Neutron Scattering

T>Tc
TTc
O O O O " O " O
8
8
" "
2 O O O i O O O
~ila
T-->T .
0 q
Figure 12 Schetnatic pictiire of a displacive phase transition corresponding to a zone-boundary mode .
dynamics, which is analyzed almost exclusively by inelastic neutron scattering since the
largest effects are expected in the Brillouin-zone .
The screening of the inter-atomic potentials through free charge carriers is determined
by the topology of the Fermi-surface .
In particular there are singularities in the electronic
susceptibility when parts of the Fermi-surface are parallel and may, hence, be connected
by a single nesting vector .
The susceptibility at this vector will be essentially increased
and may renormalize the phonon frequency of a mode just at this wave vector .
In most
cases this type of électron phonon coupling leads to a réduction of thé phonon frequency,
which shows up as a dip in thé dispersion curve, called a Kohn-anomaly .
In particular thé
conventional superconductors, for example TaC in Figure 13, exhibit such effects .
'T'he
phonon dispersion of TaC shows pronounced dips, which are not observed in thé phonon
dispersion of normal metals .
The study and interpretation of similar anomalies in thé
high-T, cuprates is subject of present research .
However, in this case thé aualysis gets
rather complicated due to thé large number of atoms in these systems .
13 .3 Magnetic excitations
13 .3 .1 Spin waves in a ferromagnet
Like thé crystal structure, magnetic order may be disturbed at finite temperature
with thé perturbation propagating through thé crystal .
Analogous to thé phonons, thé
quantisized excitations are called magnons .
The ground state of a ferromagnet results from thé interaction between spins of neighboring
atoms, which fa-, ,ors a parallel alignment . The energy of a neighboring pair, S i , S j ,
depending on thé relative orientation of thé spins is
described within thé Heisenbergmodel
by c = -JS z - S j , where J is thé Heisenberg exchange constant . For a chain of
13- 19