1. Probing magnetism and ferroelectricity with x-ray microdiffraction
Paul Evans,
University of Wisconsin
October 9, 2002

2. Outline Magnetic and Polarization Domains in Solids
Hard X-ray Microdiffraction
Antiferromagnetic domains and the “spin-flip” transition in chromium
Polarization reversal in strontium bismuth tantalate thin films
Conclusions

3. Example 1: Polarization domains in ferroelectrics
towards bulk
TEM study of BaTiO3
A. Krishnan, M. E. Bisher, and M. M. J. Treacy, Mat. Res. Soc. Symp. Proc (1998).

4. Example 2: Magnetic domain wall resistance in Fe
Resistivity and magnetoresistance depend on domain configuration in micron-scale Fe wires.
2 m
H transverse
H transverse
H longitudinal
H longitudinal
Ruediger et al., Phys. Rev. Lett (1998).

5. X-ray microdiffraction

6. Focusing X-rays Using Zone Plates
zone plate D~100 m
order sorting aperture
L~50 m
f~10 cm
Source demagnified by L/f500.
6 to 30 keV
1010 ph/s/0.01%BW
Flux Density Gain - 105
Minimum spot x 0.15 µm2

7. Hard X-ray Machine: Advanced Photon Source
Chicago 30 miles
Argonne Natl. Lab.
Murray Hill 700 miles
350 m

8. X-ray Microprobe Applications
Glasses for fibers, amplifiers: Dopant Distributions (with R. Windeler, Lucent/OFS, and J. Maser APS)
5 m
Yb x-ray
fluorescence
fiber amplifier core
in  2 scans
2 (deg.)
distance from g. b. (m)
Strain relaxation in LaSrMnO film on a bicrystal substrate
Y.-A. Soh, et al., submitted.
Strain at an artificial grain boundary
0.1 Å-1

9. X-ray Microprobe Applications
periodically poled LiNbO3 polarization domains
switching in a SrBi2Ta2O9 thin film capacitor
Domains in ferroelectric materials
Spin density wave domains in Cr
P. G. Evans, et al., Science (2002).
Magnetic x-ray microscopy
100 m

10. Spin density wave domains in chromium
Cr is a spin density wave (SDW) antiferromagnet.
SDW leads to strain wave and charge density wave (CDW).
Spins are transverse T=123 to 311 K, longitudinal for T<123 K.
Q || [001]
Cr unit cell
Antiferromagnetic Domains:
Modulation direction Q any <001>
 Three possible Q domains.
Spin polarizations S, also <001>
Two S domains in transverse phase.
Just one S (||Q) in longitudinal phase.
S || [100]
Domains are responsible for macroscopically observable magnetic, mechanical, electrical phenomena.
Previous domain imaging experiments are at the 1 mm scale.

11. Fermi surface nesting in Cr
(q) susceptibility, response of hypothetical non-magnetic system to magnetic perturbation with wavevector q
Difficult to calculate (q) directly, but common feature is
QSDW
where EK+q and EK are pairs of filled and empty states differing in wavevector by q.
Band structure of Cr: Fermi surfaces nest with Q=(0,0,1-) , incommensurate with lattice.

12. Domain effects in chromium (?)
Magnetoresistance of a Cr thin film is enhanced below spin flip transition.
Mattson et al. J. Magn. Magn. Mater (1992).
Magnetoresistance reaches 50% at 4K for H=5 T.

13. (Non-Resonant) Magnetic X-ray Scattering: Classical Picture
Force
Radiation -e
“Thomson scattering”
-eE
electric dipole E E -e
magnetic quadrupole
-eE  H E -e
electric dipole E H  -e
magnetic dipole
After F. de Bergevin and M. Brunel, Acta Cryst. A (1981).  H H

14. Cr in reciprocal space
Magnetic scattering appears near forbidden lattice reflections.
Also: Strain wave (CDW) reflections near allowed lattice reflections. K H L
SDW
near (0 0 1)
CDW
near (0 0 2)
Form images using either type of reflection.

15. Sample Orientation  Magnetic cross sections ( polarizations.
) are equal for transverse

16. Non-resonant magnetic x-ray diffraction from Cr
Most important term of cross section scales as:
Polar plot of cross section as a function of spin direction for a Q || (001) domain in our geometry.

