Knight Shift in Metals

(2)
e
2
B
0
2
B
M f E D E dE
integration by parts
0
B f
E D E dE
0
DE
F
2
3N
Me B B0
DEF DEF
2E
T independent since E k T
F
0
F
pauli
Me
3N
B
2E
2
B
2
B
F
D E
F
Pauli spin susceptibility of conduction electrons
T-independent Knight shift
e at the
nuclear site!
this is not necessarily the average one.
15
Nuclei are very small a 10 m . They are surrounded by a cloud of polarized
conduction electrons.
however, the Knight shift is determined by magnetic field B r 0
Need to sum up the contributions to the local magnetic field at the nucleus site.
Consider homogenously magnetised sphere of magnetisation M
2
out 3
e r
r
B r
r a
5
r
in 2
B r
r a
3
a
have to consider lima
0
dipolar terms
"contact-term"