Neural-network-based reconstruction of spin and orbital angular momentum from X-ray magnetic circular dichroism spectra

Tetsuro Ueno

REVIEW 2 major objections 5 minor 32 references

Neural-network-based reconstruction of spin and orbital angular momentum from X-ray magnetic circular dichroism spectra

T0 review · 2 major / 5 minor · reviewed 2026-07-14 · grok-4.5

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

Pith's one-line read A neural network can reconstruct spin and orbital moments from full XMCD spectral shapes, not just their integrals.

desk verdict Clean synthetic proof-of-concept: NN recovers multiplet ⟨Sz⟩/⟨Lz⟩ from full Fe/Co/Ni L-edge lineshapes with high test-set accuracy, but transfer to real spectra remains untested. read the letter →

arxiv 2607.11058 v1 pith:PSMMMBUN submitted 2026-07-13 cond-mat.mtrl-sci

Tetsuro Ueno This is my paper · ORCID

classification cond-mat.mtrl-sci

keywords XMCDXASneuralnetworkinverseproblemspinmomentorbitalmultipletcalculationssumrules

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

X-ray magnetic circular dichroism (XMCD) is used to measure element-specific spin and orbital magnetism, but the usual sum-rule analysis only uses integrated intensities and can fail when many physical parameters reshape the spectrum. This paper treats the problem as an inverse mapping: take the entire X-ray absorption and XMCD line shapes and recover the expectation values of spin and orbital angular momentum. Training data come from many-body multiplet calculations of Fe, Co, and Ni L-edge spectra in which crystal-field splitting, spin–orbit coupling, and exchange field are systematically varied. A feed-forward network learns the mapping and, on strictly held-out test spectra, recovers both moments with high accuracy and without obvious bias. The result is a proof of concept that the full line shape carries usable information beyond the integrals, while remaining inside the same multiplet theory that underpins conventional analysis.

What carries the argument

The inverse map y = f_θ(x), where x is the concatenated, normalized XAS+XMCD spectrum and y = (⟨Sz⟩, ⟨Lz⟩). A shared fully-connected network (256→128 hidden units with ReLU, batch-norm and dropout) learns this map from multiplet spectra whose parameters (10Dq, Slater scaling, spin–orbit strengths, exchange field) are systematically varied.

What would settle it

Apply the trained network, without re-training, to experimental Fe, Co or Ni L-edge XMCD spectra whose moments have been independently fixed by sum rules or magnetometry; large, systematic discrepancies would falsify transfer of the learned inverse map.

Watch

Extended reading notes

Core claim

A neural network trained on multiplet-generated Fe, Co, and Ni L2,3 XAS/XMCD spectra reconstructs the ground-state expectation values ⟨Sz⟩ and ⟨Lz⟩ directly from the full spectral line shapes. On strictly excluded test data the predictions track the multiplet ground truth closely (high R², low RMSE), showing that the inverse mapping is learnable and that the full line shape supplies information not captured by integrated sum rules alone.

Load-bearing premise

Success on clean, noise-free multiplet spectra generated inside a limited box of crystal-field, spin–orbit and exchange parameters will still hold for real experimental spectra that contain broadening, noise, background and possible model mismatch.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The one thing worth knowing is that this is a tightly scoped, honest proof-of-concept. Ueno trains a plain fully-connected net on Quanty multiplet XAS+XMCD spectra (Fe 3d6, Co 3d7, Ni 3d8) and recovers the ground-state ⟨Sz⟩ and ⟨Lz⟩ that come from the same wavefunctions. Test-only parity plots look good—high R², low RMSE, no obvious bias—and the paper never pretends the result is more than that.

What is actually new is the clean inverse-problem framing for XMCD moments rather than structural XAS features. Prior NN-XAS work (Timoshenko etc.) is properly cited; this simply extends the idea to the dichroic case and shows that the multi-parameter entanglement (10Dq, Hex, α3d) visible in Figs. 2–3 is learnable from the full lineshape. The methods are standard and transparent: 3240 samples per element, standard-score norm, MSE, early stopping, shared 256-128 hidden layers. Citations to the classic sum-rule papers and to Quanty are appropriate; nothing looks padded or missing.

