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REVIEW 3 major objections 6 minor 36 references

Itinerant ferromagnetism and intrinsic anomalous Hall effect in amorphous iron-germanium

T0 review · 3 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read The anomalous Hall effect in a metal with no crystal lattice is dominated by Berry curvature, not scattering.

desk verdict First AHE data on amorphous Fe-Ge plus a plausible but under-derived k-free theory; worth refereeing with real demands for derivation and side-jump estimate. read the letter →

arxiv 1908.06055 v3 pith:QUBWLDQ6 submitted 2019-08-16 cond-mat.mes-hall cond-mat.mtrl-sci

D. S. Bouma , Z. Chen , B. Zhang , F. Bruni , M. E. Flatté , R. Streubel , L.-W. Wang , R. Q. Wu
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F. Hellman
This is my paper · ORCID
classification cond-mat.mes-hallcond-mat.mtrl-sci
keywords anomalousHalleffectamorphousiron-germaniumBerrycurvatureitinerantferromagnetismspin-orbitcouplingStonermodelmagnetotransportdensityfunctionaltheory
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 asks what produces the anomalous Hall effect in a magnetic metal that has no crystal lattice. It argues that in amorphous iron-germanium the dominant mechanism is intrinsic: it arises from the electronic structure itself rather than from scattering, and it can be computed from an energy-resolved density of Berry curvature. Because that density is the sum of spin-orbit correlations of local orbital states, the calculation needs no momentum-space Brillouin zone. If the claim is right, the standard band-structure picture of the anomalous Hall effect becomes a special case of a local-orbital picture that also applies to glasses. The paper supports this with low-temperature magnetotransport measurements on composition-tuned thin films and with spin-orbit-coupled density functional calculations.

What carries the argument

The central object is the energy-resolved density of Berry curvature, $\rho_{\mathrm{DOC}}(\varepsilon)$, which is the Berry curvature $\Omega(\mathbf{k})$ summed over all states at energy $\varepsilon$; integrating it over occupied energies gives the intrinsic anomalous Hall conductivity. In a periodic crystal it reduces to the usual Brillouin-zone integral, and the paper's move is to show that in an amorphous system it can instead be written as the sum of spin-orbit correlations of local orbital states, with parallel and antiparallel correlations offset by the exchange energy. This identity carries the argument because it removes the need for a good quantum number $\mathbf{k}$ while preserving the energy scale of the curvature features.

What would settle it

Fix the composition $x$ and vary the degree of structural disorder in the films by changing deposition conditions, quench rate, or post-growth irradiation, then measure the magnetization-normalized anomalous Hall conductivity. If the value drifts with disorder or drops as disorder energies approach the roughly 5 eV scale of the curvature features, the assumption that the periodic-supercell density of curvature survives in the true amorphous limit would be falsified.

Watch

Extended reading notes

Core claim

The paper's central claim is that in amorphous $a$-Fe$_x$Ge$_{1-x}$ with $0.38 \leq x \leq 0.61$, the measured anomalous Hall conductivity is dominated by the intrinsic mechanism, with a smaller composition-independent side-jump contribution of opposite sign. The intrinsic conductivity is the integral over occupied energies of the density of Berry curvature, $\rho_{\mathrm{DOC}}(\varepsilon)=\sum_{\mathbf{k}}\Omega(\mathbf{k})\delta(\varepsilon_{\mathbf{k}}-\varepsilon)$, a quantity that in an aperiodic system is the sum of spin-orbit correlations of local orbital states and can be evaluated without any reference to $\mathbf{k}$-space. This recasts the conventional Brillouin-zone formula for the intrinsic anomalous Hall effect as a crystalline limit of a more general energy-resolved, real-space expression. The accompanying Stoner-type argument ties the same density of states that explains the magnetization to the curvature density, so the magnetization and the Hall effect in the amorphous metal are controlled by the same local electronic structure.

Load-bearing premise

The load-bearing premise is that the 128-atom periodic simulation cell reproduces the disorder of the real amorphous film well enough that the calculated density of Berry curvature is the same as in a material with no periodicity at all.

Editorial extensions

If this is right

  • The anomalous Hall effect of a low-conductivity amorphous ferromagnet can be intrinsic, so empirical scaling alone cannot distinguish intrinsic from side-jump contributions.
  • The density-of-curvature model gives a single language for crystalline and amorphous conductors, because the crystalline $\mathbf{k}$-space integral is a limit of the local-orbital sum.
  • Because spin and orbital Hall conductivities have the same Berry-curvature structure, the model should extend to predict spin and orbital Hall effects in amorphous metals without a Brillouin zone.
  • The composition dependence of the intrinsic anomalous Hall conductivity in $a$-Fe$_x$Ge$_{1-x}$ is set by the Fe-$3d$ density of states near the Fermi level, so tuning $x$ tunes the intrinsic Hall response.

