ELEMENTS OF RARE EARTH MAGNETISM - Rare Earth Magnetism: Structures and Excitations - page 30

Fig. 1.9. The band structure of dhcp Pr, calculated by Skriver. The
energy bands in the vicinity of the Fermi level are predominantly d -like,
and the 4 f states are assumed to be localized and therefore do not appear,
in contrast to Fig. 1.8.

hole sheets. However, the dHvA effect is measured in a relatively high
magnetic field, and the induced moment modifies the band structure in
a way which has been studied in detail by Wulff (1985). The exchange
coupling between a conduction-electron spin s and the 4 f spins takes
the Heisenberg form

H sf = − 2 I s · S i . (1 . 3 . 22)

i

In the ground-state manifold, this interaction may from (1.2.29) be writ-
ten

H sf = − 2( g − 1) I s · J i . (1 . 3 . 23)

i

When a magnetic field is applied, the induced moment therefore gives
rise to a splitting between the up- and down-spin energy bands. Since
Pr is magnetically highly anisotropic, this splitting depends strongly
on the direction of the field, but it can readily attain values of sev-
eral mRy, and hence have drastic effect on the Fermi surface. In par-
ticular, the seventh-band minority-spin surface changes its topology
at a critical (internal) field of about 40 kOe, as shown in Fig. 1.10,