Soft spots are exactly the ones the Discussion already flags and are proportionate: everything is noise-free, fixed T=10 K / 2 T, pure configurations, and a narrow box of parameters. No experimental spectra, no broadening, no background, no quantitative head-to-head with sum-rule integrals, and no released code or spectra. That bounds present utility but does not break the synthetic claim. The network is not just re-learning an integral; the multi-valued maps in Fig. 3 make that clear.

This is for people who already do XMCD multiplet analysis or high-throughput soft-X-ray work and want a data-driven alternative when backgrounds are ugly. It is not foundational, but it is solid enough that a serious editor should send it to referees rather than desk-reject. I would engage if the topic is on my desk; otherwise it is a clean methods note to file.

Referee Report

2 major / 5 minor

Summary. The manuscript formulates XMCD analysis as an inverse problem and trains a fully connected neural network to map full Fe, Co, and Ni L2,3 XAS and XMCD line shapes onto the ground-state expectation values ⟨Sz⟩ and ⟨Lz⟩. Training data are generated with Quanty multiplet calculations by systematically varying 10Dq, Slater-integral scaling, spin–orbit scaling factors, and exchange field (Table I); labels are taken directly from the many-body wave functions. After standard-score normalization and exclusion of vanishing-moment points, the network (shared 256/128 ReLU layers with batch-norm and dropout, two linear heads) is trained with MSE loss and early stopping. Strictly held-out test-set parity plots (Fig. 4) show high R² and low RMSE with no obvious systematic bias, establishing a proof-of-concept that full spectral shapes encode recoverable angular-momentum information beyond integral sum rules within the idealized multiplet setting.

Significance. If the reported reconstruction accuracy holds, the work supplies a concrete, reproducible demonstration that a supervised NN can invert multiplet-generated XAS/XMCD spectra for ⟨Sz⟩ and ⟨Lz⟩. The multi-parameter entanglement illustrated in Figs. 2–3 makes the inverse map non-trivial, so the result is more than a trivial integral recovery. The study is carefully scoped as a noise-free proof of concept and is therefore a useful methodological baseline for subsequent data-driven XMCD analysis. Strengths include the transparent dataset construction, the explicit train/val/test split, and the quantitative test-only metrics; these make the synthetic claim falsifiable and easy to build upon.

major comments (2)

The central claim is scoped to idealized multiplet spectra (pure 3d6/7/8, fixed T = 10 K, 2 T field, Table I ranges, noise-free). Discussion and Conclusion correctly flag transfer to experimental spectra (broadening, noise, background, possible multiplet mismatch) as future work. Because the paper already presents itself as a proof of concept, this limitation does not invalidate the reported test-only results; however, a short quantitative stress test (e.g., Gaussian broadening or additive noise applied only to the held-out test set) would strengthen the claim that the inverse map is robust enough to motivate experimental application.
Section II.C and the abstract assert that full line shapes provide information “beyond conventional sum-rule analyses.” While Figs. 2–3 show multi-parameter dependence that integrals alone cannot disentangle, the manuscript never reports a direct numerical comparison of NN predictions versus sum-rule estimates on the same test spectra. Adding such a baseline (even for the ideal multiplet data) would make the “beyond sum rules” statement quantitative rather than qualitative.

minor comments (5)

Abstract and several places in the text contain the typographical error “momentm” for “momentum.”
Figure 4 reports RMSE and R² but does not list the numerical values in the main text or a table; including them would aid readers who cannot inspect the figure closely.
The energy-grid length NE is never stated; a single sentence giving the number of energy points (or the energy range and step) would make the input dimensionality fully reproducible.
Appendix Fig. 5 shows validation loss lower than training loss; a brief remark that this is expected under dropout (already mentioned in Sec. II.E) would prevent reader confusion.
Table I ranges for Hex (0–0.01 eV) are quite small relative to typical exchange fields; a short justification of the chosen window would help non-specialist readers.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the NN learns a well-posed inverse map from multiplet spectra to wavefunction-derived labels, validated on strictly held-out test data.

