Supplementary Material
Three-dimensional ferroelectric domain imaging of epitaxial BiFeO3 thin films using angleresolved piezoresponse force microscopy
Moonkyu Park, Seungbum Hong, Jeffrey A. Klug, Michael J. Bedzyk, Orlando Auciello,
Kwangsoo No, Amanda Petford-Long
In-/out-of-plane PFM images in (100) BaTiO3 single crystal
As discussed in the text, we obtained the in-/out-of-plane PFM images while rotating the sample
from 0° to 180° with an interval of 30° between each image. 3 kinds of polarization variant
components ([010], [0-10], [-100]) are observed over the full scan area (70  70 µm2). The inplane PFM images (topography, amplitude and phase) are shown in Figs. S1 and S2. It is clear
that the in-plane phase reversal occurred near the angle of 90° over the full scan area. The ac
modulation voltage applied to Pt coated tip (Nanosensors, EFM tip) was 3 Vrms at 17 kHz.
Amplitude
Phase
250
234
200
100
50
0o
0
198
mV
150
162
126
degree
Topography
90
54
20 μm
30o
60o
Fig. S1. The in-plane PFM images over the full scan area at each angular step from 0° to 60° in (100) BaTiO3
1
single crystal.
Amplitude
Phase
250
234
200
100
50
90o
0
198
mV
150
162
126
degree
Topography
90
54
20 μm
120o
150o
180o
Fig. S2. The in-plane PFM images over the full scan area at each angular step from 90° to 180° in (100) BaTiO3
single crystal.
Fig. S3 shows the out-of-plane PFM images of the same area as that used for in-plane PFM
images. The center region marked with polarization direction into the document, i.e. [00-1]
direction showed a constant contrast while rotating the sample from 0° to 180° as expected.
2
Amplitude
Phase
4
180
V
3
2
1
0o
degree
Topography
162
144
126
20 μm
30o
60o
90o
120o
150o
180o
Fig. S3. The out-of-plane PFM images over the whole scan area of the each angular step from 0o
to 180o in (100) BaTiO3 single crystal.
3
XRD analysis of BiFeO3 thin films
As shown in Fig. S4, Phi scans of the BiFeO3 (BFO), SrRuO3 (SRO) and SrTiO3 (STO) (202)
family of reflections confirm cube-on-cube epitaxy for both the thin film layers. Data were
collected with horizontally and vertically focused Cu Ka1 radiation from an 18 kW rotating
anode source (Rigaku) and a Huber four-circle diffractometer at the J. B. Cohen X-ray
Diffraction Facility at Northwestern University.
Fig. S4. Phi scans of the BFO, SRO, and STO
Fig. S5 shows the out-of-plane XRD for the BFO, SRO, and STO. BFO and SRO films are both
pseudocubic (001) oriented. The source of the peak labeled “?” is currently unknown, although it
is present for all samples (BFO or otherwise). It is likely due to scattering from the sample holder
or otherwise related to the instrument.
4
Fig. S5. Out-of-plane XRD plot for the BFO, SRO, and STO
Out-of-plane PFM data of BiFeO3 thin films
Fig. S6 shows the out-of-plane PFM phase data collected on BiFeO3 thin film of the each angular
step from 0° to 180°. The scanned area was same as the area where we obtained in-plane PFM
data in the text. The out-of-plane PFM phase images for all the angular steps showed bright
contrast, which means the out-of-plane polarization pointed to downward direction.
5
162
0o
degree
198
126
30o
500 nm
60o
90o
120o
150o
y
180o
z
x
Fig. S6. The out-of-plane PFM phase images of BiFeO3 film.
Local distribution of in-plane polarization variants in the BiFeO3 thin films
The areal fractions of the in-plane polarization variants in regions A and B of the Fig. 4h in
manuscript are shown in Fig. S7. The numbers on the x-axis correspond to the polarization
directions shown in the inset of Fig. S7B.
6
B
A
Region A
35
30
Areal fraction (%)
Areal fraction (%)
35
25
20
15
10
30
12 1
11
2
10
3
9
4
25
5
8
20
6
7
15
10
5
5
0
Region B
0
1 2 3 4 5 6 7 8 9 10 11 12
1 2 3 4 5 6 7 8 9 10 11 12
In-plane polarization direction
In-plane polarization direction
Fig. S7. Areal fractions of in-plane polarization variants (A) in region A and (B) in region B.
The projected amount of in-plane polarization variants along [010] direction is shown in Fig. S8
for both regions A and B, which was calculated by multiplying cosine value of angle between
each variant and [010] direction with the areal fraction of each polarization variant. The sums of
the projected amount are 37.9 and -43.9 in arbitrary units for regions A and B, respectively.
B
A
30
25
20
15
10
5
0
1
-5
-10
-15
-20
-25
-30
2
3
Region B
4
5
6
7
8
Projected amount along [010] direction (a.u)
Projected amount along [010] direction (a.u.)
Region A
9 10 11 12
30
25
20
15
10
5
0
1
-5
-10
-15
-20
-25
-30
11
12 1
2
3
10
9
4
5
8
7
2
3
4
5
6
7
8
6
9 10 11 12
Fig. S8. The projected amount of in-plane polarization variants to [010] direction (A) in region A and (B) in region
B.
7
Similarly, the projected amount of in-plane polarization variants along [100] direction is shown
in Fig. S9 for both regions A and B. The sums of the projected amount are -13.4 and 23.5 in
arbitrary units for regions A and B, respectively.
B
A
30
25
20
15
10
5
0
1
-5
-10
-15
-20
-25
-30
2
3
4
5
6
7
8
Projected amount along [100] direction (a.u.)
Projected amount along [100] direction (a.u.)
Region A
9 10 11 12
Region B
30
25
20
15
10
5
0
1
-5
-10
-15
-20
-25
-30
11
12 1
3
9
4
5
8
7
2
3
4
5
6
7
8
2
10
6
9 10 11 12
Fig. S9. The projected amount of in-plane polarization variants to [100] direction (A) in region A and (B) in region
B.
8
The areal fractions of the in-plane polarization variants of submicron area (whole region
in Fig. 4h in the text) are shown in Fig. S10. The numbers on the x-axis correspond to the
polarization directions shown in the inset of Fig. S10.
25
11
12 1
2
3
Areal fraction (%)
10
20
9
4
5
8
7
6
15
10
5
0
1
2
3
4
5
6
7
8
9
10 11 12
In-polariztion vatraints
Fig. S10. Areal fractions of the in-plane polarization variants of the submicron area.
The projected amount of in-plane polarization variants along [010] direction is shown in Fig.
S11A for the submicron area (whole region in Fig. 4h in the text), which was calculated by
multiplying cosine value of angle between each variant and [010] direction with the areal
fraction of each polarization variant. The sum of the projected amount is -16 in arbitrary unit.
Similarly, the projected amount of in-plane polarization variants along [100] direction is shown
in Fig. S11B. The sum of the projected amount is 14 in arbitrary unit.
B
Projected amount along [100] direction (a.u.)
Projected amount along [010] direction (a.u.)
A
40
30
20
10
0
1
2
3
4
5
6
7
8
9 10 11 12
-10
-20
-30
-40
9
40
30
11
12 1
2
3
10
20
9
4
5
8
7
10
0
-10
-20
-30
-40
1
2
3
4
5
6
7
8
6
9 10 11 12
Fig. S11. The projected amount of the in-plane polarization variants to (A) [010] and (B) [100] directions of the
submicron area.
10