Domain-wall conduction in ferroelectric Domain wall ... · Jancar4, Gasper Tavcar5, Maja...

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SUPPLEMENTARY INFORMATIONDOI: 10.1038/NMAT4799

NATURE MATERIALS | www.nature.com/naturematerials 11

SUPPLEMENTARY INFORMATION

Domain wall conduction in ferroelectric BiFeO3 controlled

by accumulation of charged defects

Tadej Rojac1,*, Andreja Bencan1, Goran Drazic2, Naonori Sakamoto3, Hana Ursic1, Bostjan

Jancar4, Gasper Tavcar5, Maja Makarovic1,6, Julian Walker1, Barbara Malic1 and Dragan

Damjanovic7

1Electronic Ceramics Department, Jozef Stefan Institute, 1000 Ljubljana, Slovenia

2Laboratory for Materials Chemistry, National Institute of Chemistry, 1000 Ljubljana,

Slovenia

3Department of Electronics and Materials Science, Shizuoka University, 3-5-1 Naka-ku,

Hamamatsu, Japan

4Advanced Materials Department, Jozef Stefan Institute, 1000 Ljubljana, Slovenia

5Department of Inorganic Chemistry and Technology, Jozef Stefan Institute, 1000 Ljubljana,

Slovenia

6Jozef Stefan International Postgraduate School, 1000 Ljubljana, Slovenia

7Ceramics Laboratory, Swiss Federal Institute of Technology – EPFL, 1015 Lausanne,

Switzerland

*e-mail: [email protected]

Domain-wall conduction in ferroelectric BiFeO3 controlled by accumulation of charged defects

http://dx.doi.org/10.1038/nmat4799




2

S1. Lattice strain and accumulation of charged defects at 180° domain wall

(DW)

Figure S1. Evidence of lattice strain and charged defects (bismuth vacancies and Fe4+) at

180° DW in polycrystalline BiFeO3.

(a) High-angle annular dark-field (HAADF) scanning transmission electron microscopy

(STEM) image in [010] zone axis (in pseudocubic notation) where insets (full-line boxes)

show Fe-displacement directions in the adjacent domains (arrows) and the red band highlights

the DW region. Enlarged part of the DW region (in blue box) shows Bi columns splitting

(marked with red arrows) related to a DW step along the sample thickness (similarly as

reported in Lubk et al.S1). (b) Normalized distribution map of Bi-column intensities and (c)

1.00

0.85

Cou

nts

(a.u

.)

E (eV)500 550 600 650 700 750 800500 550 600 650 700 750 800

on DW

off DW

ΔE=179.50 eV

ΔE=178.25 eV

2 nm

b

c dFe L3

Fe L2

O K

DW region

2 nm

a





3

low-angle annular dark-field (LAADF) STEM image of the area marked with a dashed–red

box in panel (a). (d) Experimental electron-energy loss spectra (EELS) acquired on and off

the DW region with indicated energy onset difference (ΔE) between O-K and Fe-L3 edges.

The higher E values determined on the DW (relative to the values determined off the DW)

suggest the presence of Fe4+ in the DW region. The lower Bi-column intensities along the DW

(yellow squares in panel b) suggest accumulation of bismuth vacancies in the DW region.

HAADF and EELS analyses thus independently confirm the presence of Bi vacancies and

preferred 4+ oxidation state of Fe at the 180° DW. The contrast in LAADF STEM image

indicates a gradient in lattice strain across the 180° DW region.





4

S2. Lattice strain and accumulation of charged defects at 71° DW

Figure S2. Evidence of lattice strain and charged defects (bismuth vacancies and Fe4+) at

71° DW in polycrystalline BiFeO3.

(a) HAADF-STEM image in [010] zone axis where insets (full-line boxes) show Fe-

displacement directions in the adjacent domains (arrows) and the red band highlights the DW

region. (b) Normalized distribution map of Bi-column intensities and (c) LAADF STEM

image of the area marked with a dashed–red box in panel (a). (d) Experimental EELS spectra

acquired on and off the DW region with indicated ΔE. Similarly as explained in

Supplementary Section S1 for the 180° DW, the higher E values determined on the 71° DW

a b1.00

0.81

2 nm

DW region

2 nm

c d

500 600 700 800

Cou

nts

(a.u

.)

