Knight Shift in Metals

(7)
1
Spin lattice relaxation rate in metals
T1
due to spin-flip interaction between conduction electrons and nuclear spins.
i
e
k ,
nucleus
f
nucleus
k,
e
Concerning nucleus, consider
1
I , this corresponds to a transition
2
+ ½
- ½
E g
B
N
N
Transition rate is determined by Fermi’s golden rule (2nd order perturbation theory)
2
2
W
f H i E E
E
hf N k k
8
2
0
SI
3
with Hhf e e N
hyperfine coupling
constant a
very
small
Consider matrix elements fSIi
i ,
k
SI Sz Iz SyIy SxIy
1
SI
SI
2
1
with Sx
iSy
2
where S , I raising operator
S
, I
lowering operator
f ,
k
electron part
nuclear