17. k’-k || Cr (0 0 1-d)
APS Station 2ID-D

18. All three Q domains are present
Visit one CDW reflection from each family.
h scan near (2 0 0)
k scan near (0 2 0)
l scan near (0 0 2)
Room temperature laboratory diffractometer scans with large mm-scale beam.

19. SDW Domains at 130 K SDW magnetic reflection CDW charged reflection
incident beam h=5.8 keV
incident beam h=11.6 keV

20. Spin-flip transition Transverse SDW phase Longitudinal SDW phase
TSF=123 K
in bulk Cr
Image SDW reflection as a function of temperature.
Magnetic reflection disappears!

21. Repeat with charged CDW reflection
SDW Magnetic reflection
CDW Charged reflection
T=130 K
T=130 K
T=110 K
T=110 K

22. Spin flip transition begins at Q domain edges
Nominally first order transition is broadened by several degrees, even at micron scale.

23. Sources of broadening
Magnetic effects at ferromagnet/antiferromagnet interfaces are well described in comparison.
Not much known (yet) about antiferromagnetic domain walls.
1. Magnetic interactions across domain boundary. Q Q S S
vs. Q S Q S
2. Fermi surface effects. Simultaneous Fermi surface nesting at multiple Q directions is not allowed.
3. Strain, impurities, defects.
Challenges: length and energy scales, several types of domain walls.

24. Learning more about domain walls
1) So far we’ve looked at Q || [001].
What happens in neighboring Q domains? K
red Q || [100] green Q || [010] blue Q || [001] H L
SDW
near (0 0 1)
CDW
near (0 0 2)
2) Two spin polarizations within transverse phase.

25. Magnetic cross sections in a Q || [100] domain
transverse phase
S || [010]
longitudinal phase
S || [100]
diffracted beam k’
incident beam k
transverse phase
S || [001]
Cross section with S along [100] or [010] than along [001].

26. S domains within a [100] Q domain
Image (,0,1) reflection.
110 K
125 K
140 K
10 mm S:
longitudinal
mixed
transverse
S || [001] || Q or S || [010] Q
visible spins:
S || [001] || Q
S || [010] Q
Next steps: What’s happening in adjacent domain? Width of S domain wall?

27. Cr Summary
Self organized or artificial domains at small scales are key to macroscopic properties. Imaging is important.
Spin flip transition in Cr begins at domain walls upon cooling.
Future work in Cr:
Control of domain walls
Spin polarization relationships across domain walls?
Separation of bulk and interface effects
Thin films

28. Ferroelectric materials
c=1.01 a O Ba Ti
Example: tetragonal phase of barium titanate (BaTiO3)
6 possible polarizations
Organized naturally or artificially into domains.
Ps=26 C cm-2
What can be learned about polarization switching in ferroelectric materials?
Problems with existing techniques: time resolution, electrodes, quantification.

29. First Step: Strontium Bismuth Tantalate Thin Film Devices
P=18.2 C/cm2
Built-in polarization is along crystalline a-axis.
 Grow films with surface normal not along c-axis. k
q || (1 1 6) k’
100 nm Pt electrode
Vapplied
250 nm SrBi2Ta2O9
SrTiO3 (110) substrate

30. Imaging Domains by Breaking Friedel’s Law
Four types of domains:
(+)
(+)
(-)
(-) c b
(116) a
Intensity of SrBi2Ta2O9 reflection is different for (+) and (-).
contrast of (2,2,12)
“flipping ratio”
(I(+)-I(-))/(I(+)+I(-))
Ta L3 resonance
keV
Incident beam energy (keV)

31. - = Image Polarization Switching
Map SBT (2,2,12) reflection following voltage pulses to top electrode.
20 m - =
after +8V
after -8V
3 m
–8V then:
–4V
+4.4V
+5.2V
+6V
+8V

32. Structural Constrast is Quantitative
Peak Voltage
Films reach electrical breakdown before the ferroelectric polarization is completely switched.

33. Conclusions
New tools for materials where domains and interfaces are important:
Antiferromagnetic domains and the spin flip transition in Cr
New microscopy for ferroelectric materials
Strain relaxation at artificial grain boundaries
Future: time resolved measurements, lower T, applied fields…

34. People Eric Isaacs, Glen Kowach, John Grazul, Lucent
Gabe Aeppli, Yeong-Ah Soh, NEC
Barry Lai, Zhonghou Cai, Eric Dufresne, Advanced Photon Source
Alain Pignolet, Ho-Nyung Lee, Dietrich Hesse, MPI Halle