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