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.
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References
J. Zak, E. R. Moog, C. Liu, and S. D. Bader, Phys. Rev. B 43, 6423 (1991).
A. Bourzami, O. Lenoble, Ch. Fe’ry, J. F. Bobo, and M. Piecuch, Phys. Rev. 59, 11489 (1999).
N. Ishimatsu, H. Hashizume, S. Hamada, et al., Phys. Rev. B 60, 9596 (1999).
S. A. Stepanov and S. A. Sinha, Phys. Rev. B 61, 15302 (2000).
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).
M. A. Andreeva and A. G. Smekhova, Appl. Surf. Sci. 252, 5619 (2006).
M. A. Andreeva, A. G. Smekhova, B. Lindgren, et. al., J. Magn. Magn. Mater. 300(1), e371 (2006).
M. A. Andreeva and A. G. Smekhova, Izv. Akad. Nauk, Ser. Fiz. 72(5), 693 (2008).
E. Kravtsov, D. Haskel, T. Velthuis, et al., Phys. Rev. 79, 134438 (2009).
E. E. Odintsova and M. A. Andreeva, Poverkhnost, No. 11, 46 (2010).
D. A. Tatarskii and A. A. Fraerman, Poverkhnost, No. 7, 10 (2012).
H. Ott, C. Schubetaler-Langeheine, E. Schierle, et al., Appl. Phys. Lett. 88, 212507 (2006).
L. Sève, N. Jaouen, J. M. Tonnerre, et al., Phys. Rev. B 60, 9662 (1999).
N. Jaouen, J. M. Tonnerre, E. Bontempi, et al., Physica B 283, 175 (2000).
A. G. Smekhova, M. A. Andreeva, E. E. Odintsova, et al., Kristallografiya 55, 906 (2010).
I. W. Hamley and J. Pedersen, J. Appl. Crystallogr. 27, 29 (1994).
M. A. Andreeva and B. Lindgren, Phys. Rev. B 72, 125422 (2005).
Yu. N. Khaidukov and M. A. Andreeva, Vestn. Mosk. Univ., Ser. 3: Fiz. Astron., No. 2, 30 (2004).
A. G. Smekhova, Candidate’s Dissertation in Physics and Mathematics (Faculty of Physics, Mosk. Univ., Moscow, 2006).
L. M. Barkovskii, G. N. Borzdov, and V. Lavrukovich, Zh. Prikl. Spektrosk. 25, 526 (1976).
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.
B. L. Henke, E. M. Gullikson, and J. C. Davis, At. Data Nucl. Data Tables 54(2), 181 (1993).
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.
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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
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DOI: https://doi.org/10.1134/S106377451307002X