Environmental Engineering Reference
In-Depth Information
Fig. 6.1.
Spin-wave dispersion relations and exchange in the
c
-
direction, in the helical and ferromagnetic phases of Tb
90
Ho
10
.Inthe
helical phase, the energy of the phason excitations goes linearly to zero
at long wavelengths, owing to the broken rotational symmetry around
the
c
-axis, but that of the mode at
Q
remains non-zero, because of the
axial anisotropy. The peak in the exchange function, which stabilizes the
periodic structure, is reduced and shifted as the magnetic order increases.
In the ferromagnetic phase at 185 K, the energy rises quadratically from
a non-zero value, and the peak in the exchange is absent.
the relatively large hexagonal anisotropy makes the use of this theory
somewhat marginal in this case. As we shall see in the next section, the
very large value of
B
6
has a decisive influence on the excitations in Ho.
The dispersion relation for the cone may be derived by the same
procedure. In the conical structure the moments along the
c
-axis are
non-zero, so that
2
=
2
+
2
.
J
iζ
=
J
=
J
z
cos
θ
0
;
J
z
J
J
⊥
(6
.
1
.
13)
Introducing the transformation (2.2.8), which corresponds to (6.1.3) in
the case where cos
θ
0
= 0, we may derive the effective coupling param-
eters within the rotating coordinate system. For the (
xy
)-part of the
Search WWH ::
Custom Search