E (eV)

on DW

off DW

Fe L3

Fe L2

O K

ΔE=179.75 eV

ΔE=178.00 eV





5

suggest the presence of Fe4+ in the DW region, while the lower Bi-column intensities along

the DW (yellow squares in panel b) suggest the accumulation of bismuth vacancies in the DW

region. The contrast in LAADF STEM image indicates a gradient in lattice strain across the

wall. The results on 71° DW shown here are fully consistent with the 180° DW

(Supplementary Section S1) and 109° DW (Fig. 1, 2 in the paper).





6

S3. Experimental details of HAADF, annular bright-field (ABF), LAADF

imaging, EELS analysis and quantification

HAADF, ABF, LAADF

During analysis of the samples, HAADF and ABF detectors were used simultaneously at 68–

180 and 10–16 mrad collection semi angles, respectively. LAADF images were acquired with

a secondary ADF detector with collection semi angle between 40 and 120 mrad. To minimize

the specimen drift, images were taken several hours after the insertion of the sample in the

microscope and at least 20 minutes after the last sample positioning to minimize the

goniometer drift. HAADF images used for Fe displacement measurements were taken in

[010] zone axis and the scan rotation was set so that a and c crystal directions were parallel to

the horizontal and vertical sides of the image, respectively. Coordinates of atomic column

intensity maxima were determined using 2D Gaussian fit. The error of the Fe-displacement

determination was estimated from the HAADF images of cubic SrTiO3 single crystal standard

and was found to be 10 pm, defined as one standard deviation (σ) of measurements.

Normalized Bi-column intensities were measured using the approach by LeBeau &

StemmerS2 where average intensity of the background and HAADF STEM detector signal

were measured from the image of HAADF detector (without sample) at non-saturating

settings of brightness and contrast. The detector background intensity was subtracted from the

intensity of each pixel in experimental images. The resulting intensity was divided by

background-corrected average intensity signal of the detector. This normalized intensity

corresponds to the relative scattering of each atom column.





7

Bi intensities were extracted form HAADF images as intensity peak integral, integrated

within one sigma by approximating a Gaussian-type peak. Due to the use of this integral

method, the splitting of the Bi columns observed at 180° DWs (see inset of Fig. S1a) has a

minor influence on the measured Bi intensities (within the experimental error).

To correlate the normalized intensities of individual Bi-atom columns with the concentration

of Bi vacancies inside each column, we compared the experimental intensities with calculated

intensities. Calculations were performed using quantitative STEM (QSTEM) codeS3 with a

multi-slice method and frozen phonon approximation. To include the influence of thermal

diffuse scattering (TDS), 30 repetitions of calculations per one image were used. We created

an R3c BiFeO3 structural model (ICSD #97591) consisting of 9 x 9 x 9 unit cells (Fig. S3_1a).

In four Bi columns positioned in the middle of the structure (red dashed box) we introduced

22, 33 or 55 at% Bi vacancies. Using this model we then simulated the HAADF images and

extracted the corresponding Bi-column intensity ratios between columns with Bi vacancies

and those with fully filled Bi positions for thicknesses up to 80 nm.





8

Figure S3_1. (a) Structural model of R3c BiFeO3 with 9 x 9 x 9 unit cells and (b) example

of simulated HAADF image where 33 at% of Bi vacancies were introduced in four

middle Bi-columns (see dashed red box in panel a). The corresponding Bi-column

intensity profile is added. Calculations were done for sample thickness of 40 nm.

In Fig. S3_2 we display the intensity ratio between columns with and without Bi vacancies

(VBi/Bi) as a function of Bi-vacancy concentration calculated for several sample thicknesses.

By comparing the calculated intensity ratios with the experimental ratio (~0.8), it was

concluded that ~30% of Bi vacancies are present in the DW regions (see blue lines in Fig.

S3_2).





9

Figure S3_2: Calculated Bi-column intensity ratio between columns containing Bi

vacancies and those with fully filled Bi positions (VBi/Bi) as a function of Bi-vacancy

(VBi) concentration (22, 33 and 55 at%) for different sample thicknesses. As indicated by

the blue lines, the intensity ratio 0.8 corresponds to ~30 at% of Bi vacancies.

EELS

EELS spectra were collected in STEM mode where we scanned areas of ~15 x 1 unit cells on

the DW and, as a reference, few nm away from the DW. 24 mrad convergence and 60 mrad

collection semi angles were used. Low and core loss were acquired simultaneously using

Dual-EELS option of the system. Sample thickness where EELS spectra were collected at

DWs was between 30 and 50 nm.