Reading between the lines

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

  • If the local-orbital density-of-curvature picture is right, the boundary between intrinsic and disorder-driven Hall physics is set not by periodicity but by whether disorder energies stay below the few-electron-volt scale of the spin-orbit-correlated states; mapping that scale quantitatively would test how far the idea extends.
  • A direct experiment could vary the quench rate during growth to change the short-range order at fixed composition; if the normalized anomalous Hall conductivity stays constant, the intrinsic picture holds beyond the specific films studied here.
  • The absence of a measurable topological Hall signal is consistent with global chirality averaging out in the amorphous structure, and films with engineered chirality might reveal a topological contribution layered on the intrinsic one.
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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 / 6 minor

Summary. The manuscript reports a combined experimental and computational study of amorphous Fe_xGe_{1-x} for 0.38 ≤ x ≤ 0.61, including SQUID magnetization, longitudinal and Hall transport at T = 2 K, and DFT electronic-structure calculations on 64- and 128-atom supercells. It shows that the magnetization follows a Stoner-model trend, that the anomalous Hall resistivity is large, and that a scaling analysis in σ_xx with M_z n_h^{2/3} normalization yields an approximately constant AHC. The paper argues that the intrinsic Berry-curvature mechanism dominates, on the basis of a comparison between measured AHC and DFT-computed intrinsic AHC, and introduces an energy-resolved density of Berry curvature ρ_DOC that is claimed to be equivalent to a sum of spin-orbit correlations of local orbital states and therefore computable without k-space. It concludes with a Stoner-like model for intrinsic AHC in both crystalline and amorphous systems.

Significance. If the central theoretical claim were fully supported, this would be an important advance: it would take a well-established k-space Berry-curvature concept and give a local-orbital, k-free formulation applicable to amorphous ferromagnets, with a plausible experimental demonstration. The experimental data set is valuable, the DFT calculations are extensive, and the comparison between measured and calculated AHC is not circular, since the DFT input is independent of the transport measurements. However, the key equivalence is not derived in the present manuscript, so the significance is provisional; the paper currently states the theoretical foundation rather than establishing it.

major comments (3)
  1. [Section IV B, Eq. (3)] The central claim that ρ_DOC(ε) can be computed 'without reference to k-space by adding together the partial densities of states for local orbital states with spin-orbit correlation parallel and antiparallel' is asserted without derivation. No formula is given, and the cited Refs. 13 and 14 are not shown to contain this equivalence. Because this equivalence is the basis for the paper's central conclusion that the intrinsic mechanism dominates and for the claim that the AHC can be calculated k-free, it is load-bearing. In addition, the DFT results in Fig. 10 are obtained with a 3x3x3 Monkhorst-Pack mesh for periodic 128-atom supercells, so the k-free formulation is not tested by the presented calculation. The authors should either provide a derivation (or an explicit theorem with conditions) or soften the claims to reflect that the k-free equivalence is a conjecture.
  2. [Section IV B, Fig. 10] The robustness of the density-of-curvature calculation against the artificial periodicity of the supercell rests on the statement that 'disorder potentials are typically smaller than 5 eV,' but no evidence is given for this energy scale or for the strength of the disorder potentials in the simulated structures. This is a load-bearing assumption: if the artificial periodicity changes the energy-resolved curvature, the comparison in Fig. 9 loses its meaning. The authors should quantify the disorder potential scale, or provide convergence tests with supercell size and k-mesh, or state explicitly that this is an unverified assumption.
  3. [Section IV B, Fig. 9] The decomposition of the measured AHC into an intrinsic contribution plus a 'composition-independent side-jump component' is not quantified. The figure shows good agreement in the x-dependence, but the offset is effectively a free parameter. Without stating the assumed side-jump value or demonstrating that a composition-independent offset is sufficient, the conclusion that the intrinsic mechanism dominates is weaker than claimed. A quantitative fit or at least an explicit statement of the offset and its uncertainty is needed.
minor comments (6)
  1. [Introduction] The word 'intially' appears in the paragraph discussing the empirical scaling argument; it should read 'initially'.
  2. [Equation (1)] The notation ρ_xy^AH(H) is used for the anomalous Hall resistivity, but later in Section III B ρ_xy^AH is defined as ρ_xy(H) − R_0H; the two uses should be reconciled so the zero-field limit is clear.
  3. [Section IV B] The terms 'density of curvature', 'density of Berry curvature', and ρ_DOC are used interchangeably; please define the notation once and use it consistently throughout.
  4. [References 13 and 14] The references to Ref. 13 (Sahin and Flatté) and Ref. 14 (Guo et al.) should be expanded to make clear which parts of the density-of-curvature framework are prior work and which parts are new in this paper.
  5. [Conclusion] The Conclusion states that the study covers 0.45 ≤ x ≤ 0.61, while the abstract and experimental sections include x = 0.38; please reconcile the compositional range.
  6. [Fig. 7(b)] The normalization by n_h^{2/3} is described as 'free-electron-type' but the derivation of this factor from the carrier lifetime is not shown; a brief explanation would improve clarity.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular reduction found: the DFT intrinsic AHC is computed independently of the transport data; only a minor self-citation attaches to the k-free density-of-curvature equivalence.

