Skip to main content
Log in

Kinematical limit in the theory of X-ray magnetic reflectivity

  • Surface and Thin Films
  • Published:
Crystallography Reports Aims and scope Submit manuscript

Abstract

A kinematical approximation has been derived from the general formulas for calculating the reflectivity from a multilayer anisotropic structure. An explicit form of reflection matrices at the boundary of layers and the refraction tensors has been obtained for a particular case where the layer magnetization is oriented in the surface plane and for an arbitrary form of X-ray susceptibility tensors. Calculations of the reflectivity from a Nb(4 nm)/[Dy(5 nm)/Lu(3 nm)]420 model structure with helicoidal ordering of Dy magnetic layers show that kinematical approximation can be applied for grazing angles that are larger than the critical total-reflection angle and that the “magnetic” refraction must be taken into account.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. J. Zak, E. R. Moog, C. Liu, and S. D. Bader, Phys. Rev. B 43, 6423 (1991).

    Article  ADS  Google Scholar 

  2. A. Bourzami, O. Lenoble, Ch. Fe’ry, J. F. Bobo, and M. Piecuch, Phys. Rev. 59, 11489 (1999).

    Article  Google Scholar 

  3. N. Ishimatsu, H. Hashizume, S. Hamada, et al., Phys. Rev. B 60, 9596 (1999).

    Article  ADS  Google Scholar 

  4. S. A. Stepanov and S. A. Sinha, Phys. Rev. B 61, 15302 (2000).

    Article  ADS  Google Scholar 

  5. M. Elzo, E. Jal, O. Bunau, S. Grenier, Y. Joly, A. Y. Ramos, H. C. N. Tolentino, J. M. Tonnerre, and N. Jaouen, J. Magn. Magn. Mater. 324, 105 (2012).

    Article  ADS  Google Scholar 

  6. M. A. Andreeva and A. G. Smekhova, Appl. Surf. Sci. 252, 5619 (2006).

    Article  ADS  Google Scholar 

  7. M. A. Andreeva, A. G. Smekhova, B. Lindgren, et. al., J. Magn. Magn. Mater. 300(1), e371 (2006).

    Article  ADS  Google Scholar 

  8. M. A. Andreeva and A. G. Smekhova, Izv. Akad. Nauk, Ser. Fiz. 72(5), 693 (2008).

    Google Scholar 

  9. E. Kravtsov, D. Haskel, T. Velthuis, et al., Phys. Rev. 79, 134438 (2009).

    Article  Google Scholar 

  10. E. E. Odintsova and M. A. Andreeva, Poverkhnost, No. 11, 46 (2010).

    Google Scholar 

  11. D. A. Tatarskii and A. A. Fraerman, Poverkhnost, No. 7, 10 (2012).

    Google Scholar 

  12. H. Ott, C. Schubetaler-Langeheine, E. Schierle, et al., Appl. Phys. Lett. 88, 212507 (2006).

    Article  ADS  Google Scholar 

  13. L. Sève, N. Jaouen, J. M. Tonnerre, et al., Phys. Rev. B 60, 9662 (1999).

    Article  ADS  Google Scholar 

  14. N. Jaouen, J. M. Tonnerre, E. Bontempi, et al., Physica B 283, 175 (2000).

    Article  ADS  Google Scholar 

  15. A. G. Smekhova, M. A. Andreeva, E. E. Odintsova, et al., Kristallografiya 55, 906 (2010).

    Google Scholar 

  16. I. W. Hamley and J. Pedersen, J. Appl. Crystallogr. 27, 29 (1994).

    Article  Google Scholar 

  17. M. A. Andreeva and B. Lindgren, Phys. Rev. B 72, 125422 (2005).

    Article  ADS  Google Scholar 

  18. Yu. N. Khaidukov and M. A. Andreeva, Vestn. Mosk. Univ., Ser. 3: Fiz. Astron., No. 2, 30 (2004).

    Google Scholar 

  19. A. G. Smekhova, Candidate’s Dissertation in Physics and Mathematics (Faculty of Physics, Mosk. Univ., Moscow, 2006).

  20. L. M. Barkovskii, G. N. Borzdov, and V. Lavrukovich, Zh. Prikl. Spektrosk. 25, 526 (1976).

    Google Scholar 

  21. L. M. Barkovskii, G. N. Borzdov, and F. I. Fedorov, Wave Operators in Optics, Preprint of Inst. of Physics, Belarusian Acad. Sci., Minsk, 1983, no. 304.

    Google Scholar 

  22. B. L. Henke, E. M. Gullikson, and J. C. Davis, At. Data Nucl. Data Tables 54(2), 181 (1993).

    Article  ADS  Google Scholar 

  23. http://henke.lbl.gov/optical-constants/getdb2.html.

  24. C. Sorg, Magnetic Properties of 3d and 4f Ferromagnets Studied by X-Ray Absorption Spectroscopy (2005). http://users.physik.fu-berlin.de/~bab/startframe2/diss/CSdiss.pdf.

    Google Scholar 

  25. http://kftt.phys.msu.ru/personalii/Andreeva/XRMR.zip.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. A. Andreeva.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Andreeva, M.A., Repchenko, Y.L. Kinematical limit in the theory of X-ray magnetic reflectivity. Crystallogr. Rep. 58, 1037–1042 (2013). https://doi.org/10.1134/S106377451307002X

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S106377451307002X

Keywords

Navigation