Neutron Scattering

Ferromagnetic materials are still of considerable interest due to their enormous technical
potential in the context of data storage media .
Attempts to optiraize the technical
properties lead to binary or ternary compounds, where the complexity of the magnetic
order is considerably increased .
In all cases the study of the magnon dispersion given an
almost unique insight to the microscopic coupling terms .
13 .3 .2 Antiferromagnetic Excitations
Antiferromagnetic order results from a negative exchange constant J in U = -2J EP, S p -
SP+1 . The anti-parallel alignment of neighboring spins however, leads to a
magnetic cell which is larger than the nuclear one . A classical example is given by the
antiferromagnetic order observed in MnO at 120 K (Shull et al . 1951) . Again one may
find excitations in an antiferromagnet, which have lower energy than the simple flip of a
single spin .
Again each spin deviates from the ordered position by a component given by
a plane wave .
'T'he calculation of the antiferromagnetic dispersion more closely resembles
that of the phonon case
4J S ) 2 (1 - co .s 2 (q . a,))
w W , (q) - (
(q
-MS Isira(q - a,)I (13 .25) .
In contrant to the ferromagnetically ordered structure and in close similarity to the
acoustic phonons, the frequency becomes linear in q for sufficiently small q . Figure 16
shows the magnon dispersion observed in RbMnF 3 .
In general both dispersion relations (13 .23) and (13 .25)
are not gaped, the magnon
energy vanishes for q approaching the zone conter, like in case of an acoustic phonon .
For
the acoustic phonon the zone-conter limit corresponds to an infinitely small translation of
the entire crystal which does not cost any energy, since no force constant is stretched .
In
case of the magnons the lirait corresponds to a rotation of the ordered moment, which in
the Heisenberg-model does not involve any energy shift (the interaction depends only on
the relative orientation) .
However, in general this model is not sufficient, there are always
interactions faworing the orientation of a certain spin direction .
'These interactions yield
a finite gap in the excitation spectrum, however much smaller than the spin flip energy.
Antiferromagnetic materials have much less technical importance compared to ferromagnetism
.
However, antiferromagnetic corrélations in metallic systems are often essential
for thé understanding of thé electronic properties .
For instance thé physics of
high-température cuprate superconductors seems to be determined by thé closelyness of
13-23