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Short-Range Order Above TC

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Dynamic Spin-Fluctuation Theory of Metallic Magnetism

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Abstract

Inelastic neutron scattering measurements give the most direct experimental information on spin fluctuations. In particular, the polarized neutron scattering analysis is one of the most important methods of investigating the spin-density correlations and short-range order (SRO).

A mathematician may say anything he pleases, but a physicist must be at least partially sane. (J.W. Gibbs)

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Notes

  1. 1.

    For a brief introduction to neutron scattering in itinerant electron magnets, see [18].

  2. 2.

    For selected temperatures, calculations of the spin-density correlator and its Fourier transform in static and dynamic approximations of spin fluctuation theory were carried out by Hasegawa [49] and Grebennikov [11, 50], respectively.

  3. 3.

    In the Heisenberg model, this reduces to C j = 〈S jS 0〉∕〈S 0S 0〉, where the jth spin S j is a vector of the modulus S 0. Therefore, in the paramagnetic region, C j is the mean cosine of the angle between the spins.

  4. 4.

    For discussion of the Ornstein-Zernike correlator in the Ising model see, e.g. [18].

  5. 5.

    Calculations in the renormalized Gaussian approximation with uniform fluctuations (RGA+UF) of the DSFT give close results [14, 16].

  6. 6.

    We consider only the spin contribution from the electron subsystem. The magnetic force arising from the orbital motion of electrons gives only a small cross-section for the neutron scattering and may be ignored [22]. As for the phonon contribution, it is not the main one in the ferromagnetic metals (see, e.g. [16, 19]). In detail the phonon mechanism is discussed in [54].

  7. 7.

    Experimental measurements up to the Brillouin zone boundary [29] confirm the results of [5, 27, 28].

  8. 8.

    A slightly larger experimental value of m L = 1. 3 μ B is obtained in [5, 27, 28] with the use of another measurement, and the value m L = 1. 55 μ B presented in [1] corresponds to the energy cutoff 200 meV.

  9. 9.

    Roughly speaking, the higher the peak of M 2(κ), the wider the correlator, and hence the larger is the SRO domain (for details, see [21]).

  10. 10.

    Correlation length of approximately 2a (a is the lattice constant) was reported by Tao et al. [59].

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    Nikolai B. Melnikov

  2. Institute of Metal Physics, Russian Academy of Sciences, Ekaterinburg, Russia

    Boris I. Reser

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Melnikov, N.B., Reser, B.I. (2018). Short-Range Order Above TC . In: Dynamic Spin-Fluctuation Theory of Metallic Magnetism. Springer, Cham. https://doi.org/10.1007/978-3-319-92974-3_15

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