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[JPSJ_95(2026)106001_Yaji.pdf](https://mdr.nims.go.jp/filesets/3716247c-e54e-4c71-901b-907bc4f38b98/download)

## Creator

[Koichiro Yaji](https://orcid.org/0000-0002-0721-1316), [Shunsuke Tsuda](https://orcid.org/0000-0001-6209-8048)

## Rights

[Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/)

## Other metadata

[Comment on “Spin and Orbital Polarizations of Au(111) Surface State Determined by Photoelectron Momentum Microscope”](https://mdr.nims.go.jp/datasets/1303c35f-2c77-4932-98dc-d8277466d5a7)

## Fulltext

Comment on “Spin and Orbital Polarizations of Au(111) Surface State Determinedby Photoelectron Momentum Microscope”[J. Phys. Soc. Jpn. 94, 114707 (2025)]Koichiro Yaji1,2,3+ and Shunsuke Tsuda11Center for Basic Research on Materials, National Institute for Materials Science (NIMS), Tsukuba, Ibaraki 305-0047, Japan2Unprecedented-scale Data Analytics Center, Tohoku University, Sendai 980-8577, Japan3Photon Science Innovation Center (PhoSIC), Sendai 980-0845, Japan(Received July 7, 2026; revised August 16, 2026; accepted August 17, 2026; published online September 4, 2026)Matsui et al. recently reported spin- and angle-resolvedphotoemission spectroscopy (SARPES) measurements of theAu(111) surface state and discussed the spin texture of theRashba-split surface-state bands.1) In their paper, theypointed out that previous studies have reported inconsistentclockwise (cw) and counterclockwise (ccw) assignments ofthe spin orientation in Rashba surface states, as viewed fromthe vacuum side, and emphasized the importance of resolvingthis discrepancy. This issue is not limited to Au(111),2–6) butis also relevant to SARPES studies of noble-metal (111)Rashba surface states, including Ag(111) and Cu(111).7,8)In this Comment, we point out that, in comparing such cw=ccw assignments, it is essential to distinguish the definition ofthe “spin direction”. In particular, the apparent discrepancybetween the assignment in Ref. 1 and those in Refs. 6 and 8for noble-metal (111) Rashba surface states can be under-stood by distinguishing the direction of the spin magneticmoment from the expectation value of the Pauli spinoperator, or equivalently, the direction of the spin angularmomentum.For an electron, the spin magnetic moment �s isantiparallel to the spin angular momentum S, and is given by�s ¼ �gs�B Sħ;where gs, �B, and ħ denote the electron spin g-factor, theBohr magneton, and the reduced Planck constant, respec-tively. Therefore, even for the same physical spin texture, thecw=ccw assignment is reversed depending on whether thespin arrows represent S or �s.In Appendix A of Ref. 1, Matsui et al. discussed thecalibration of the spin-detection sign using remanentlymagnetized Ni(110). In particular, Fig. A·1(b) shows the“spin” direction in relation to the magnetization direction andthe majority=minority spin bands. Since this calibration isbased on the magnetization direction, the spin arrows inFig. A·1(b) are interpreted as representing the direction ofthe spin magnetic moment rather than the spin angularmomentum. The cw=ccw assignment for the Au(111) Rashbasurface state in Ref. 1 is then understood to follow thisconvention. On the other hand, in Refs. 6 and 8, the spintexture was represented in terms of the spin angularmomentum. Taking this distinction into account, the cw=ccw assignment in Ref. 1 and those in Refs. 6 and 8 can beunderstood as the same physical spin texture expressed usingdifferent definitions of the spin direction.Although the present Comment does not attempt todetermine which convention was used in every previousreport, this example shows that an apparent discrepancy incw=ccw assignments can arise from different definitions ofthe spin direction. Therefore, when comparing spin texturesin Rashba systems, topological surface states, and relatedspin–orbit-coupled electronic states, it is important to specifywhether the spin arrows or cw=ccw labels represent the spinangular momentum or the spin magnetic moment.Acknowledgment The authors thank F. Matsui for fruitful discussions.Through these discussions, the authors and F. Matsui mutually recognized that theapparent discrepancy in the cw=ccw assignment of the spin direction betweenRef. 1 and Refs. 6 and 8 stems from different definitions of the spin direction,namely the spin angular momentum and the spin magnetic moment.+yaji.koichiro@nims.go.jp1) F. Matsui, K. Hagiwara, Y. Sato, R. Sagehashi, and S. Suga, J. Phys.Soc. Jpn. 94, 114707 (2025).2) D. Vasilyev, C. Tusche, F. Giebels, H. Gollisch, R. Feder, and J.Kirschner, J. Electron Spectrosc. Relat. Phenom. 199, 10 (2015).3) C. Tusche, A. Krasyuk, and J. Kirschner, Ultramicroscopy 159, 520(2015).4) G. Nicolay, F. Reinert, S. Hüfner, and P. Blaha, Phys. Rev. B 65, 033407(2001).5) M. Hoesch, M. Muntwiler, V. N. Petrov, M. Hengsberger, L. Pathey, M.Shi, M. Falub, T. Greber, and J. Osterwalder, Phys. Rev. B 69, 241401(2004).6) S. Tsuda and K. Yaji, e-J. Surf. Sci. Nanotechnol. [DOI: 10.1380/ejssnt.2026-012].7) H. J. Dil, F. Meier, and J. Osterwalder, J. Electron Spectrosc. Relat.Phenom. 201, 42 (2015).8) K. Yaji, A. Harasawa, K. Kuroda, R. Li, B. Yan, F. Komori, and S. Shin,Phys. Rev. B 98, 041404(R) (2018).Journal of the Physical Society of Japan 95, 106001 (2026)https://doi.org/10.7566/JPSJ.95.106001Comments106001-1 ©2026 The Physical Society of Japanmaintain attribution to the author(s) and the title of the article, journal citation, and DOI.©2026 The Author(s)This article is published by the Physical Society of Japan under the terms of the Creative Commons Attribution 4.0 License. Any further distribution of this work mustJ. Phys. Soc. Jpn.Downloaded from journals.jps.jp by 2a02:fe0:c42f:80c0:c060:78c8:3172:4622 on 09/04/26https://doi.org/10.7566/JPSJ.94.114707https://orcid.org/0000-0002-0721-1316https://orcid.org/0000-0001-6209-8048https://doi.org/10.7566/JPSJ.94.114707https://doi.org/10.7566/JPSJ.94.114707https://doi.org/10.1016/j.elspec.2014.12.006https://doi.org/10.1016/j.ultramic.2015.03.020https://doi.org/10.1016/j.ultramic.2015.03.020https://doi.org/10.1103/PhysRevB.65.033407https://doi.org/10.1103/PhysRevB.65.033407https://doi.org/10.1103/PhysRevB.69.241401https://doi.org/10.1103/PhysRevB.69.241401https://doi.org/10.1380/ejssnt.2026-012https://doi.org/10.1380/ejssnt.2026-012https://doi.org/10.1016/j.elspec.2014.10.009https://doi.org/10.1016/j.elspec.2014.10.009https://doi.org/10.1103/PhysRevB.98.041404https://doi.org/10.1103/PhysRevB.98.041404https://doi.org/10.7566/JPSJ.95.106001http://creativecommons.org/licenses/by/4.0/http://crossmark.crossref.org/dialog/?doi=10.7566%2FJPSJ.95.106001&domain=pdf&date_stamp=2026-09-04