epitaxial thin films

(1)

Ultra-low coercive field of improper ferroelectric Ca

₃

Ti

₂

O

₇

epitaxial thin films

X.Li,^1,a)L.Yang,²C. F.Li,¹M. F.Liu,¹Z.Fan,²Y. L.Xie,¹C. L.Lu,^3,a)L.Lin,¹Z. B.Yan,¹ Z.Zhang,⁴J. Y.Dai,⁴J.-M.Liu,^1,2and S. W.Cheong⁵

1Laboratory of Solid State Microstructures and Innovative Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China

2Institute for Advanced Materials, South China Normal University, Guangzhou 510006, China

3School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China

4Department of Applied Physics, Hong Kong Polytechnic University, Hong Kong, China

5Rutgers Center for Emergent Materials and Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA

(Received 20 September 2016; accepted 8 December 2016; published online 23 January 2017) Hybrid improper ferroelectrics have their electric polarization generated by two or more combined non-ferroelectric structural distortions, such as the rotation and tilting of Ti-O octahedral in the Ca₃Ti₂O₇(CTO) family. In this work, we prepare the high quality (010)-oriented CTO thin films on (110) SrTiO₃ (STO) substrates by pulsed laser deposition. The good epitaxial growth of the CTO thin films on the substrates with the interfacial epitaxial relationship of [001]CTO//[001]STO and [100]CTO//[-110]STO is revealed. The in-plane ferroelectric hysteresis unveils an ultralow coercive field of5 kV/cm even at low temperature, nearly two orders of magnitude lower than that of bulk CTO single crystals. The huge difference between the epitaxial thin films and bulk crystals is most likely due to the lattice imperfections in the thin films rather than substrate induced lattice strains, suggesting high sensitivity of the ferroelectric properties to lattice defects.

Published by AIP Publishing.[http://dx.doi.org/10.1063/1.4974217]

Ferroelectrics and the underlying mechanisms have undergone a rapid revival in recent years due to the discov- ery of a series of emergent phenomena on one hand and promising applications in the next generation of data sto- rages and spintronics on the other hand.^1,2 Two parallel roadmaps have been proceeding. One roadmap goes ahead by down-scaling ferroelectrics into nanostructures. This in turn stimulates interest in the dynamics of domain walls and new polar structures.³ The other roadmap, much broader and more attractive, is to search for novel ferroelectrics and multiferroics as an extended discipline of correlated electronic physics and materials science. The magnetoelectric (ME) coupling associated with multiferroicity was once placed high expectation to functionalize the electro-control of magnetism with ultralow power consumption.^4,5 While the second roadmap has made substantial progress, some major issues remain. In 2011, Fennie and colleagues predicted hybrid improper ferroelectricity in 327 Ruddlesden- Popper layered A₃B₂O₇ compounds⁶ and the controls of both ferromagnetism and ferroelectricity in the magnetic compound Ca₃Mn₂O₇.^7–10So far, such a prediction has not yet been confirmed experimentally, and nevertheless, the 327-type ferroic oxides have again come to researchers’

vision.¹¹

In fact, some hybrid improper ferroelectrics as a subclass of geometric ferroelectrics have been known.¹² The electric polarization P is generated via a collective distortion of non-ferroelectric structural order parameters.^6,9,13 Ca₃Ti₂O₇ (CTO) and similar A₃B₂O₇titanates belong to this subclass.

The CTO lattice, as shown in Fig. 1(a), exhibits the A21am space group and orthorhombic structure at room temperature

with lattice constants a¼5.423 A˚ , b¼5.417 A˚ , and c¼19.417 A˚ .¹⁴ The collective distortion of TiO₆ octahedral rotation around thec-axis and tilting around thea-axis allows the net displacement of the A-site ions along theadirection, leading to the net polarization, as shown in Fig.1(b). To get a straightforward view of the epitaxy with some substrates, a pseudo-tetragonal lattice is also labeled as [100]_ptand [010]_pt, as shown in Fig. 1(c), which have a 45 rotation relative to the orthorhombica- andb-axes of CTO, respectively.