full rationale

The paper formulates XMCD analysis as a supervised inverse problem (Eq. 1: y = f_ heta(x) with x = concatenated XAS/XMCD spectra and y = (⟨Sz⟩, ⟨Lz⟩)). Spectra and labels are generated together from the same Quanty multiplet Hamiltonian by systematically varying parameters (Table I); labels are ground-state expectation values evaluated directly from the many-body wave functions, not fitted post-hoc. The dataset is split into mutually exclusive train/validation/test subsets (2 268/486/486 per element), zeros are excluded, and Fig. 4 reports high R^{2}/low RMSE only on the never-seen test set. This is ordinary supervised regression of a known forward map, not a self-definitional loop, fitted-input-as-prediction, or load-bearing self-citation chain. Citations to sum rules, Quanty, and prior ML spectroscopy are external and non-circular. The Discussion explicitly flags the idealized, noise-free scope and the interpolation-vs-generalization question; no central claim reduces by construction to its inputs. Score 0 is therefore required.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The central claim rests on standard multiplet theory (Quanty) and a conventional supervised NN. Free parameters are the multiplet Hamiltonian ranges and the network hyperparameters; no new physical entities are postulated. The main domain assumptions are that the chosen 3d configurations and parameter box adequately sample the relevant physics and that the inverse map learned on ideal spectra is meaningful.

free parameters (5)

10Dq range = 0.8–1.6 eV
Crystal-field splitting scanned 0.8–1.6 eV (Table I); bounds chosen by hand as 'physically relevant'.
Slater-integral scaling Sl = 0.7–0.9
Coulomb reduction factor scanned 0.7–0.9; conventional but hand-chosen range.
α3d, α2p spin–orbit scaling = 0.7–1.3 / 0.9–1.1
Valence and core SOC scaling factors scanned 0.7–1.3 and 0.9–1.1 relative to Hartree–Fock.
Hex exchange-field range = 0–0.01 eV
Effective exchange field 0–0.01 eV; upper bound chosen by hand.
NN architecture widths and dropout = 256-128, p=0.1
Hidden layers 256/128, dropout p=0.1, ReLU+BatchNorm; selected by validation tuning.

assumptions (4)

domain assumption Full-multiplet many-body theory as implemented in Quanty correctly generates both spectra and ground-state ⟨Sz⟩, ⟨Lz⟩ for the chosen 3d configurations.
Section II.B; the entire training set and labels are produced by this model.
domain assumption Fe, Co, Ni can be represented as pure 3d6, 3d7, 3d8 configurations with octahedral crystal field and an effective exchange field.
Section II.B; hybridization, charge-transfer, and non-octahedral environments are omitted.
standard math A fully connected network with shared latent representation can learn the inverse map from discretized spectra to continuous moments.
Universal-approximation style assumption implicit in the architecture choice (Sec. II.D).
ad hoc to paper Data points with vanishing moments (⟨Sz⟩=⟨Lz⟩=0) can be excluded without biasing the learned inverse map.
Section II.C; exclusion is stated without quantitative sensitivity analysis.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Neural-network-based reconstruction of spin and orbital angular momentum from X-ray magnetic circular dichroism spectra." pith.science (2026). https://pith.science/paper/PSMMMBUN

@misc{pith2026260711058,
  author       = {Pith},
  title        = {Pith review of: Neural-network-based reconstruction of spin and orbital angular momentum from X-ray magnetic circular dichroism spectra},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PSMMMBUN}},
  note         = {Machine review of arXiv:2607.11058}
}

abstract

X-ray magnetic circular dichroism (XMCD) is a powerful probe of element-specific spin and orbital angular momentum. Conventional analyses based on sum rules, however, rely on integrated spectral intensities and can become insufficient when multiple parameters influence the spectral line shape. Here, we formulate XMCD analysis as an inverse problem and develop a neural-network (NN) based approach to reconstruct spin and orbital angular momentum directly from full spectral line shapes. Using many-body multiplet calculations of Fe, Co, and Ni $L_{2,3}$-edge X-ray absorption spectra (XAS) and XMCD spectra as a physically well-defined training dataset, we systematically vary key parameters including crystal-field splitting, spin--orbit coupling, and exchange field. The NN is trained to map spectral line shapes onto the expectation values of spin and orbital angular momentm $\langle S_z \rangle$ and $\langle L_z \rangle$, and validated using strictly test-only data. The results demonstrate accurate and unbiased reconstruction, establishing a proof of concept for data-driven inverse reconstruction from XAS and XMCD spectra. These findings show that exploiting the full XAS and XMCD line shapes provide access to information beyond conventional sum-rule analyses while remaining consistent with established theoretical frameworks.