Oxidation state of iron can be determined using two main approachesS4,S5. The first approach

is based on K L3/L2 intensity ratios using arcus tangensS6 or second derivativeS7 methods for





10

extracting the intensities. The second approach is based on the difference between the onset

energy of O K and Fe L3 edgesS4.

To determine the iron oxidation state locally in the BiFeO3 samples we used the energy onset

difference between O-K and Fe-L3 edges (ΔE). This is because the approach using the Fe

L3/L2 intensity ratio is not suitable for determination of the Fe4+ oxidation state as reported by

Tan et al.S4. Calibration curves (ΔE vs Fe oxidation state) were derived from EELS spectra of

standard materials as shown in Table S3. Each experimental ΔE value shown in the table is

the average of 5–10 measurements. The energy onset was determined at 10 % of O-K and Fe-

L3 edge height. The E values determined here on the standards are consistent with those

reported in the literatureS4 for oxides containing Fe2+, Fe3+ and Fe4+.





11

Table S3: Experimental ΔE values with standard deviation () and EELS spectra of

compounds containing Fe in different oxidation states (OS) used as standards for EELS

analysis.

Compound Fe OS ΔE (eV) +/– σ EELS spectrum

FeTiO3I 2+ 176.7 +/– 0.3

Co0.6Fe2.4O4 II 2.7+ 177.5 +/– 0.4

Fe2O3III 3+ 178.3 +/– 0.2

BaFeO3IV 4+ 179.9 +/– 0.4

I – Iron (II) titanium oxide, 99.8% , Alfa Aesar, product number 1317.

II – Synthesized according to S. Gyergyek et al. S8.

III - Iron (III) oxide, 99.945% , Alfa Aesar, product number 14680.

IV – Synthesized by solid-state reaction similar as reported in ref.S9 but using 1 MPa of pure oxygen in all stages

of the reaction.





12

S4. Point-defect model for BiFeO3

In this section we show that the identification of Fe4+ and Bi vacancies at the DWs (Fig. 2 in

the paper and supplementary sections 1 and 2) and the experimental results related to the

control of DW conductivity with annealing atmosphere (Fig. 3 in the paper) are consistent

with the thermodynamic point-defect model recently proposed for BiFeO3S10–S12. This model

assumes two point-defect equilibria; the first describes the volatility of Bi2O3 at elevated

temperatures (equation 1), while the second describes the oxidation/reduction (redox)

reactions (equation 2 and 3), which are associated with the ambient O2 and thus depend on the

partial pressure of O2 during annealingS12:

2𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝑋𝑋 + 3𝑂𝑂𝑂𝑂𝑋𝑋 2𝑉𝑉𝐵𝐵𝐵𝐵′′′ + 3𝑉𝑉𝑂𝑂 + 2𝐵𝐵𝐵𝐵(𝑔𝑔) + 32𝑂𝑂2(𝑔𝑔) (1)

2𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝑋𝑋 + 𝑉𝑉𝑂𝑂 + 12 𝑂𝑂2(𝑔𝑔) 2𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 + 𝑂𝑂𝑂𝑂

𝑋𝑋 (2)

2𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝑋𝑋 + 𝑂𝑂𝑂𝑂𝑋𝑋 2𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹′ + 𝑉𝑉𝑂𝑂 + 1

2𝑂𝑂2(𝑔𝑔) (3)

𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝑋𝑋 , 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝑋𝑋 and 𝑂𝑂𝑂𝑂𝑋𝑋 correspond to regular lattice sites occupied by Bi3+, Fe3+ and O2–; 𝐵𝐵𝐵𝐵(𝑔𝑔)

and 𝑂𝑂2(𝑔𝑔) correspond, respectively, to gaseous (g) Bi and O2; 𝑉𝑉𝐵𝐵𝐵𝐵′′′ , 𝑉𝑉𝑂𝑂 , 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹′ and 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹

correspond, respectively, to bismuth vacancies, oxygen vacancies (both are considered fully

charged), Fe2+ and Fe4+ cations. The equations are presented in Kröger-Vink notationS13. The

point-defect model has been validated by measurements of the bulk electrical conductivity of

BiFeO3-related materials in atmospheres with different partial pressure of O2S10–S12,S14 .

