An Introduction to Neutron Scattering - Spallation Neutron Source
An Introduction to Neutron Scattering - Spallation Neutron Source
An Introduction to Neutron Scattering - Spallation Neutron Source
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Inelastic Magnetic <strong>Scattering</strong> of <strong>Neutron</strong>s<br />
• In the simplest case, a<strong>to</strong>mic spins in a ferromagnet precess<br />
about the direction of mean magnetization<br />
r r r r<br />
+<br />
H = J ( l − l ')<br />
S . S = H + hω<br />
b b<br />
with<br />
hω<br />
q<br />
∑<br />
l,<br />
l'<br />
=<br />
2<br />
q Dq = ω h<br />
exchange coupling<br />
2S(<br />
J<br />
0<br />
−<br />
J<br />
q<br />
l<br />
)<br />
l'<br />
is the dispersion<br />
0<br />
where<br />
∑<br />
q<br />
ground state energy<br />
J<br />
q<br />
=<br />
q<br />
∑<br />
l<br />
q<br />
q<br />
r<br />
J ( l ) e<br />
relation for a ferromagnet<br />
Spin wave animation courtesy of A. Zheludev (ORNL)<br />
r r<br />
iq.<br />
l<br />
spin waves (magnons)<br />
Fluctuating spin is<br />
perpendicular <strong>to</strong> mean spin<br />
direction => spin-flip<br />
neutron scattering
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