Figures

Figures reproduced from arXiv: 2607.11058 by the authors.

**Figure 2.** FIG. 2. Representative sets of Fe, Co, and Ni [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗

**Figure 3.** FIG. 3. Parameter dependences of (a,c,e) [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: FIG. 4. Test-only parity plots for (a,c,e) [PITH_FULL_IMAGE:figures/full_fig_p012_4.png]

**Figure 5.** Figure 5: FIG. 5. Training and validation loss curves of the neural-network model for (a) Fe, (b) Co, and [PITH_FULL_IMAGE:figures/full_fig_p015_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

32 extracted references · 1 linked inside Pith

[1]

van der Laan and A

G. van der Laan and A. I. Figueroa, X-ray magnetic circular dichroism—A versatile tool to study magnetism, Coord. Chem. Rev.277–278, 95 (2014)

2014
[2]

C. A. F. Vaz, G. van der Laan, S. A. Cavill, H. A. D¨ urr, A. Fraile Rodr´ ıguez, F. Kronast, W. Kuch, Ph. Sainctavit, G. Sch¨ utz, H. Wendeet al., X-ray magnetic circular dichroism, Nat. Rev. Methods Primer5,27 (2025)

2025
[3]

Fischer, Magnetic imaging with polarized soft x-rays, J

P. Fischer, Magnetic imaging with polarized soft x-rays, J. Phys. D: Appl. Phys.50,313002 (2017)

2017
[4]

Wadati, K

H. Wadati, K. Yamamoto, and K. Yamagami, Recent Progress in Ultrafast Dynamics of Transition-Metal Compounds Studied by Time-Resolved X-Ray Techniques, X-ray Spectrom. 1–28 (2026)

2026
[5]

Miyakaze, S

R. Miyakaze, S. Sakamoto, T. Kawabe, T. Tsukahara, Y. Kotani, K. Toyoki, T. Nakamura, M. Goto, Y. Suzuki, and S. Miwa, Voltage-controlled magnetic anisotropy in an ultrathin nickel film studied by operando x-ray magnetic circular dichroism spectroscopy, Phys. Rev. B 102,014419 (2020)

2020
[6]

B. T. Thole, P. Carra, F. Sette, and G. van der Laan, X-ray circular dichroism as a probe of orbital magnetization, Phys. Rev. Lett.68,1943 (1992). 15

1943
[7]

Carra, B

P. Carra, B. T. Thole, M. Altarelli, and X. Wang, X-ray circular dichroism and local magnetic fields, Phys. Rev. Lett.70,694 (1993)

1993
[8]

C. T. Chen, Y. U. Idzerda, H.-J. Lin, N. V. Smith, G. Meigs, E. Chaban, G. H. Ho, E. Pellegrin, and F. Sette, Experimental Confirmation of the X-Ray Magnetic Circular Dichroism Sum Rules for Iron and Cobalt, Phys. Rev. Lett.75,152 (1995)

1995

Show all 32 references

[9]

van der Laan, Sum rules and beyond, J

G. van der Laan, Sum rules and beyond, J. Electron Spectrosc. Relat. Phenom.101–103,859 (1999)

1999
[10]

Yokoyama, K

H. Yokoyama, K. Amemiya, H. Naganuma, and M. Suzuki-Sakamaki, Expert-guided back- ground processing framework for depth-resolved X-ray magnetic circular dichroism analysis, Jpn. J. Appl. Phys.64,105501 (2025)

2025
[11]

Ishizuki, R

N. Ishizuki, R. Shimizu, and T. Hitosugi, Autonomous experimental systems in materials science, Sci. Tech. Adv. Mater.: Meth.3,2197519 (2023)

2023
[12]