full rationale

Walking the derivation chain, the central comparison is experiment versus DFT intrinsic anomalous Hall conductivity in Fig. 9. The DFT values come from spin-orbit-coupled 128-atom supercell band-structure calculations with a 3x3x3 Monkhorst-Pack mesh (Section II.B and Section IV.B), so they do not use the measured rho_xy as input. No fitted parameter is renamed as a prediction: the side-jump offset is described qualitatively as a composition-independent component, not extracted and then reused as the intrinsic contribution. The only self-referential element is the density-of-curvature/local-orbital-correlation equivalence stated after Eq. (3), which is imported from Refs. 13 and 14; Ref. 13 includes coauthor Flatté. That equivalence is asserted rather than re-derived here, which is a support gap, but it is not used to generate the Fig. 9 DFT points, which come from a k-space Berry-curvature calculation of the supercell. The k-free claim is therefore not a circular reduction of the paper's main experimental conclusion; it is an under-derived conceptual statement backed by prior published work. Under the rule that published first-principles citations count as independent evidence, this self-citation does not force the result, so no circular step is exhibited. The score is 2 for the minor, non-load-bearing self-citation associated with the density-of-curvature framework.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The central claim rests on a theoretical framework borrowed from earlier work by the same research group, on an unquantified assumption about disorder potentials relative to the curvature energy scale, and on the standard Stoner and DFT modeling. One effective free parameter, the side-jump offset, is used to reconcile the measured total AHC with the calculated intrinsic contribution.

free parameters (1)
  • side_jump_conductivity_offset = not explicitly reported; implied by difference between measured total AHC and DFT intrinsic AHC
    In the comparison of Fig. 9, the mismatch between experimental sigma_AH and calculated intrinsic sigma_AH is attributed to a composition-independent side-jump contribution, but no first-principles side-jump calculation is provided, so the offset is effectively chosen to make the data and calculation consistent.
assumptions (4)
  • domain assumption The density of Berry curvature framework and its equivalence to spin-orbit correlations of local orbital states (Eq. 3 and following discussion).
    Taken from Refs. 13 and 14 (Sahin and Flatte; Guo et al.), with the same research group as co-authors; the equivalence is asserted here without derivation.
  • ad hoc to paper The disorder potentials in a-FeGe are small compared with the roughly 5 eV energy scale of the density of curvature features.
    Invoked to justify that the periodically repeated supercell represents the amorphous material; no direct calculation of disorder potential strength is given. Section IV B.
  • domain assumption The Stoner band model describes the magnetization of a-FexGe1-x above x approximately 0.4.
    Standard itinerant ferromagnetism model used to interpret the density of states; no quantitative Stoner criterion fit is performed. Section IV A.
  • domain assumption GGA-PBE exchange-correlation functional within DFT provides adequate electronic structure for these amorphous alloys.
    Standard computational method, but its accuracy for amorphous transition-metal alloys is not separately validated in this paper.