Studies on Ca-doped BiFeO3S14 showed a reduction of the bulk conductivity of at least four

orders of magnitude by sintering and cooling the samples from 800°C in N2 atmosphere,





13

suggesting a suppression of the p-type electronic conduction, which was regained by

annealing the samples in O2. According to the model (equations 1–3), the p-type conduction

character suggest the presence of Fe4+ (𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 ) point defects, which are responsible for the p-

type bulk conductivity (through electron-hole hopping between Fe4+ (𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 ) and Fe3+ (𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝑋𝑋 )

sites) and are compensated by 𝑉𝑉𝐵𝐵𝐵𝐵′′′. For this case, the point-defect equilibrium can be

expressed by summing up equations 1 and 2:

𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝑋𝑋 + 3𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝑋𝑋 𝑉𝑉𝐵𝐵𝐵𝐵′′′ + 3𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 + 𝐵𝐵𝐵𝐵(𝑔𝑔) (4)

The two defects (Fe4+ and Bi vacancies) that we identified at the DWs are thus fully

consistent with the proposed defect model (equation 4).

Results shown in Fig. 3 in the paper reveal a reduction of DW conductivity when the sample

is annealed at 700°C in N2. This is consistent with the reduction in the concentration of Fe4+ at

DWs and can be understood with the equilibrium reaction, expressed by equation 2, forced

toward the left-hand side (𝑂𝑂2(𝑔𝑔) is expelled from the sample during annealing in N2 and thus

Fe4+ is reduced to Fe3+). As also shown in the paper, the DW conductivity can be re-gained by

annealing the sample in O2 atmosphere, thus by forcing the equilibrium reaction (equation 2)

toward the right-hand side (sample regains O2 by filling 𝑉𝑉𝑂𝑂 and produces Fe4+ cations, which

are responsible for the DW conductivity). We finally note that the transition to n-type

conductivity (equation 3 forced toward right-hand side where 𝑂𝑂2(𝑔𝑔) is expelled from the

sample, producing Fe2+) has been reported in the literature during annealing the samples in

reducing Ar/H2 (95/5) atmosphere (see, for example, Morozov et al.S10).





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S5. Hopping conduction in BiFeO3

Figure S5. Macroscopic (bulk) dielectric response of polycrystalline BiFeO3.

(a) Real (𝜀𝜀′) and imaginary (𝜀𝜀′′) components of relative dielectric permittivity and (b) real

part of complex electrical conductivity (𝜎𝜎′) as a function of driving-field frequency. The

sample was driven with 0.03 kV/mm of field amplitude. A setup based on a charge amplifier

and a lock-in, as described in ref.S15, was used for measurements in the frequency range 10–2–

103 Hz, while an LCR meter (HP 4284A) was used for measurements in the frequency range

103–106 Hz. For the analysis of the conductivity, we adopt the formalism described in

refsS16,S17 according to which the complex AC conductivity (𝜎𝜎) can be expressed in terms of

the real (𝜎𝜎′) and imaginary (𝜎𝜎′′) components as 𝜎𝜎(𝜔𝜔) = 𝜎𝜎′ + 𝑖𝑖𝜎𝜎′′ = 𝜔𝜔𝜀𝜀0𝜀𝜀′′(𝜔𝜔) + 𝑖𝑖𝜔𝜔𝜀𝜀0𝜀𝜀′(𝜔𝜔)

where 𝜔𝜔 is angular frequency and 𝜀𝜀0 is the permittivity of vacuum. The real component of the

conductivity (𝜎𝜎′ ) can be further expressed as a sum of the frequency independent DC

conductivity (𝜎𝜎0) and frequency dependent dielectric loss (𝜀𝜀𝑑𝑑′′), that is, 𝜎𝜎′ = 𝜎𝜎0 + 𝜔𝜔𝜀𝜀0𝜀𝜀𝑑𝑑′′(𝜔𝜔).