Yoshikawa, Y

N. Yoshikawa, Y. Asano, D. N. Futaba, K. Harada, T. Hitosugi, G. N. Kanda, S. Matsuda, Y. Nagata, K. Nagato, M. Naitoet al., Self-driving laboratories in Japan, Digit. Discov.4, 1384 (2025)

2025
[13]

Yamazaki, T

T. Yamazaki, T. Kawasaki, A. L. Foggiatto, R. Toyama, K. Fuku, V. K. Kushwaha, Y. Kotani, T. Ohkochi, K. Higashi, N. Kawamuraet al., Uncovering the origin of magnetic moment enhancement in Fe–Co–Ir alloys via high-throughput XMCD, Phys. Rev. Mater.9,034408 (2025)

2025
[14]

Yamasaki, N

Y. Yamasaki, N. Sasabe, Y. Ishii, Y. Sekiguchi, A. Sumiyoshiya, Y. Tanimoto, Y. Kotani, T. Nakamura, and H. Nomura, High-throughput mapping of magnetic properties via the on- the-fly XMCD spectroscopy in a combinatorial Fe-Co-Ni film, Sci. Tech. Adv. Mater.: Meth. 5,2544528 (2025)

2025
[15]

Ueno and H

T. Ueno and H. Iwasawa, Measurement Informatics in Synchrotron Radiation X-Ray Spec- troscopy, Synchrotron Radiat. News35,3 (2022)

2022
[16]

Aoyagi, Application of machine learning to spectrum and image data, J

S. Aoyagi, Application of machine learning to spectrum and image data, J. Vac. Sci. Technol. A 41,063202 (2023)

2023
[17]

Penfold, L

T. Penfold, L. Watson, C. Middleton, T. David, S. Verma, T. Pope, J. Kaczmarek, and C. Rankine, Machine-learning strategies for the accurate and efficient analysis of x-ray spec- troscopy, Mach. Learn.: Sci. Technol.5,021001 (2024). 16

2024
[18]

Westermayr and P

J. Westermayr and P. Marquetand, Machine learning spectroscopy to advance computation and analysis, Chem. Sci.16,21660 (2025)

2025
[19]

Timoshenko, A

J. Timoshenko, A. Anspoks, A. Cintins, A. Kuzmin, J. Purans, and A. I. Frenkel, Neural Network Approach for Characterizing Structural Transformations by X-Ray Absorption Fine Structure Spectroscopy, Phys. Rev. Lett.120,225502 (2018)

2018
[20]

X. Han, H. Yao, F. Zhan, X. Song, J. Zhao, and H. Zhao, A new framework for X-ray absorp- tion spectroscopy data analysis based on machine learning:XASDAML, J. Synchrotron. Ra- diat.32,1244 (2025)

2025
[21]

A. A. Guda, S. A. Guda, A. Martini, A. N. Kravtsova, A. Algasov, A. Bugaev, S. P. Kubrin, L. V. Guda, P. ˇSot, J. A. van Bokhoveet al., Understanding X-ray absorption spectra by means of descriptors and machine learning algorithms, npj Comput. Mater.7,203 (2021)

2021
[22]

Haykin, Neural Networks and Learning Machines (Pearson Education, Upper Saddle River,

S. Haykin, Neural Networks and Learning Machines (Pearson Education, Upper Saddle River,
[23]

M. W. Haverkort,Quantyfor core level spectroscopy - excitons, resonances and band excita- tions in time and frequency domain, J. Phys.: Conf. Ser.712,012001 (2016)

2016
[24]

Ackermann, K

K. Ackermann, K. Arnold, M. Braß, C. Cardot, R. Green, S. Heinze, P. Hill, Y. Lu, S. Macke, M. Reteganet al., QUANTY, a quantum many-body scripting toolkit, SciPost Physics Code- bases, scipost 202412 00045v1 (2024)

2024
[25]

Paszke, S

A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury, G. Chanan, T. Killeen, Z. Lin, N. Gimelshein, L. Antigaet al., PyTorch: An Imperative Style, High-Performance Deep Learning Library, arXiv:1912.01703

1912 arXiv
[26]

