Neutron Scattering

ole, compared to the stronger exchange interactions, which result from Coulomb interaction
and the Pauli principle . In ionic compounds, we observe direct exchange, ifthe orbitals of two
magnetic ions overlap or super-exchange and double exchange, if the interaction is mediated
via an intervening anion . In itinerant electron systems, the interaction is mediated by the
conduction electrons and has an oscillating character . This indirect coupling of magnetic
moments by conduction electrons is referred to the Rudermann-Kittel-Kasaya-Yosida
(RKKY) interaction . If the energy equivalent kT is in the order of the interaction energy, a
phase transition from the paramagnetic high temperature state to a magnetically long-range
ordered low temperature state can eventually take place . Systems with spontaneous
macroscopic magnetisations such as ferromagnets (FM) and fenimagnets have to be
distinguished from antiferromagnets (AF), for which the zero-field magnetisation vanishes .
The microscopie arrangement of spin- and orbital- magnetic moments, the so-called magnetic
structure, can be rather complex, especially in the case of antiferromagnets .
Neutron scattering is a most powerful technique for the investigation of magnetism due to the
magnetic dipole interaction between the magnetic moments ofthe electrons in the sample and
the nuclear magnetic moment of the neutron. We have seen in chapter 3 that for elastic
events, the neutron scattering cross section is directly related to the Fourier transform of the
magnetic moment density distribution. For the inelastic case, one can show that the double
differential cross section for magnetic neutron scattering is connected with the most
fundamental quantity, the Fourier transform of the linear response fonction or susceptibility
(16 .2) x(r,t) in microscopie space and time variables r and t, respectively . In contrast to
macroscopic methods it allows one to study magnetic structures, fluctuations and excitations
with a spatial and energy resolution well adapted to atomic dimensions . Traditionally neutron
scattering is the method to study magnetism on an atomic level, only recently complemented
by the new technique ofmagnetic x-ray scattering .
In what follows, we will give a few examples for applications of neutron scattering in
magnetism . Obviously it is completely impossible to give an representative overview within
the limited time, nor is it possible to reproduce the full formalism . Therefore we will just
quote a few results and concentrate on the most simple examples . Even so polarisation
analysis experiments are extremely important in the field, we will not discuss these rather
complex experiments and refer to chapter 4 .
16-3