SQUID-amplified low noise torque magnetome- ter for high fields and low temperatures, PHYSICS OF UN- CONVENTIONAL METALS AND SUPERCONDUCTORS, https://www.cpfs.mpg.de/has/squid.pdf

    work page