Nair and G

V. Nair and G. Hinton, Rectified Linear Units Improve Restricted Boltzmann Machines, ICML’10: Proceedings of the 27th International Conference on International Conference on Machine Learning, J. F¨ urnkranz and T. Joachims eds. (Omnipress, Madison, 2010) pp. 807– 814

2010
[27]

Ioffe and C

S. Ioffe and C. Szegedy, Batch Normalization: Accelerating Deep Network Training by Re- ducing Internal Covariate Shift, ICML’15: Proceedings of the 32nd International Conference on Machine Learning, F. Bach and D. Blei eds. (JMLR.org, 2015) pp. 448–456

2015
[28]

Srivastava, G

N. Srivastava, G. Hinton, A. Krizhevsky, I. Sutskever, and R. Salakhutdinov, Dropout: A Simple Way to Prevent Neural Networks from Overfitting, J. Mach. Learn. Res.15,1929 (2014). 17

1929
[29]

D. E. Rumelhart, G. E. Hintorn, and R. J. Williams, Learning representations by back- propagating errors, Nature323,533 (1986)

1986
[30]

Piamonteze, P

C. Piamonteze, P. Miedema, and F. M. F. de Groot, Accuracy of the spin sum rule in XMCD for the transition-metalLedges from manganese to copper, Phys. Rev. B80,184410 (2009)

2009
[31]

ˇSipr, J

O. ˇSipr, J. Min´ ar and H. Ebert, On the importance of the magnetic dipole term Tz in analyzing X-ray magnetic circular dichroism spectra of clusters, Europhys. Lett.87,67007 (2009)

2009
[32]

Goering, X-ray magnetic circular dichroism sum rule correction for the light transition metals, Philos

E. Goering, X-ray magnetic circular dichroism sum rule correction for the light transition metals, Philos. Mag.85,2895 (2005). 18

2005

Pith tools

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

[1] [1]

van der Laan and A

G. van der Laan and A. I. Figueroa, X-ray magnetic circular dichroism—A versatile tool to study magnetism, Coord. Chem. Rev.277–278, 95 (2014)

2014

[2] [2]

C. A. F. Vaz, G. van der Laan, S. A. Cavill, H. A. D¨ urr, A. Fraile Rodr´ ıguez, F. Kronast, W. Kuch, Ph. Sainctavit, G. Sch¨ utz, H. Wendeet al., X-ray magnetic circular dichroism, Nat. Rev. Methods Primer5,27 (2025)

2025

[3] [3]

Fischer, Magnetic imaging with polarized soft x-rays, J

P. Fischer, Magnetic imaging with polarized soft x-rays, J. Phys. D: Appl. Phys.50,313002 (2017)

2017

[4] [4]

Wadati, K

H. Wadati, K. Yamamoto, and K. Yamagami, Recent Progress in Ultrafast Dynamics of Transition-Metal Compounds Studied by Time-Resolved X-Ray Techniques, X-ray Spectrom. 1–28 (2026)

2026

[5] [5]

Miyakaze, S

R. Miyakaze, S. Sakamoto, T. Kawabe, T. Tsukahara, Y. Kotani, K. Toyoki, T. Nakamura, M. Goto, Y. Suzuki, and S. Miwa, Voltage-controlled magnetic anisotropy in an ultrathin nickel film studied by operando x-ray magnetic circular dichroism spectroscopy, Phys. Rev. B 102,014419 (2020)

2020

[6] [6]

B. T. Thole, P. Carra, F. Sette, and G. van der Laan, X-ray circular dichroism as a probe of orbital magnetization, Phys. Rev. Lett.68,1943 (1992). 15

1943

[7] [7]

Carra, B

P. Carra, B. T. Thole, M. Altarelli, and X. Wang, X-ray circular dichroism and local magnetic fields, Phys. Rev. Lett.70,694 (1993)

1993

[8] [8]

C. T. Chen, Y. U. Idzerda, H.-J. Lin, N. V. Smith, G. Meigs, E. Chaban, G. H. Ho, E. Pellegrin, and F. Sette, Experimental Confirmation of the X-Ray Magnetic Circular Dichroism Sum Rules for Iron and Cobalt, Phys. Rev. Lett.75,152 (1995)

1995