Knight Shift in Metals
Knight Shift in Metals
Knight Shift in Metals
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(8)<br />
S<br />
S<br />
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<br />
S or 0<br />
z<br />
<br />
0<br />
1<br />
<br />
, k<br />
IzSz<br />
IS IS<br />
,<br />
k <br />
2 2<br />
8<br />
fH 0<br />
<br />
3<br />
2 2<br />
hf i<br />
el e N<br />
<br />
F<strong>in</strong>ally we need to consider the density of available electronic states.<br />
i must be occupied f must be empty<br />
2<br />
f<br />
f E<br />
kB<br />
T<br />
1<br />
f E<br />
E F <br />
E<br />
only this range of<br />
energies contributes<br />
<br />
1<br />
<br />
W<br />
dE dE D E f E<br />
D E f E<br />
s<strong>in</strong>ce E E<br />
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<br />
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E<br />
EF<br />
<br />
exp<br />
<br />
2<br />
kB<br />
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1<br />
dE dE D E <br />
with f E<br />
<br />
E EF<br />
E EF<br />
<br />
1exp 1exp <br />
kB<br />
T kB<br />
T<br />
<br />
<br />
f E<br />
kB<br />
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E<br />
f<br />
s<strong>in</strong>ce dE E E<br />
E<br />
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W<br />
D E k T<br />
<br />
F<br />
<br />
B<br />
F<br />
<br />
8<br />
2 <br />
consider<strong>in</strong>g the matrix element fHfh i e 0<br />
e N <br />
3 2<br />
2<br />
2<br />
2<br />
8<br />
2 <br />
W <br />
e0 e N DEFkB<br />
T<br />
3 2 <br />
<br />
<br />
<br />
<br />
<br />
density of available<br />
states<br />
2
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