ELEMENTS OF RARE EARTH MAGNETISM - Rare Earth Magnetism: Structures and Excitations - page 65

is the angle between the a -axis and the magnetization in the plane.
The dominant contribution to the magnetoelastic energy is

− 2 − 2 Nc γ ( C 2 + 4

Nc γ ( γ 1 + γ 2 )= A 2

H γ = − CA cos 6 φ ) . (1 . 5 . 32)

The cos 6 φ term makes a contribution to the hexagonal anisotropy, which
is in total, from (1.5.24), (1.5.15), and (1.5.31),
κ 6 ( T )= B 6 J (6) σ 21 + 2

c γ CA

(1 . 5 . 33)

1
c γ

= B 6 J (6) σ 21 B γ 2 J (2) B γ 4 J (4) σ 13 .

−

The hexagonal anisotropy can readily be deduced from the critical field
H c necessary to rotate the moments from an easy direction to a neigh-
bouring hard direction in the plane (respectively a b -axis and an a -axis
in Tb), which is given by

κ 6 ( T ) gµ B JσH c =36 | | . (1 . 5 . 34)

Values of the critical field for Tb are given as a function of σ in Fig. 1.21.

Fig. 1.21. The critical field H c necessary to rotate the moments from
an easy direction to a neighbouring hard direction in the plane in Tb, as
a function of the reduced magnetization. The closed circles denote the
results of neutron-scattering experiments, and the other signatures are
deduced from macroscopic measurements.