probing magnetism and ferroelectricity with x-ray microdiffraction paul evans, university of...
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Probing magnetism and ferroelectricity with x-ray
microdiffraction
Paul Evans,
University of Wisconsinevans@engr.wisc.edu
October 9, 2002
OutlineI. Magnetic and Polarization Domains in
Solids
II. Hard X-ray Microdiffraction
III. Antiferromagnetic domains and the “spin-flip” transition in chromium
IV. Polarization reversal in strontium bismuth tantalate thin films
V. Conclusions
Example 1: Polarization domains in ferroelectrics
• TEM study of BaTiO3
A. Krishnan, M. E. Bisher, and M. M. J. Treacy, Mat. Res. Soc. Symp. Proc. 541 475 (1998).
towards bulk
Example 2: Magnetic domain wall resistance in Fe
2 m
Resistivity and magnetoresistance depend on domain configuration in micron-scale Fe wires.
Ruediger et al., Phys. Rev. Lett. 80 5639 (1998).
H transverse
H longitudinal
H longitudinal
H transverse
X-ray microdiffraction
Focusing X-rays Using Zone Plates
• 6 to 30 keV
• 1010 ph/s/0.01%BW
• Flux Density Gain - 105
• Minimum spot - 0.15 x 0.15 µm2
x
L~50 m
zone plate D~100 m
f~10 cm
order sorting aperture
Source demagnified by L/f500.
350 m
Hard X-ray Machine: Advanced Photon Source
Chicago 30 miles
Murray Hill 700 miles
Argonne Natl. Lab.
X-ray Microprobe Applications
Glasses for fibers, amplifiers: Dopant Distributions (with R. Windeler, Lucent/OFS, and J. Maser APS)
5 mYb x-rayfluorescencefiber amplifier core
0.1 Å-1
2
(de
g.)
in
2
scan
s
distance from g. b. (m)
0 1 2 3 447.2
47.3
47.4
47.5
47.6
Strain relaxation in LaSrMnO film on a bicrystal substrate
Y.-A. Soh, et al., submitted.
Strain at an artificial grain boundary
Spin density wave domains in Cr
P. G. Evans, et al., Science 295 1042 (2002).
Magnetic x-ray microscopy
X-ray Microprobe Applications
100 m
periodically poled LiNbO3 polarization domains
10 m
Domains in ferroelectric materials
3 m
switching in a SrBi2Ta2O9 thin film capacitor
Spin density wave domains in chromium
• Domains are responsible for macroscopically observable magnetic, mechanical, electrical phenomena.
• Previous domain imaging experiments are at the 1 mm scale.
Cr is a spin density wave (SDW) antiferromagnet.
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.
Cr unit cell
S || [100]
Q || [001]
•SDW leads to strain wave and charge density wave (CDW).
•Spins are transverse T=123 to 311 K, longitudinal for T<123 K.
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
K KqK
qEE
1)(
where EK+q and EK are pairs of filled and empty states differing in wavevector by q.
QSDW
Band structure of Cr: Fermi surfaces nest with Q=(0,0,1-) , incommensurate with lattice.
Domain effects in chromium (?)Magnetoresistance of a Cr thin film is enhanced below spin flip transition.
Mattson et al. J. Magn. Magn. Mater. 109 179 (1992).
nHHTTHTH )/)((),0(),( 0
Magnetoresistance reaches 50% at 4K for H=5 T.
Force Radiation
-eE electric dipole “Thomson scattering”
-eEmagnetic quadrupole
electric dipole)( H
H magnetic dipole
After F. de Bergevin and M. Brunel, Acta Cryst. A 37 314 (1981).
EE
EH
H E
H H
-e
-e
-e
-e
(Non-Resonant) Magnetic X-ray Scattering: Classical Picture
Cr in reciprocal space
CDWnear (0 0 2)
SDWnear (0 0 1)
L
K
Magnetic scattering appears near forbidden lattice reflections.
Also: Strain wave (CDW) reflections near allowed lattice reflections.
Form images using either type of reflection.
H
Sample Orientation
Magnetic cross sections ( polarizations.
2)ˆˆ( 'kkS ) are equal for transverse
incident beam k
diffracted beam k’
ST
SL
ST
Non-resonant magnetic x-ray diffraction from Cr
Most important term of cross section scales as:
2)ˆˆ( 'kkS
Polar plot of cross section as a function of spin direction for a Q || (001) domain in our geometry.
k’-k || Cr (0 0 1-)
APS Station 2ID-D
All three Q domains are present
Room temperature laboratory diffractometer scans with large mm-scale beam.
h scan near (2 0 0)
k scan near (0 2 0)
l scan near (0 0 2)0.4
0.6
0.8
1
1.2
0.04 0.06 0.08 0.1
inte
nsity
(a.u
.)
