X-ray scattering as a probe of magnetic order in rare-earth compounds k′ εσ ε1
επ θf
ε2
επ ε3 θi
k εσ
The Advanced Photon Source You are here
6-ID-A
6-ID-D
6-ID-B
6-ID-C
MUCAT Main Undulator Line
Outline • Resonant and nonresonant magnetic scattering • Polarization dependence – Magnetic moment directions
• An example: GdNi2Ge2 – Magnetic structure and transitions – AFM domain imaging – Magnetic powder diffraction
• Summary
k′ εσ ε1
επ θf
ε2
επ ε3 θi
k εσ
Solving magnetic structures • Determine the magnetic wavevector (what is the “magnetic unit cell”) • Determine the magnetic moment directions • Determine the magnitude of the ordered magnetic moment.
Long-range order
Bragg peaks QBragg=2π/d τ = 2π/2d
I 1
τ
τ 10-6
2d d 2π/d
Q
X-ray Magnetic Scattering For nonresonant scattering we directly probe the “magnetic electrons
L3 - edge
For resonant scattering:
EF
•(L2, L3)-edge for rare-earths (610KeV) •Electric multipole transition (E1: 2p – 5d, E2: 2p – 4f) • 4f : magnetic properties 5d : exchange splitting by 4f outgoing photon
Incoming photon
P3/2 P1/2
f
res el
=
4π
λ
∑ [εˆ′ L
*
M =− L
() () ]
* ⋅ YLM kˆ′ YLM kˆ′ ⋅ εˆ FLM (ω )
TbNi2B2C
Nonresonant scattering ……. Scattering from the unpaired magnetic electrons (e.g. 4f electrons for rare earth elements)
Magnetic moment direction Discrimination of charge scattering
Resonant scattering amplitude Relating the magnitude of the resonant scattering to the details of the resonant processes • Atomic models vs. solid state effects • SOC in 5d bands • CEF effects
We still have a lot of work to do!!
FIG. 1 Schematic view of scattering geometries (a) σ to π geometry (b) π to σ geometry
We can do this by plotting the q-dependence of integrated intensities (a la neutrons) Angular dependence of the scattering at (0 0 L ± τ) of GdCo2Ge2 measured by resonant and nonresonant diffraction
Gd L3 edge
X-ray resonant magnetic scattering azimuth scans
Q Gd5Ge4 θ
θ
f
i
k
Gd5Ge4 (0 3 0) at T = 8 K
Orthorhombic structure with moments along the b-axis
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 Ψ (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)
Magnetic and charge satellite peaks
Second transition β=~0.409 (0 0 6+τ)
A(1-T/ TN)2β
(0 0 4+2τ)
B(1-T/ TN)4β
(0 0 8+3τ)
C(1-T/ TN)6β
Modulation vector τ Lattice parameter c
But… fitting the angular and azimuth dependence of the scattering to extract the moment direction never quite worked! Issue: We presume that our samples consist of small multiple domains Let’s shrink the incident beam size and look again.
One single magnetic domain T < Tt
Tt < T < TN
Q
Q
T < Tt
15 K Tt < T < TN
17 K
Q : magnetic modulation vector direction
Imaging Antiferromagnetic domains of GdNi2Ge2 by X-ray resonant magnetic scattering
How to get the images Scattered X-ray
Sample Beam Size
0.1 mm
0.1 mm
Incoming X-ray
0.1 mm
0.05 mm
How to get the images Scattered X-ray Beam Size Incoming X-ray
0.1 mm
0.05 mm
How to get the images Scattered X-ray Beam Size Incoming X-ray
0.1 mm
0.05 mm
How to get the images Scattered X-ray Beam Size Incoming X-ray
0.1 mm
0.05 mm
(a)
0.2mm
10K
Beam direction
(b) 3.5 2.8 2.1 1.4 7.0 0
17K
Beam direction
(c)
3
1
17K
Beam direction
(d)
2
Beam direction
(e)
(f) Normalized Intensity
17K
4 3 2 1 0 4 3 2 1 0 4 3 2 1 0 0
1 2 3 45 90 135 180 225 270 315 360
Azimuth angle ψ (degree)
What happens if you don’t have the slightest idea where to look for the magnetic peak, or if there can be more than one magnetic wavevector? • Powder Diffraction! – Problem is that the resonant scattering crosssection is still tiny w.r.t. charge and fluorescence scattering.
Magnetic powder diffraction from UO2 • Resonant scattering length at the U M4 edge is a significant fraction (0.2%) of charge scattering. • U-edge energies don’t allow a broad coverage of reciprocal space. • Resonant scattering at the R L-edges is a thousand times smaller! not possible!
The Challenge • Signal-to-Noise – Scattering from the sample – Fluorescence from the sample – General background (scattering from everything else) For Si (333) at the Gd L2-edge: analyzer
sample
cos2 2θanalyzer = 9 x 10-4 ΔE/E ~ 10-4 Reduce background and fluorescence to ~ 1ct /sec
The Result
Good agreement between measured peak integrated intensities and the magnetic structure determined from single crystal studies
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.
Harmonics for collinear and spiral structures Diffraction Pattern ≈ Fourier transform of the charge (magnetic) distribution
