Resonant magnetic x-ray scattering Resonant magnetic x-ray scattering and Summaryand 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 cross-sections to determine magnetic moment directions.Scattering amplitudes → magnitude of the ordered magnetic moment.
2/d
d
Q
2d
= 2/2d
Long-range order Bragg peaks
1
10-6
I
QBragg=2/d
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)
EF
P3/2
P1/2
L3 - edge
Incoming photonoutgoing photon
LM
L
LMLMLM
resel FkYkYf
ˆˆˆˆ4 **
•(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
TbNi2B2C
Non-resonant: d/dS2sinoutgoing - pol.) 2sin2cos(L1+S1) + S3sin}]2 (outgoing - pol.)
Resonant (E1): d/d outgoing - pol.)
M1cos+ M3sin(outgoing - pol.)
(k′· M)2
Resonant (E2): Much more complicated, but can probe M1, M2, M3
kk
if
1M
2M
3M
^ ^
^
analyzer
sample
We can do this by plotting the q-dependenceof integrated intensities (a la neutrons)
Alternatively…
Angular dependence of the scattering at (0 0 L ± ) of GdCo2Ge2 measured by resonant and nonresonant diffraction
Gd L3 edge
X-ray resonant magnetic scattering azimuth scans
0 30 60 90 120 150 1800.0
0.5
1.0
ab inscattering plane
bc inscattering plane
Inte
gra
ted
In
ten
sity
(a
rb.
un
it.)
Azimuth (deg.)
Gd5Ge
4 (0
3
0) at T = 8 K
bc inscattering plane
Intensity |k' • M|2
Gd5Ge4
Q
kθ
f
θ
i
k'
I (M•k’)2
Crystal structure
Gd
NiGe
Magnetization measurement
S.L. Bud’ko, Z. Islam, T.A. Wiener, I.R. Fisher, A.H. Lancerda, P.C. CanfieldJournal of Magnetic Materials 205, 53 (1999)
GdNi2Ge2 – An Example
TNTt
1st harmonic
2nd harmonic
3rd harmonic
(magnetic)
(magnetic)
(charge)
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
20 30 40 50 60 70 80
100
1000
10000
Sn traces
Si standard
CaFe2As
2
311
301
310
224
222
206
21500
8
007
116
21120
2
006
114
112
103
004
101
Inte
nsity
(co
unts
)
2 (deg)45.60 45.65 45.70
0
200
400
Fig. X1
Rockingcurve
FWHM =0.017 deg
Cou
nts
/ s
(deg)
(1 1 10)
Powder after grinding Single crystal mosaic
Integrated Intensities
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