The significant increase in the permittivity of BiFeO3 below 0.1 Hz (panel a) where 𝜀𝜀′′

diverges, reaching values as large as 1.2106 (at 0.04 Hz), suggest that the dielectric response

of BiFeO3 at low frequencies is dominated by electrical conduction. According to JonscherS16,

the low-frequency dispersion of 𝜀𝜀′, which accompanies the strong dispersion of 𝜀𝜀′′, indicates

that the conduction processes not only dissipate energy but also contribute to the dielectric

polarization of the material, which is consistent with hopping conductivityS17. In this

0

400000

800000

1200000

1600000

2000000

0

100

200

300

400

500

600

700

800

0.001 0.1 10 1000 100000

e''(/)

e'(/)

Frequency (Hz)

1E-07

1E-06

1E-05

1E-04

0.001 0.1 10 1000 100000

' (o

hm-1

m-1

)

Frequency (Hz)

a b





15

mechanism, charge carriers contribute to both dielectric polarization by short-range hopping

over localized sites and to conductivity by overcoming higher potential barriers and thus by

hopping over longer distances in the materialS16. In support to the hopping conductivity is also

the frequency behaviour of 𝜎𝜎′ (panel b). 𝜎𝜎′ is frequency independent in the range from 0.004

Hz to 10 Hz and levels off at 310–7 ohm–1m–1, which corresponds to the specific DC

conductivity (𝜎𝜎0 ) of BiFeO3. At higher frequencies, from 10 Hz to 106 Hz, 𝜎𝜎′ shows

frequency dependence. Such 𝜎𝜎′-versus-frequency behaviour has been observed in a number of

disordered materials, such as amorphous semiconductors and conductive glasses and

polymers, and has been rationalized in terms of the hopping (AC) conductivityS17,S18. The

macroscopic dielectric behavior of BiFeO3 is thus consistent with hopping conductivity and

supports the DW conduction model associated with the electron-hole (Fe4+-related) hopping

(see paper for details). We also note that the polaron hopping, which is strongly linked to the

oxidation state of Fe, is common to a number of Fe-based perovskites other than

BiFeO3S10,S12,S19, such as LaFeO3

S20, SrFeOxS21 and LnFeO3 (Ln=La, Pr, Nd, Sm)S22.





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S6. c-AFM analysis of DW conductivity in BiFeO3

Reduction of DW conductivity by annealing BiFeO3 in nitrogen atmosphere

Figure S6. Reduction of DW conductivity after annealing polycrystalline BiFeO3 in

nitrogen atmosphere evidenced by analyzing the same sample area before and after the

annealing.

Out-of-plane piezo-response force microscopy (PFM) amplitude and phase images, and c-

AFM images of the same sample region in air-sintered and N2-annealed BiFeO3 sample. The

c-AFM images were acquired by aplying to the tip +17 V of DC bias. For these analyses, the

sample was prepared in the following way. A polished, air-sintered sample was first analyzed

by PFM and c-AFM (see methods for details of sample preparation and analysis). PFM was

used to identify domains and DWs in a number of selected regions, while c-AFM was used to

probe the local current signal at the DWs. In the subsequent step, the sample was annealed at

500°C in flowing nitrogen with zero holding time and 2 K/min of heating/cooling rate, after

which the same regions were again analyzed by PFM and c-AFM. By comparing the PFM

images of the same sample regions before and after annealing in N2, we noticed that in most

of the analyzed regions the domain structure changed. An example of such a change of the

domain structure induced by N2-annealing can be seen by comparing the circled areas on

PFM images. In some regions, however, we observed no or minor changes in the domain

air-sintered

N2-annealed

PFM amplitude PFM phase c-AFM

5 mm





17

structure after the annealing. These regions are marked with green arrows on the PFM images.

A comparison of the c-AFM signal in these regions shows that the enhanced electrical current

detected at DWs in the air-sintered sample (white arrows on c-AFM image) is no longer

observed after the annealing in N2. This result suggests a reduction in the DW conductivity by

annealing BiFeO3 in N2, which is consistent with the proposed p-type conductive behavior of

DWs (see paper for detailed explanations).

Statistical analysis of local electrical current at DWs

Results presented in Fig 3 in the paper reveal a reduction in the electrical current signal at

DWs after the air-sintered BiFeO3 sample was post-annealed in N2 atmosphere. The local

current at DWs was re-established after re-annealing the N2-treated sample in O2. To verify

these results, we performed a rigorous statistical analysis of the local current at DWs. In each

of the three samples (air-sintered, N2- and O2-annealed), we analyzed several regions with c-

AFM, probing a total of 30–60 DWs per sample. From the acquired c-AFM images, we

determined the fraction of those DWs that were accompanied by the enhanced current signal.

For the air-sintered, N2- and O2-annealed BiFeO3, these fractions were 84 %, 3 % and 88 %,

respectively, and thus strongly support our conclusion on the key role of Fe4+ in the DW

conduction.





18

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