(2+,0,0)
(0,2+,0)
(0,0,2+)
Domain populationsH : K : L4.65 : 1.35 : 1 Visit one CDW
reflection from each family.
B C D W 1 0 0 m
0
4
8
0 . 9 5 0 . 9 5 3 0 . 9 5 6L
C
1
2
SD
W
inte
nsity
co
unts
s-1
A S D W 1 0 0 m
2 1
*
SDW Domains at 130 KSDW magnetic reflection
CDWcharged reflection
incident beam h=5.8 keV
incident beam h=11.6 keV
Spin-flip transitionTransverse SDW phase Longitudinal SDW phase
TSF=123 Kin bulk Cr
Image SDW reflection as a function of temperature.
Magnetic reflection disappears!
10 m 2
4 3
1
10 m 10 m 10 m
10 m 10 m 10 m
140 K 130 K 125 K 120 K
110 K 119 K 115 K 1
4
Q || (001) and SQ
Q (001) or S||Q
Repeat with charged CDW reflectionSDW Magnetic reflection CDW Charged reflection
T=130 K T=130 K
T=110 K T=110 K
Spin flip transition begins at Q domain edges
Nominally first order transition is broadened by several degrees, even at micron scale.
8.6
8.7
0
5
10
110 120 130 140
T (K)
2
3
4
1
mea
n in
tens
ity
(cou
nts
s-1
)
mag
net
iza
tion
(em
u/cm
3 )
H=2 kG
H=0
T (K)
10 m 2
4 3
1
10 m 10 m 10 m
10 m 10 m 10 m
140 K 130 K 125 K 120 K
110 K 119 K 115 K 1
4
Q || (001) and SQ
Q (001) or S||Q
Sources of broadening
QS
Q
S
QS
Q
S
1. Magnetic interactions across domain boundary.
2. Fermi surface effects. Simultaneous Fermi surface nesting at multiple Q directions is not allowed.
3. Strain, impurities, defects.
Magnetic effects at ferromagnet/antiferromagnet interfaces are well described in comparison.
Not much known (yet) about antiferromagnetic domain walls.
Challenges: length and energy scales, several types of domain walls.
vs.
Learning more about domain walls
CDWnear (0 0 2)
SDWnear (0 0 1)
L
K
H
red Q || [100] green Q || [010] blue Q || [001]
1) So far we’ve looked at Q || [001]. What happens in neighboring Q domains?
2) Two spin polarizations within transverse phase.
transverse phase
S || [010]
transverse phase
S || [001]
longitudinal phase
S || [100]
Magnetic cross sections in a Q || [100] domain
incident beam k
diffracted beam k’
Cross section with S along [100] or [010] than along [001].
S domains within a [100] Q domain
Image (,0,1) reflection.
mixedlongitudinal transverse
10 m
110 K 125 K 140 K
S || [001] || Q S || [001] || Q or S || [010] Q
S || [010] Q
S:
visible spins:
Next steps: What’s happening in adjacent domain? Width of S domain wall?
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
a=3.995 Å
c=1.01 aO
Ba
Ti
Ferroelectric materials
• 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.
First Step: Strontium Bismuth Tantalate Thin Film DevicesP=18.2 C/cm2
q || (1 1 6)
SrTiO3 (110) substrate
250 nm SrBi2Ta2O9
100 nm Pt electrode
k k’
Vapplied
Built-in polarization is along crystalline a-axis. Grow films with surface normal not along c-axis.
9.8 9.85 9.9 9.95
-0.1
0.1
0.2
0.3
0.4
0.5
0.6
Imaging Domains by Breaking Friedel’s Law
Four types of domains:
(+) (+) (-) (-)
Incident beam energy (keV)
contrast of (2,2,12)“flipping ratio”(I(+)-I(-))/(I(+)+I(-))Ta L3 resonance
9.8835 keV
Intensity of SrBi2Ta2O9 reflection is different for (+) and (-).
c
b
a(116)
3 m
20 m
Image Polarization Switching
after +8V after -8V
–4V +4.4V +5.2V +6V +8V
- =
–8V then:
Map SBT (2,2,12) reflection following voltage pulses to top electrode.
Structural Constrast is Quantitative
(a) 4 V
0
0.02
0.04
0.06
0.08
0.1
0.12
0 100 200 300
mea
n flippin
g r
atio
peak applied electric field
(kV cm-1)
0 7.5
Peak Voltage
Films reach electrical breakdown before the ferroelectric polarization is completely switched.
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…
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
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