Magnetic Dipole Term \(T_{z}\) and its Importance for Analysing XMCD Spectra

Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 204)

Abstract

Magnetism of nanostructures is often studied by means of x-ray magnetic circular dichroism (XMCD). The XMCD sum rules are a very powerful tool but they allow for the spin magnetic moment \(\mu _{\mathrm {spin}}\) to be determined only in combination with the magnetic dipole term \(T_{z}\). This chapter presents few examples demonstrating that neglecting \(T_{z}\) could in some cases lead to completely wrong conclusions about the trends of \(\mu _{\mathrm {spin}}\) with the size of the system or with the magnetisation direction. Further, we inspect conditions that have to be met so that eliminating of \(T_{z}\) from the XMCD sum rules is possible.

Notes

Acknowledgements

The author would like to thank to Hubert Ebert, Jan Minár and Jiří Vackář for numerous stimulating discussions and collaboration on this line of research. Support by the Ministry of Education, Youth and Sport (Czech Republic) within the project LD15097 is gratefully acknowledged.

References

  1. 1.
    P. Gambardella, S. Rusponi, M. Veronese, S.S. Dhesi, C. Grazioli, A. Dallmeyer, I. Cabria, R. Zeller, P.H. Dederichs, K. Kern, C. Carbone, H. Brune, Science 300, 1130 (2003)ADSCrossRefGoogle Scholar
  2. 2.
    F. Donati, A. Singha, S. Stepanow, C. Wäckerlin, J. Dreiser, P. Gambardella, S. Rusponi, H. Brune, Phys. Rev. Lett. 113, 237201 (2014)ADSCrossRefGoogle Scholar
  3. 3.
    F. Donati, S. Rusponi, S. Stepanow, C. Wäckerlin, A. Singha, L. Persichetti, R. Baltic, K. Diller, F. Patthey, E. Fernandes, J. Dreiser, Ž. Šljivančanin, K. Kummer, C. Nistor, P. Gambardella, H. Brune, Science 352, 318 (2016)ADSCrossRefGoogle Scholar
  4. 4.
    B.T. Thole, P. Carra, F. Sette, G. van der Laan, Phys. Rev. Lett. 68, 1943 (1992)ADSCrossRefGoogle Scholar
  5. 5.
    P. Carra, B.T. Thole, M. Altarelli, X. Wang, Phys. Rev. Lett. 70, 694 (1993)ADSCrossRefGoogle Scholar
  6. 6.
    J. Stöhr, J. Electron. Spectrosc. Relat. Phenom. 75, 253 (1995)CrossRefGoogle Scholar
  7. 7.
    J. Stöhr, J. Magn. Magn. Mater. 200, 470 (1999)ADSCrossRefGoogle Scholar
  8. 8.
    S.H. Vosko, L. Wilk, M. Nusair, Can. J. Phys. 58, 1200 (1980)ADSCrossRefGoogle Scholar
  9. 9.
    H. Ebert, D. Ködderitzsch, J. Minár, Rep. Prog. Phys. 74, 096501 (2011)ADSCrossRefGoogle Scholar
  10. 10.
    H. Ebert, R. Zeller, The spr-tb-kkr package, version Feb05 (2005), http://olymp.cup.uni-muenchen.de/ak/ebert/SPR-TB-KKR
  11. 11.
    R. Zeller, P.H. Dederichs, B. Újfalussy, L. Szunyogh, P. Weinberger, Phys. Rev. B 52, 8807 (1995)ADSCrossRefGoogle Scholar
  12. 12.
    S. Bornemann, J. Minár, S. Polesya, S. Mankovsky, H. Ebert, O. Šipr, Ph. Transit. 78, 701 (2005)CrossRefGoogle Scholar
  13. 13.
    S.P. Collins, D. Laundy, C.C. Tang, G. van der Laan, J. Phys. Condens. Matter 7, 9325 (1995)ADSCrossRefGoogle Scholar
  14. 14.
    R.Q. Wu, A.J. Freeman, Phys. Rev. Lett. 73, 1994 (1994)ADSCrossRefGoogle Scholar
  15. 15.
    M. Komelj, C. Ederer, J.W. Davenport, M. Fähnle, Phys. Rev. B 66, 140407(R) (2002)ADSCrossRefGoogle Scholar
  16. 16.
    S. Stepanow, A. Mugarza, G. Ceballos, P. Moras, J.C. Cezar, C. Carbone, P. Gambardella, Phys. Rev. B 82, 014405 (2010)ADSCrossRefGoogle Scholar
  17. 17.
    O. Šipr, J. Minár, H. Ebert, Europhys. Lett. 87, 67007 (2009)ADSCrossRefGoogle Scholar
  18. 18.
    O. Šipr, M. Košuth, H. Ebert, Phys. Rev. B 70, 174423 (2004)ADSCrossRefGoogle Scholar
  19. 19.
    P. Mavropoulos, S. Lounis, R. Zeller, P.H. Dederichs, S. Blügel, Appl. Phys. A 82, 103 (2006)ADSCrossRefGoogle Scholar
  20. 20.
    O. Šipr, S. Bornemann, J. Minár, S. Polesya, V. Popescu, A. Šimůnek, H. Ebert, J. Phys. Condens. Matter 19, 096203 (2007)Google Scholar
  21. 21.
    D. Weller, J. Stöhr, R. Nakajima, A. Carl, M.G. Samant, C. Chappert, R. Megy, P. Beauvillain, P. Veillet, G.A. Held, Phys. Rev. Lett. 75, 3752 (1995)ADSCrossRefGoogle Scholar
  22. 22.
    J. Bartolomé, F. Bartolomé, L.M. García, G. Filoti, T. Gredig, C.N. Colesniuc, I.K. Schuller, J.C. Cezar, Phys. Rev. B 81, 195405 (2010)ADSCrossRefGoogle Scholar
  23. 23.
    O. Šipr, S. Bornemann, H. Ebert, S. Mankovsky, J. Vackář, J. Minár, Phys. Rev. B 88, 064411 (2013)ADSCrossRefGoogle Scholar
  24. 24.
    J. Stöhr, H. König, Phys. Rev. Lett. 75, 3748 (1995)ADSCrossRefGoogle Scholar
  25. 25.
    G. van der Laan, Phys. Rev. B 57, 5250 (1998)ADSCrossRefGoogle Scholar
  26. 26.
    C. Ederer, M. Komelj, J.W. Davenport, M. Fähnle, J. Electron. Spectrosc. Relat. Phenom. 130, 97 (2003)CrossRefGoogle Scholar
  27. 27.
    T. Oguchi, T. Shishidou, Phys. Rev. B 70, 024412 (2004)ADSCrossRefGoogle Scholar
  28. 28.
    D. Schmitz, C. Schmitz-Antoniak, A. Warland, M. Darbandi, S. Haldar, S. Bhandary, O. Eriksson, B. Sanyal, H. Wende, Sci. Rep. 4, 5760 (2014)ADSCrossRefGoogle Scholar
  29. 29.
    O. Šipr, J. Minár, H. Ebert, Phys. Rev. B 94, 144406 (2016)ADSCrossRefGoogle Scholar
  30. 30.
    O. Šipr, S. Mankovsky, S. Polesya, S. Bornemann, J. Minár, H. Ebert, Phys. Rev. B 93, 174409 (2016)ADSCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Physics, Czech Academy of SciencesPrahaCzech Republic

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