The ferroelectricity in CTO-based systems has not been confirmed until recently, probably due to either the large coercive field or lattice imperfections.⁶A prominent progress is the observations of well-defined ferroelectric hysteresis

FIG. 1. (a) Crystal structure of CTO with theA21amspace group. (b) The proposed ionic displacements for ferroelectric polarization of CTO, repre- sented by the arrows pointing from ions’ initial positions (green dashed circles) for each Ca^2þlayer. (c) The relationship between the axes ofA21am and its pseudo-tetragonal unit cell. The black square line represents the CTO pseudo-tetragonal unit cell with arrows pointing out the directions. Both c-axes (or [001] direction) are perpendicular to the screen.

a)Electronic addresses: [email protected] and [email protected]

0003-6951/2017/110(4)/042901/5/$30.00 110, 042901-1 Published by AIP Publishing.

APPLIED PHYSICS LETTERS110, 042901 (2017)

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and rich domain structure in CTO single crystals.^15,16 Ferroelectricity and weak ferromagnetism were found in (Ca_ySr_1–y)_1.15Tb_1.85Fe₂O₇-CTO¹⁷ where the strong ME control and ferroelectric hysteresis remain to be confirmed.

Even though the coercive field of (Ca,Sr)₃Ti₂O₇is as high as 130 kV/cm, the first-principles calculations predicted that coercive field is even much higher. Such a high coercive field hinders substantially potential applications of these novel ferroelectrics. In addition, the collective distortion rather than a single distortion induced polarization would make the ferroelectricity sensitive to intrinsic/external per- turbations such as lattice strain and imperfections.¹⁸A recent theoretical prediction revealed the polar-nonpolar transition driven by a relatively small lattice strain.¹⁹

Our main motivation is to explore the ferroelectricity of the CTO thin films and its possible difference from the bulk single crystals. On one hand, preparation of high quality films is the pre-requisite for practical applications.^20–22 On the other hand, checking the CTO thin films may provide additional knowledge on the microstructure-property relationship for hybrid ferroelectrics, in particular, on how to reduce the reported high coercive field for polarization switching. It comes to us that the best lattice match can be between the CTO (010) plane and the cubic SrTiO₃(STO) (110) plane (a¼3.905 A˚ ), with a slight in-plane tension strain and weak out-of-plane contraction. The proposed epitaxy is shown in Fig.2(a) where five unit periods of STO along the [001]-axis match well with one unit period on CTO along the c-axis, leading to epitaxial relationships of [001]CTO//[001]STO and [100]CTO//[110]STO. In addition, two issues should be addressed. First, given thea-axis polarization, a slight in-plane tension strain may anyway affect the ferroelectricity including the polarization and coercive field. Second, for thin films, lattice imperfections exist inevitably allowing opportunity to check the sensitivity of ferroelectricity, e.g., the coercive fieldEc, to these defects.

A brief description of the CTO film deposition on (110) STO substrates using pulsed laser deposition and property characterizations is presented in thesupplementary material.

For typical cases, the thin films are60 nm in thickness. For electric characterization, the gold inter-digital surface electrodes were sputtered via the standard photolithography and lift-off procedures.^23,24The room-temperature X-ray diffraction (XRD)h–2hspectrum of one as-prepared sample is plotted in Fig. 2(b)where only the CTO (010) and STO (110) reflections can be detected. The full-widths at the half-height (FWHH) of the CTO peaks are comparable with those of the STO peaks. For the epitaxy identification, one performed the XRD/-scan on the CTO (115) and STO (111) reflections, as shown in Figs. 2(c) and 2(d). The four sharp CTO (115) reflections with the inter-peak separations of 70.6 and 109.4, respectively, are probed, consistent with the calculated values of 71.2 and 108.8. The inter-angle of 70.6 between two (115) peaks is symmetrically divided by the STO (111) peak, confirming that the in-plane lattice of CTO thin film does match epitaxially with the substrate via the [100]CTO//[-110]STO and [001]CTO//[001]STO alignment.

