Neutron Scattering

21
[ooç 1 " -
19
18
17
16
"" 298 K
4
3
O
0 0.2 0.4 0 .6 0.8 1.0 0.8 0.6 0.4 0.2 0 0.1 0.2 0.3 0.4 0.3
Reduced wave vector coordinate (c)
Figure 13 Phonon dispersion of TaC, the dips, for example at (0 0 0 .7) andd at (0 .6 0 .6 0), indicate
modes renormalized throiigh the electron phonon coiipling, from reference [2] .
coupled spins the energy of the magnetic interaction amounts to
n,
U = -2J ~7 Sp - Sp+1 (13 .20) .
p=1
In the ground state all spins are parallel and Uo = -2NJS 2 ,
this corresponds to figure
14a . A possible excitation might consist in the flip of just one spin, like it is shown in
figure 14b . 'This perturbation yields a finite increase in energy of 8JS 2 . However, the temperature
dependence of several macroscopic properties like specific heat or magnetization
does not correspond to an exponential law, as it
has to be expected for a finite excitation
energy.
Spin waves (magnons) must have a much smaller energy than the single spin flip,
like phonons may have lower energy than an ionic vacancy for instance .
The distortion of the magnetic order corresponds to
a plane magnetic wave (with
propagation vector q and frequency w) and is drawn in Figure 14c .
Spins are precessing
around the direction of magnetic order (here z) with components
Sp - u - exp[i(p(ja - wt)] (13 .21),
13-20