Spin-density correlator and its Fourier transform in the dynamic spin-fluctuation theory


  • G.V. Paradezhenko
  • N.B. Melnikov
  • B.I. Reser


scattering function
spin fluctuations
dynamic susceptibility
magnetic neutron scattering


A formula relating the magnetic contribution to a polarized neutron scattering cross-section with the Fourier transform of the spin-density correlator is derived. A method of calculating the spin-density correlator and its Fourier transform in the dynamic spin-fluctuation theory is described. Calculation formulas and Fortran program modules are presented. By the example of iron, it is shown that the numerical results obtained for the Fourier transform of the spin-density correlator are in good agreement with experimental data.





Section 1. Numerical methods and applications

Author Biographies

G.V. Paradezhenko

N.B. Melnikov

Lomonosov Moscow State University
• Associate Professor

B.I. Reser


  1. T. Moriya, Spin Fluctuations in Itinerant Electron Magnetism (Springer, Heidelberg, 1985; Mir, Moscow, 1988).
  2. J. Schweizer, “Polarized Neutrons and Polarization Analysis,” in Neutron Scattering from Magnetic Materials , Ed. by T. Chatterji (Elsevier, Amsterdam, 2006), pp. 153-213.
  3. K. R. A. Ziebeck and P. J. Brown, “Measurement of the Paramagnetic Response Function in the Weak Itinerant Magnetic Compound MnSi Using Polarised Neutron Scattering,” J. Phys. F: Metal Phys. 10 (9), 2015-2024 (1980).
  4. N. B. Melnikov, G. V. Paradezhenko, and B. I. Reser, “Correlations of Spin Density and Magnetic Neutron Scattering in Ferromagnetic Metals,” Theor. Math. Phys. 191 (2017) (in press).
  5. A. N. Tikhonov and V. Ya. Arsenin, Solution of Ill-Posed Problems (Nauka, Moscow, 1979; Wiley, New York, 1977).
  6. Y. Wang, A. G. Yagola, and C. Yang (Eds.), Optimization and Regularization for Computational Inverse Problems and Applications (Springer, Berlin, 2010).
  7. P. J. Brown, H. Capellmann, J. Déportes, et al., “Observations of Ferromagnetic Correlations at High Temperatures in Paramagnetic Iron,” J. Magn. Magn. Mater. 30 (2), 243-248 (1982).
  8. J. Hubbard, “Panel Discussion on Itinerant Electron Magnetism,” Inst. Phys. Conf. Ser. 55, 669-687 (1981).
  9. N. B. Melnikov, B. I. Reser, and V. I. Grebennikov, “Extended Dynamic Spin-Fluctuation Theory of Metallic Magnetism,” J. Phys.: Condens. Matter 23 (2011).
    doi 10.1088/0953-8984/23/27/276003
  10. N. B. Melnikov and B. I. Reser, “Short-Range Order above the Curie Temperature in the Dynamic Spin-Fluctuation Theory,” J. Magn. Magn. Mater. 397, 347-351 (2016).
  11. N. B. Melnikov, B. I. Reser, and G. V. Paradezhenko, “Spin-Density Correlations in the Dynamic Spin-Fluctuation Theory: Comparison with Polarized Neutron Scattering Experiments,” J. Magn. Magn. Mater. 411, 133-139 (2016).
  12. G. Shirane, P. Böni, and J. P. Wicksted, “Paramagnetic Scattering from Fe(3.5 at. % Si): Neutron Measurements up to the Zone Boundary,” Phys. Rev. B 33 (3), 1881-1885 (1986).
  13. L. I. Schiff, Quantum Mechanics (McGraw-Hill, New York, 1955; Inostrannaya Literatura, Moscow, 1959).
  14. G. L. Squires, Introduction to the Theory of Thermal Neutron Scattering (Dover, New York, 1996).
  15. R. M. White, Quantum Theory of Magnetism (Springer, Heidelberg, 1983; Mir, Moscow, 1985).
  16. K. Blum, Density Matrix Theory and Applications (Plenum, New York, 1981; Mir, Moscow, 1983).
  17. B. I. Reser and N. B. Melnikov, “Problem of Temperature Dependence in the Dynamic Spin-Fluctuation Theory for Strong Ferromagnets,” J. Phys.: Condens. Matter 20 (2008).
    doi 10.1088/0953-8984/20/28/285205
  18. B. I. Reser, “Numerical Method for Calculation of the Fermi Integrals,” J. Phys.: Condens. Matter 8 (18), 3151-3160 (1996).
  19. B. I. Reser, “Calculation of the Magnetic Properties of Fe, Co and Ni with Account Taken of the Real Band Structure and Spin Fluctuations,” J. Phys.: Condens. Matter 11 (25), 4871-4885 (1999).
  20. J. Crangle and G. M. Goodman, “The Magnetization of Pure Iron and Nickel,” Proc. Roy. Soc. London Ser. A 321 (1547), 477-491 (1971).
  21. V. L. Moruzzi, J. F. Janak, and A. R. Williams, Calculated Electronic Properties of Metals (Pergamon, New York, 1978).
  22. B. I. Reser and V. I. Grebennikov, “Temperature Dependence of Magnetic Properties of Ferromagnetic Metals with Account Taken of the Dynamics and Nonlocality of Spin Fluctuations,” Fiz. Met. Metalloved. 85 (1), 30-42 (1998).
  23. B. I. Reser and N. B. Melnikov, Software Package MAGPROP: Calculation of the Magnetic Properties of Transition Metals and Alloys within the Theory of Spin Fluctuations (Scientific and Educational Collection of Electronic Resources, Moscow, 2011), Certificate No. 17257.
  24. D. Kahaner, C. Moler, and S. Nash, Numerical Methods and Software (Prentice Hall, Englewood Cliffs, 1989; Mir, Moscow, 1998).