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Pith. "Pith review of Itinerant ferromagnetism and intrinsic anomalous Hall effect in amorphous iron-germanium." pith.science (2026). https://pith.science/paper/QUBWLDQ6

@misc{pith2026190806055,
  author       = {Pith},
  title        = {Pith review of: Itinerant ferromagnetism and intrinsic anomalous Hall effect in amorphous iron-germanium},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QUBWLDQ6}},
  note         = {Machine review of arXiv:1908.06055}
}
abstract

The amorphous iron-germanium system ($a$-Fe$_x$Ge$_{1-x}$) lacks long-range structural order and hence lacks a meaningful Brillouin zone. The magnetization of \aFeGe is well explained by the Stoner model for Fe concentrations $x$ above the onset of magnetic order around $x=0.4$, indicating that the local order of the amorphous structure preserves the spin-split density of states of the Fe-$3d$ states sufficiently to polarize the electronic structure despite $\mathbf{k}$ being a bad quantum number. Measurements reveal an enhanced anomalous Hall resistivity $\rho_{xy}^{\mathrm{AH}}$ relative to crystalline FeGe; this $\rho_{xy}^{\mathrm{AH}}$ is compared to density functional theory calculations of the anomalous Hall conductivity to resolve its underlying mechanisms. The intrinsic mechanism, typically understood as the Berry curvature integrated over occupied $\mathbf{k}$-states but shown here to be equivalent to the density of curvature integrated over occupied energies in aperiodic materials, dominates the anomalous Hall conductivity of $a$-Fe$_x$Ge$_{1-x}$ ($0.38 \leq x \leq 0.61$). The density of curvature is the sum of spin-orbit correlations of local orbital states and can hence be calculated with no reference to $\mathbf{k}$-space. This result and the accompanying Stoner-like model for the intrinsic anomalous Hall conductivity establish a unified understanding of the underlying physics of the anomalous Hall effect in both crystalline and disordered systems.

Figures

Figures reproduced from arXiv: 1908.06055 by the authors.

Figure 1
Figure 1. FIG. 1. Structural characterization of [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Comparison of magnetic and structural properties [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Longitudinal charge transport properties of [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Measured Hall resistivity [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Calculated density of states (DOS) near the Fermi [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Scaling plot of the anomalous Hall conductivity [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Density of Berry curvature as a function of chemical [PITH_FULL_IMAGE:figures/full_fig_p009_10.png]

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Reference graph

Works this paper leans on

36 extracted references · 19 canonical work pages

  1. [1]

    Nagaosa , author J

    author author N. Nagaosa , author J. Sinova , author S. Onoda , author A. H. \ MacDonald , \ and\ author N. P. \ Ong ,\ 10.1103/RevModPhys.82.1539 journal journal Rev. Mod. Phys. \ volume 82 ,\ pages 1539 ( year 2010 ) NoStop

    doi:10.1103/revmodphys.82.1539 2010

  2. [2]

    Sinova , author S

    author author J. Sinova , author S. O. \ Valenzuela , author J. Wunderlich , author C. H. \ Back , \ and\ author T. Jungwirth ,\ 10.1103/RevModPhys.87.1213 journal journal Rev. Mod. Phys. \ volume 87 ,\ pages 1213 ( year 2015 ) NoStop

    doi:10.1103/revmodphys.87.1213

  3. [3]

    note While the AHE was long understood to be present exclusively in ferromagnets, recent results indicate that certain noncollinear antiferromagnets also host a substantial AHE [A. K. Nayak et al. , Sci. Adv. 2 , e1501870 (2016)]. Stop

    work page 2016

  4. [4]

    author author E. M. \ Pugh ,\ 10.1103/PhysRev.36.1503 journal journal Phys. Rev. \ volume 36 ,\ pages 1503 ( year 1930 ) NoStop

    work page doi:10.1103/physrev.36.1503 1930

  5. [5]

    Smit ,\ 10.1016/S0031-8914(55)92596-9 journal journal Physica \ volume 21 ,\ pages 877 ( year 1955 ) NoStop

    author author J. Smit ,\ 10.1016/S0031-8914(55)92596-9 journal journal Physica \ volume 21 ,\ pages 877 ( year 1955 ) NoStop

    doi:10.1016/s0031-8914(55)92596-9 1955

  6. [6]

    Berger ,\ 10.1103/PhysRevB.2.4559 journal journal Phys

    author author L. Berger ,\ 10.1103/PhysRevB.2.4559 journal journal Phys. Rev. B \ volume 2 ,\ pages 4559 ( year 1970 ) NoStop

    doi:10.1103/physrevb.2.4559 1970

  7. [7]

    Xiao , author M.-C

    author author D. Xiao , author M.-C. C. \ Chang , \ and\ author Q. Niu ,\ 10.1103/RevModPhys.82.1959 journal journal Rev. Mod. Phys. \ volume 82 ,\ pages 1959 ( year 2010 ) NoStop

    doi:10.1103/revmodphys.82.1959 1959

  8. [8]