We discuss the lattice distortion of the thin films. The orthorhombic unit of CTO is grown on a (3.905冑2 A˚ ) (3.9055 A˚ ) rectangular STO lattice (Fig. 2(a)). The

FIG. 2. (a) The proposed in-plane epitaxial relationships across the CTO and STO interface: [001]CTO//[001]STO and [100]CTO//[-110]STO. (b) X-rayh–2hspectrum for the CTO film grown on the (110)STO substrate. (c) In-plane projections of the vectors perpendicular to the CTO (115) and STO (111) reflections. (d) The XRD /-scans of the CTO (115) (red line) and STO (111) (black line) reflections.

042901-2 Liet al. Appl. Phys. Lett.110, 042901 (2017)

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interfacial lattice misfit is only 1.0% along the a-axis and 0.6% along thec-axis, and the strain inside the film far from the interface is slightly smaller, as confirmed by the XRD data. Besides, the symmetric and asymmetric XRD reciprocal space mapping (RSM) results are presented in Figs.3(a)–3(c), respectively. For the symmetric STO (220) and CTO (040) reflections, the CTO (040) spot exhibits some broadening along wavevector Q_?, implying a slight variation in lattice constantb. The broadening along the wavevector Q//suggests a consistent FWHH with the direct rocking curve. Fig.3(b) gives the asymmetric STO (310) and CTO (240) reflections, with wavevector Q_//parallel to thea-axis of CTO. The lattice along thea-axis is partially relaxed. Fig.3(c)gives the asymmetric STO (222) and CTO (0 4 10) reflections, with wavevector Q_// parallel to thec-axis of CTO. As indicated by the red dashed line, the lattice of the CTO film along thec-axis is coherent with the STO. The RSM images reveal a clear pattern from all the directions including the (a,b,c)-axes of the CTO film.

The transmission electron microscopy (TEM) images across the CTO-STO interface are summarized in Fig.4. The low-amplified image reveals the microstructural homogene- ity over a big scale. The selected area electron diffraction

(SAED) pattern along the [001] axis of CTO and STO in Fig. 4(b) confirms the out-of-plane (020)CTO//(110)STO and in-plane (200)CTO//(1–10)STO relationships. The spots from the CTO are much weaker than those from STO, suggesting the relatively high density of lattice imperfections in the CTO. A relatively detailed discussion on the possible lattice defects in the CTO thin films is given in thesupplementary material (Figs. S1 and S2), suggesting the interstitial and vacancy defects in the films. Near the interface, the CTO b-axis lattice constant is 5.402 A˚ , twice of the Ca-Ca distance 2.701 A˚ . Thea-axis lattice constant is 5.516 A˚ , twice of the Ca-Ca distance 2.758 A˚ . Thea-axis constant in this region is larger than that of the bulk crystal, whereas the b-axis constant is smaller, confirming the slight in-plane tension and out-of-plane contract. Towards the region far from the interface, theb-axis anda-axis constants are 5.416 A˚ and 5.496 A˚

(twice of the Ca-Ca distances 2.708 A˚ and 2.748 A˚, respectively), close to the bulk crystal values, indicating the grad- ual lattice relaxation of the film, as schematically drawn in Fig. 4(d). This relaxation can be also detected by the spot splitting in the SAED pattern where the CTO (260) and STO (420) are no longer overlapped but in two separated spots.

The positive-up and negative-down (PUND) method was used to measure the total electric current (J) across the two sets of electrode stripes, as shown in thesupplementary material(Fig. S3) where several sets of J-Edata at T¼2 K with theE//a-axis and relevant discussion are presented. It is noted that the data by the PUND measurement at room temperature are unreliable due to the large electric leakage, and here, we present the data at low temperature. Based on these J-E data, one evaluates the P-E loops at different E-amplitudes (E0), and the representative results are summarized in Fig.5(a). First, the well-developed loops are identified at low temperature, and the measured “maximum”

polarization increases with increasingE0. The remnant polarization is8lC/cm²atE0¼20 kV/cm on the same order of magnitude as the bulk single crystals.¹⁵ Second, in spite of

FIG. 3. The measured RSM images of the CTO film on the STO substrate:

(a) the symmetric STO (220) and CTO (040) reflections; (b) the asymmetric STO (310) and CTO (240); and (c) the asymmetric STO (222) and CTO (0 4 10).

