Chemistry Reference
In-Depth Information
E
F
d band
s band
g
(
E
)
g
(
E
)
Figure 7.12
Schematic density of states of ferromagnetic Ni, showing the density of
spin-up states as a function of energy on the left-hand side, and spin-
down states on the right-hand side. There is a large density of states near
the Fermi energy,
E
F
, associated with the Ni 3d electrons. The exchange
interaction shifts the spin-up and spin-down states with respect to each
other, leading here to a preferential occupation of the spin-up band and
an overall net gain in energy. The wider band in the figure, with a much
lower density of states is due predominantly to interactions between 4s
states on the Ni atoms.
shift
E
as
E
=
2
µ
µ
B
H
+
J
N
(7.42)
0
Since all the changes occur near the Fermi energy, we can relate
N
to
E
as
N
=
g
(
E
F
)
E
/
2
(7.43)
where
g
is the total density of states at the Fermi energy. We now
substitute eq. (7.42) in (7.43) to determine the induced magnetisation
M
(
E
F
)
=
µ
N
as
B
2
1
2
µ
JM
µ
M
=
B
g
(
E
F
)
µ
µ
B
H
+
(7.44)
0
B
We can re-arrange eq. (7.44) as we did for eqs (7.11) and (7.21) to find that
M
=
χ
H
, with the susceptibility
χ
given by
2
B
g
µ
µ
(
E
F
)
0
χ
=
(7.45)
1
1
−
2
Jg
(
E
F
)
