Neutron Scattering

These magnetic structures can be understood on the basis of magnetic interactions, which
again can be determined by neutron scattering from measurements of the magnetic excitation
spectra. Magnetic structures are only stable in a certain range of theromdynamic parameters,
such as temperature, pressure or magnetic field . As we approach the limits of a stability
region, magnetic phase transitions into a différent magnetic phase occur. An example is thé
transition from a long-range magnetic order at low temperatures to a paramagnetic high
temperature phase . By means of neutron scattering, thé spectra of magnetisation fluctuations
close to a magnetic phase transition can be determined . Such measurements provide thé
experimental foundation of thé famous renormalisation group theory ofphase transitions .
In what follows, we will give an introduction into the formalism of magnetic neutron
scattering . Again, we will restrict ourselves to the case of elastic magnetic scattering .
Examples for magnetic scattering will we given in a later chapter.
To derive thé magnetic scattering cross section ofthermal neutrons, we consider thé situation
shown in figure 3 .9 : a neutron with thé nuclear moment gN is at position R with respect to an
electron with spin S, moving with a velocity _ve.
Fit. 3 .9 : Geometryfor thé dérivation ofthé interaction between neutron and electron .
Due to its
electron according to :
magnetic dipole moment, the neutron interacts with the magnetic field of the
(3 .43)
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