    Jungwirth , author Q

    author author T. Jungwirth , author Q. Niu , \ and\ author A. H. \ Macdonald ,\ 10.1103/PhysRevLett.88.207208 journal journal Phys. Rev. Lett. \ volume 88 ,\ pages 207208 ( year 2002 ) NoStop

    doi:10.1103/physrevlett.88.207208 2002

Show all 36 references
  1. [9]

    Onoda \ and\ author N

    author author M. Onoda \ and\ author N. Nagaosa ,\ 10.1143/JPSJ.71.19 journal journal J. Phys. Soc. Japan \ volume 71 ,\ pages 19 ( year 2002 ) NoStop

    2002 doi

  2. [10]

    Onoda , author N

    author author S. Onoda , author N. Sugimoto , \ and\ author N. Nagaosa ,\ 10.1103/PhysRevLett.97.126602 journal journal Phys. Rev. Lett. \ volume 97 ,\ pages 126602 ( year 2006 ) NoStop

    2006 doi

  3. [11]

    \ Liu , author X

    author author X.-J. \ Liu , author X. Liu , \ and\ author J. Sinova ,\ 10.1103/PhysRevB.84.165304 journal journal Phys. Rev. B \ volume 84 ,\ pages 165304 ( year 2011 ) NoStop

    2011 doi

  4. [12]

    Karel , author C

    author author J. Karel , author C. Bordel , author D. S. \ Bouma , author A. de Lorimier-Farmer , author H. J. \ Lee , \ and\ author F. Hellman ,\ 10.1209/0295-5075/114/57004 journal journal EPL (Europhysics Lett.) \ volume 114 ,\ pages 57004 ( year 2016 ) NoStop

    doi

  5. [13]

    S ahin \ and\ author M

    author author C. S ahin \ and\ author M. E. \ Flatt \' e ,\ 10.1103/PhysRevLett.114.107201 journal journal Phys. Rev. Lett. \ volume 114 ,\ pages 107201 ( year 2015 ) NoStop

    2015 doi

  6. [14]

    author author G. Y. \ Guo , author S. Murakami , author T.-W. \ Chen , \ and\ author N. Nagaosa ,\ 10.1103/PhysRevLett.100.096401 journal journal Phys. Rev. Lett. \ volume 100 ,\ pages 096401 ( year 2008 ) NoStop

    2008 doi

  7. [15]

    Marrazzo \ and\ author R

    author author A. Marrazzo \ and\ author R. Resta ,\ 10.1103/PhysRevB.95.121114 journal journal Phys. Rev. B \ volume 95 ,\ pages 121114(R) ( year 2017 ) NoStop

    2017 doi

  8. [16]

    author author S. X. \ Huang \ and\ author C. L. \ Chien ,\ 10.1103/PhysRevLett.108.267201 journal journal Phys. Rev. Lett. \ volume 108 ,\ pages 267201 ( year 2012 ) NoStop

    2012 doi

  9. [17]

    author author N. A. \ Porter , author J. C. \ Gartside , \ and\ author C. H. \ Marrows ,\ 10.1103/PhysRevB.90.024403 journal journal Phys. Rev. B \ volume 90 ,\ pages 024403 ( year 2014 ) NoStop

    2014 doi

  10. [18]

    author author J. C. \ Gallagher , author K. Y. \ Meng , author J. T. \ Brangham , author H. L. \ Wang , author B. D. \ Esser , author D. W. \ McComb , \ and\ author F. Y. \ Yang ,\ 10.1103/PhysRevLett.118.027201 journal journal Phys. Rev. Lett. \ volume 118 ,\ pages 027201 ( y...

    doi

  11. [19]

    Suran , author H

    author author G. Suran , author H. Daver , \ and\ author J. C. \ Bruyere ,\ in\ 10.1063/1.30562 booktitle AIP Conf. Proc. ,\ Vol. volume 29 \ ( publisher AIP ,\ year 1976 )\ pp.\ pages 162--164 NoStop

    1976 doi

  12. [20]

    Daver \ and\ author O

    author author H. Daver \ and\ author O. Massenet ,\ 10.1016/0038-1098(77)90240-X journal journal Solid State Commun. \ volume 23 ,\ pages 393 ( year 1977 ) NoStop

    1977 doi

  13. [21]

    Terzieff , author K

    author author P. Terzieff , author K. Lee , \ and\ author N. Heiman ,\ 10.1063/1.326101 journal journal J. Appl. Phys. \ volume 50 ,\ pages 1031 ( year 1979 ) NoStop