FIG. 4. (a) The TEM image showing the CTO film on the STO substrate. (b) The SAED pattern along the [001] axis of CTO. The orange and white colored numbers represent the spots of CTO and STO, respectively. (c) Cross- section TEM image of the CTO film around the CTO/STO interface. The insets represent the fast Fourier trans- form patterns from the selected areas.

(d) An enlarged relaxation schematic of lattice relaxation.

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E0-dependence, the measured coercive field (Ec) is 2.0 kV/

cm–5.0 kV/cm, dependent of E0 but much lower than that (>100 kV/cm) for bulk single crystals. In the other words, the ferroelectricity in the CTO thin films seems to be very different from the bulk single crystal. While the remnant polarization remains nearly the same as the bulk system, the coercive field is dramatically reduced, favorable for practical applications.

Besides, we measured the dielectric constanteas a func- tion of temperatureT, and thee(T) curves at several frequencies are plotted in Fig.5(b). We see a monotonous increasing ofewith decreasingT tillT10 K below which a dielectric plateau is identified. In the log-log scale, one observes no any anomaly over the whole T-range, suggesting no ferroelectric transition below room temperature, similar to the bulk system whose transition temperature is far above room temperature.

Here, several facts deserve to be mentioned. First, the typical quantum paraelectric behavior in terms of the dielectric response at low T is identified, suggesting that the major dielectric response is from the underlying STO. Second, no fre- quency dispersion of the dielectric response in the covered fre- quency range implies the same consequence. Third, this trivial quantum paraelectric behavior implies that the surface layer of STO is not affected by the interfacial lattice mismatch, and the measured polarization comes from the CTO film. Fourth and more importantly, for our PUND measurements, the underlying STO of high dielectric constant at lowTmay possibly dis- turb the electric potential distribution during the PUND probing, making the coercive field data inaccurate. Here, we prepared a set of CTO films with different thicknesses to verify our calculation of the coercive field. The experimental results prove that the evaluated coercive field is indeed the actual coercive field of the film, and detailed discussion can be found in thesupplementary material(Figs. S4 and S5).

To this stage, one concludes that the CTO thin films in the present condition have their ferroelectric polarization comparable with the bulk single crystals but with much lower coercive field Ec for polarization switching. The reasons for the big differences can be complicated. The lattice strain, defect state, domain structure, and dimensionality- relevant consequences can account for the big differences, considering the rich domain structure and the prediction that lattice strain may suppress the ferroelectricity.^16,19,25 Here, the lattice strain effect should be checked carefully, and we consult to the first principles calculations while the others remain open for a satisfactory understanding. We employ the first-principles calculations based on the projected aug- mented wave (PAW) pseudo-potentials using the ViennaAb- initioSimulation Package (VASP). More details of the calculation procedure are given in the supplementary material, and the results are summarized there too (Fig. S6). For the bulk lattice, we discuss the initial state (A2₁am), intermediate state (Pbcn), and final state (A2₁am). The fully relaxed lattice constants for the A2₁am ferroelectric phase area¼5.442 A˚ , b¼5.393 A˚ , andc¼19.336 A˚ , with a unit volume of 567.53 A˚³.¹⁴ The evaluated polarizationP is12.9lC/cm², consistent with measured polarization at room temperature.¹⁵ The energy barrier for polarization switching is 31 meV/Ti, giving an equivalent coercive field of3000 kV/cm at near zero-temperature ifP¼20lC/cm². This value is one order of magnitude larger than the room-temperature value.²⁶For the CTO thin films, the lattice relaxation is performed by fixing lattice constants a¼5.522 A˚ andc¼19.525 A˚ as determined from the in-plane lattices of the (110)STO substrate. Again, the Pbcn state is chosen as the intermediate switching state.

The barrier for the switching is 43 meV/Ti, slightly larger than that of the bulk crystal. The a-axis polarization is 17.6lC/cm², and the volume is 575.34 A˚³. These calculations suggest that the lattice tension induced by the STO substrates may not be the main reason for the huge difference in the coercive field between the bulk and thin films.

