1. The Advanced Photon Source
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6-BM-A
6-BM-B
6-ID-A
6-ID-B
6-ID-C
6-ID-D

2. Diffraction from ordered structures
• Incoming X-rays diffract from crystal planes.
Adapted from Fig. 3.2W, Callister 6e.
d= n l
/2sin q c 2q
Measurement of the scattered intensity as a function of 2q provides the atomic spacing, d.
Intensity

3. Magnetic periodicity leads to magnetic Bragg peaks
t =2p/2d t 1
10-6 d Q
2p/d

4. Why Bother? For magnetic scattering compared to charge
or nuclear scattering:
(ds/dW)X-ray = 10-5 10-6 (ds/dW)Neutron
Why Bother?
Many of the technologically important RE compounds contain neutron opaque elements.
Superior reciprocal space (Q) resolution allows more detailed study … reinvestigation of “solved” structures.
Can be used for investigations of submillimeter-sized single crystals.
Resonant magnetic scattering occurs at well-defined energies specific to elements of interest -- probe local magnetism.
Studies of magnetic surfaces and interfaces.

5. X-ray Resonant Magnetic Scattering (XRMS)
(L2, L3)-edge for rare-earths (6-10KeV)
Electric multipole transition
(dipole : 2p – 5d, quadrupole 2p – 4f)
Dipole transition is dominant
4f : magnetic properties
5d : exchange splitting by 4f EF
P3/2
P1/2
LIII & LII
Incoming photon
outgoing photon
Scattering matrix element is identical to
the matrix element for XMCD!

7. The angular piece is used to determine moment directions
Non-resonant: ds/dW  [S2sinQ] (outgoing s- pol.)
 [2sin2Q  cosQ{(L1+S1) + S3sinQ}]2 (outgoing p- pol.)
Resonant (E1): ds/dW  (outgoing s- pol.)
 (-M1cosQ + M3sinQ)2 (outgoing p- pol.)
 (k′· M)2
Resonant (Quadrupole): Much more complicated, but can probe M1, M2, M3
How do we measure magnetic scattering.
1) Orient crystal axes with respect to scattering plane
2) incident and outgoing wavevectors k and k’ define the scattering plane. Incident polarization is sigma, outgoing polarization is sigma or pi and we can do polarization analysis.
For nonresonant scattering we are scattering directly from the magnetic electrons (e.g. 4f) - primarily sensitive (except at high angles) to the comp. of the moment out of the scattering plane along u2
Resonant scattering involves eletric dipole transitions from the p-d states. Sensitive to magnetization through polarization from f-electrons - sensitive to the components of the moment in the scattering plane.
J. P. Hill, and D. F. McMorrow, Acta Crystallogr. Sec.A 52, 236 (1996).
M. Blume, and Doon Gibbs, Phys. Rev. B 37, 1779 (1988).