    1979 doi

  14. [22]

    Randhawa , author L

    author author H. Randhawa , author L. K. \ Malhotra , \ and\ author K. L. \ Chopra ,\ 10.1063/1.329649 journal journal J. Appl. Phys. \ volume 52 ,\ pages 1600 ( year 1981 ) NoStop

    1981 doi

  15. [23]

    author author R. D. \ Lorentz , author S. S. \ Laderman , \ and\ author A. I. \ Bienenstock ,\ in\ 10.1007/978-3-642-46522-2_70 booktitle EXAFS Near Edge Struct. III \ ( year 1984 )\ pp.\ pages 280--283 NoStop

    1984 doi

  16. [24]

    author author A. X. \ Gray , author J. Karel , author J. Min \' a r , author C. Bordel , author H. Ebert , author J. Braun , author S. Ueda , author Y. Yamashita , author L. Ouyang , author D. J. \ Smith , author K. Kobayashi , author F. Hellman , \ and\ author C. S. \ Fadley ...

    doi

  17. [25]

    author author L. J. \ van der Pauw ,\ @noop journal journal Philips Res. Reports \ volume 13 ,\ pages 1 ( year 1958 ) NoStop

    1958

  18. [26]

    author author P. E. \ Bl \" o chl ,\ 10.1103/PhysRevB.50.17953 journal journal Phys. Rev. B \ volume 50 ,\ pages 17953 ( year 1994 ) NoStop

    1994 doi

  19. [27]

    Kresse \ and\ author D

    author author G. Kresse \ and\ author D. Joubert ,\ 10.1103/PhysRevB.59.1758 journal journal Phys. Rev. B \ volume 59 ,\ pages 1758 ( year 1999 ) NoStop

    1999 doi

  20. [28]

    Kresse \ and\ author J

    author author G. Kresse \ and\ author J. Hafner ,\ 10.1103/PhysRevB.47.558 journal journal Phys. Rev. B \ volume 47 ,\ pages 558 ( year 1993 ) NoStop

    1993 doi

  21. [29]

    Kresse \ and\ author J

    author author G. Kresse \ and\ author J. Furthm \" u ller ,\ 10.1103/PhysRevB.54.11169 journal journal Phys. Rev. B \ volume 54 ,\ pages 11169 ( year 1996 ) NoStop

    1996 doi

  22. [30]

    author author J. P. \ Perdew , author K. Burke , \ and\ author M. Ernzerhof ,\ 10.1103/PhysRevLett.77.3865 journal journal Phys. Rev. Lett. \ volume 77 ,\ pages 3865 ( year 1996 ) NoStop

    1996 doi

  23. [31]

    author author X. M. \ Chen , author D. S. \ Bouma , author N. Kent , author R. Streubel , author S. Roy , author S. Kevan , author P. Fischer , \ and\ author F. Hellman ,\ @noop note In preparation NoStop

  24. [32]

    Streubel , author D

    author author R. Streubel , author D. S. \ Bouma , author N. Kent , author S. Roy , author S. Kevan , author P. Fischer , \ and\ author F. Hellman ,\ @noop note In preparation NoStop

  25. [33]

    Karel , author Y

    author author J. Karel , author Y. N. \ Zhang , author C. Bordel , author K. H. \ Stone , author T. Y. \ Chen , author C. A. \ Jenkins , author D. J. \ Smith , author J. Hu , author R. Q. \ Wu , author S. M. \ Heald , author J. B. \ Kortright , \ and\ author F. Hellman ,\ 10.1...

    doi

  26. [34]

    author author N. A. \ Spaldin ,\ @noop title Magnetic Materials \ ( publisher Cambridge University Press ,\ year 2010 ) NoStop

    2010

  27. [35]

    author author E. C. \ Stoner ,\ 10.1098/rspa.1938.0066 journal journal Proc. R. Soc. London. Ser. A. Math. Phys. Sci. \ volume 165 ,\ pages 372 ( year 1938 ) NoStop

    1938

  28. [36]

    Karel , author D

    author author J. Karel , author D. S. \ Bouma , author J. Martinez , author Y. N. \ Zhang , author J. A. \ Gifford , author J. Zhang , author G. J. \ Zhao , author D. R. \ Kim , author B. C. \ Li , author Z. Y. \ Huang , author R. Q. \ Wu , author T. Y. \ Chen , \ and\ author ...

    doi

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