Other possible reasons for such a difference come from the lattice imperfections in the thin films, including the lattice defects (Fig. S2,supplementary material), domain structures, and possible non-stoichiometry. Again, it is mentioned that the hybrid improper ferroelectricity in CTO is the consequence of collective distortion of oxygen octahedral rotation and tilting. The local lattice defects can be vital for ferroelectric ordering. In addition, the CTO single crystals have complicated domain patterns with high domain wall energy due to the high density of head-to-head and tail-to-tail walls. The domain structures in thin films of high density of lattice imperfections can be more complicated, probably allowing the low coercive field for polarization switching. Details of the physics remain open to us at this stage.

In conclusion, we have prepared high-quality epitaxial CTO thin films on (110) STO substrates. A series of microstructural characterizations have been presented, identify- ing the epitaxial relationship of [001]CTO//[001]STO and [100]CTO//[-110]STO. The measurements reveal that the ferroelectric polarization aligns along the in-plane a-axis, and extra-high coercive field in the bulk single crystals can be markedly reduced down to5 kV/cm. The first principles calculations suggest that the in-plane tension and out-of-plane

FIG. 5. Ferroelectric hysteresis loop measured along thea-axis of CTO using the PUND method: (a) loops with differentE-amplitudes (E0) at T¼2 K. The schematic of the sample with inter-digital electrodes is dis- played on the top right. (b) Measured dielectric constante(T) curves along thea-axis at several frequencies in the log-log scale.

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contraction of the lattice may not be the reason for the difference in the coercive field between the thin films and bulk crystals. These variations can be the consequence of lattice imperfections in the thin films.

Seesupplementary materialfor more details of the epitaxial representations, ferroelectric measurements, and first- principles calculation.

The authors acknowledge the financial support from the State Key Research Program of China (Grant No.

2016YFA0300101) and the National Natural Science Foundation of China (Grant Nos. 51431006, 11234005, 11374112). X. Li was supported by the program for Outstanding PhD candidate of Nanjing University. S.W.C was partially supported by the Distinguished Visiting Professorship of China through Nanjing University.

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Cover pa

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1 Supplementary Material

Ultra-low coercive field of improper ferroelectric Ca

3

Ti

2

O

7

epitaxial thin films

X. Li

¹

, L. Yang

²

, C. F. Li

¹

, M. F. Liu

¹

, Z. Fan

²

, Y. L. Xie

¹

, C. L. Lu

³

, L. Lin

¹

, Z. B. Yan

¹

, Z.

Zhang

⁴

, J. Y. Dai

⁴

, J. –M. Liu

^1,2

, and S. W. Cheong

⁵

1

Laboratory of Solid State Microstructures and Innovative Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China

2

Institute for Advanced Materials, South China Normal University, Guangzhou 510006, China

3

School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China

4

Department of Applied Physics, Hong Kong Polytechnic University, Hong Kong, China

5

Rutgers Center for Emergent Materials and Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey, 08854, USA

1. A brief description of film deposition & characterizations

In our experiments, the CTO thin films on STO substrates were prepared using pulsed laser deposition (PLD). The stoichiometric CTO target was obtained using the standard solid-state sintering. The deposition was carried out at a substrate temperature of ~ 850 °C in oxygen ambient of 0.3 mbar. The KrF excimer laser (248 nm) was used to ablate the target and the focused energy density was ~ 1.0 J/cm

²

with a repetition rate of 4 Hz. After the deposition, the films were cooled down at a rate of 4 °C/min in the 500 mbar oxygen ambient to avoid oxygen deficiency. For typical cases, the thin films are ~ 60 nm in thickness.

The epitaxy characters of the thin films were checked by X-ray diffraction (XRD) in the

 -2  mode, pole  -scan mode, and reciprocal space mapping (RSM) mode using the

PANalytical XPert PRO machine. Transmission electron microscopy (TEM) in the

cross-section mode was carried out using the JEM 2100F TEM facility, with special attention

to the high-resolution TEM analysis on the epitaxial interface. For electric characterization,

the gold inter-digital electrodes on the film surface were sputtered via the standard

photolithography and lift-off procedures since the electric polarization was supposed to align

along the a-axis. The polarization-electric field (P-E) loops at various temperatures (T) were

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carried Properti (PUND electrod dielectri contribu exhibit

2. Latti To along [1 1(c)). A rock-sal ions in t differen bright s stripes.

Fig. S1.

