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