Environmental Engineering Reference
In-Depth Information
4
MAGNETIC SCATTERING OF NEUTRONS
The scattering of low-energy neutrons provides an extremely powerful
experimental technique for studying the properties of solids. The neu-
tron has a number of special characteristics, on which its utility as a
tool for examining magnetic materials depends. Because it is a neutral
particle, it can penetrate deeply into most crystals, interacting through
its magnetic moment with the electronic moments strongly enough to be
measurably scattered, but without disturbing the magnetic system too
severely. As a consequence, the great majority of neutrons participate
in at most one scattering event, and they sense the properties of the
unperturbed crystal.
Thermal neutrons
, with energies of the order of
25 meV, corresponding to wavelengths of the order of 2 A, match both
the interatomic spacings and the energies and momenta of the mag-
netic excitations, and are generated with adequate intensity by research
reactors.
Cold neutrons
, with energies around 5 meV and wavelengths
about 4 A, which are emitted from cooled moderators in reactors, may
be even more ideally suited for studying the spatial arrangement and
the dynamics of the magnetic moments.
The neutron-scattering cross-section contains precisely that infor-
mation which is needed to characterize a magnetic material, and to make
a stringent comparison with theoretical calculations of its properties.
The elastic
Bragg scattering
or
neutron diffraction
provides a systematic
procedure for determining the magnetic structure, or the mean values
of the magnetic-moment vectors on the different atomic sites.
Inelastic
neutron scattering
may be looked upon in three complementary ways.
Through conservation of energy and momentum, the scattered neutrons
measure the
dispersion relation
of the magnetic excitations. The scat-
tering cross-section is also directly related to the
time-dependent pair-
correlation function
, which describes the evolution in space and time
of the system of moments. Finally, through the fluctuation-dissipation
theorem presented in the last chapter, the cross-section may be expressed
in terms of the
generalized susceptibility
of the magnetic crystal, the
function describing the dynamics of the moments which is most read-
ily calculated theoretically. No other experimental technique can aspire
to providing such detailed microscopic information about magnetic sys-
tems.
This chapter does not pretend to be a complete exposition of the
theory of magnetic neutron scattering. We shall rather, by elementary
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