Resonant magnetic x-ray scattering
and Summary
• Resonant scattering
– Why do it?
– What is it?
– How is it done?
– Example(s)
• The Real World …. CaFe2As2
Solving
magnetic
structures
Determine the magnetic wavevector
(what is the “magnetic unit cell”)
Use the angular dependence of resonant
and nonresonant scattering crosssections to determine magnetic moment
directions.
Scattering amplitudes → magnitude of
the ordered magnetic moment.
Long-range order
Bragg peaks
QBragg=2p/d
t = 2p/2d
I
1
t
t
10-6
2d
d
2p/d
Q
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.
X-ray Resonant Magnetic Scattering
(XRMS)
•(L2, L3)-edge for rare-earths (6-10KeV)
L3 - edge
•Electric multipole transition
(dipole : 2p – 5d, quadrupole 2p – 4f)
EF
•Dipole transition is dominant
• 4f : magnetic properties
5d : exchange splitting by 4f
outgoing photon
P3/2
P1/2
Incoming photon
f
res
el

4p

 ˆ
L
*
M  L
  
*
 YLM kˆ YLM
kˆ  ˆ FLM  
TbNi2B2C
k
s
p
f
M1
k
M3
i
analyzer
s
sample
M2
Non-resonant: ds/dW  S2sinQ2
outgoing s- pol.)
 2sin2Q  cosQ{(L1+S1) + S3sinQ}]2 (outgoing p- pol.)
Resonant (E1): ds/dW  0
^
^
 M1cosQ + M3sinQ2

outgoing s- pol.)
(outgoing p- pol.)
^ 2
(k′· M)
Resonant (E2): Much more complicated, but can probe M1, M2, M3
We can do this by plotting the q-dependence
of integrated intensities (a la neutrons)
Angular dependence of the scattering at (0 0 L ± t) of GdCo2Ge2 measured
by resonant and nonresonant diffraction
Gd L3 edge
Alternatively…
X-ray resonant magnetic scattering azimuth scans
Q
Gd5Ge4
θ
θ
f
i
k
Gd5Ge4 (0 3 0) at T = 8 K
I
(M•k’)2
Integrated Intensity (arb. unit.)
k'
Intensity  |k' • M|2
1.0
0.5
bc in
scattering
plane
0.0
0
30
ab in
scattering
plane
60
90
120
Azimuth  (deg.)
bc in
scattering
plane
150
180
GdNi2Ge2 – An Example
Crystal structure
Magnetization measurement
Tt
TN
Gd
Ni
Ge
S.L. Bud’ko, Z. Islam, T.A. Wiener, I.R. Fisher, A.H. Lancerda, P.C. Canfield
Journal of Magnetic Materials 205, 53 (1999)
1st harmonic
(magnetic)
2nd harmonic
(charge)
3rd harmonic
(magnetic)
So, what do you learn from
diffraction?
• From peak positions
– Lattice parameters and how they change with environmental
conditions (e.g. temperature and pressure)
• From peak widths
– Crystal quality (e.g. mosaic)
– Presence of strain (e.g. longitudinal widths)
• From integrated intensities
– Contents of the unit cell
– Positions of atoms within the unit cell; magnetic ordering
– Thermal parameters (thermal disorder)
CaFe2As2…an example
Peak positions: Temperature
dependent studies
Peak Positions: Pressure dependent studies
Peak Widths – strain, crystallite
size and mosaic
10000
103
(1 1 10)
206
200
FWHM =
0.017 deg
222
301
215
008
116
007
211
202
224 310
311
006
112
Rocking
curve
Counts / s
114
Sn traces
100
20
400
Si standard
004
1000
101
Intensity (counts)
CaFe2As2
0
30
40
50
2 (deg)
60
Powder after grinding
70
80
Fig. X1
45.60
45.65
 (deg)
45.70
Single crystal mosaic
Integrated Intensities