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¹

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passes. Cons PUND mode ed in Fig. S3 hin films d

l and vacan crystallogra

observe the while the alt m the view on, we foun .

s and (b) va s of the CT

he PUND m m surface ar

is 0.1 mm. T e equivalent

(FEA) is a he thin film 1 mm

²

, rep sequently, t e.

3(c) with E/

deposited o

ncy defects aphic shear ese shear pl ternate laye of the bc- nd no other

acancy defec O film.

method re illustrated

To evaluate cross area applied to s

m can be presenting t

he P-E loop

//a-axis. Fo on conduct

s occur in t planes in t lanes, if exi ers of rock- -plane cross r dislocation

cts marked

d in Figs. S e the current

S

eq

. With a solve the M seen as tw the equival p is evaluat

or a compar tive (110)

the film, the CTO ist, since -salt and s section ns in our

as blue

3(a) and t density full-size Maxwell wo shunt

lent area ted from

ison, the

Nb:STO

(10)

4

substrates are prepared, with the J-E curves measured along the out-of-plane direction (E//b-axis) shown as Fig. S3(d). The polarization current can be reliably extracted from the PUND data as shown in Fig. S3(c) where the four electrical pulses (P, U, N, D) are marked.

Fig. S3. Measured electric current (J) vs. electric field (E) loops at T = 2 K between the two sets of inter-digital electrodes as shown in (a) and (b), with (c) E//a-axis and (d) E//b-axis.

In addition, as the large contribution to the dielectric constant of the CTO film comes from the STO substrate, the electric field may tend to drop much more vertically down from the electrodes and then run horizontally through the STO substrate. As a consequence, it seems that the electrodes distance, relevant to the coercive field, might be much closer to the thickness of the film (t) than the spacing of the interdigitated electrodes (d).

To verify whether the deduced coercive field is strongly relevant to the film thickness, we have grown a number of films with different thicknesses ranging from 30 to 220 nm. The films were deposited under the same condition as that for the previous ~ 60 nm thick CTO film. We took essential characterization like X-ray diffraction (XRD)  -2  spectrum, followed

-8 -4 0 4 8

-3 -2 -1 0 1 2 3

-9000-4500 0 4500 9000 -2

-1 0 1 2 (a) (b)

[110]

ST O [001]

[001]

[100] CTO

CTO equal area S

_eq

[100]

el ec tr ode

(c)

ND PU

D N

U

J ( μ A/ cm

2

)

T = 2 K E // a-axis

P

T = 2 K E // b-axis (d)

D N

U P

E (kV /cm )

x10

^-5

Electric bias

tim e

(11)

by sputt lift-off thicknes coercive error ba between As the coer thicknes the meth

Fig. S4

tering the g procedures sses of ~30, e fields are ars is drawn n the two el

discussed b rcive voltag ss t increas hod of calcu

4. Ferroelect

gold inter-d s. The mea

, 60, 100, 15 roughly the n in Fig. S5 ectrodes an before, if th ge U

_c

finally es. The me ulating the c

tric hysteres

digital surfa asured PUN 50, 220 nm e same. The 5. Here E

_c

i nd d is the se

he film thick y obtained in easured resu

coercive fie

sis loops me t

5

ace electrod ND loops

, are presen e evaluated is simply d eparation.

kness is str n the experi ult is incons eld in our m

easured alo thicknesses

des via the s for these nted in Fig. S

coercive fi etermined b

rongly relev iments wou sistent with model is roug

ng the a-ax s.

standard ph samples w S4. It is see eld E

c

vs. fi by U/d whe

vant to the e uld increase h this scenar

ghly reasona

is of CTO f

hotolithogra with differe en that the m film thickne

ere U is the

electrodes d considerab ario, sugges

able.

films with d

aphy and nt CTO measured

ss t with e voltage

distance, bly as the ting that

different

(12)

Fig

4. First We pseudo- interacti of the g optimiz The pla electrica climbin switchin the inter For phase an are relax with the which e (i.e. the ferroele

g. S5. The c

t-principles employ the -potentials

ions are de generalized

ed iterative ane-wave cu

al polarizat ng Nudged

ng path. For rmediate sta r the bulk

nd Pbcn ph xed again b e lattice ene each point i e ferroelectr ectric switch

coercive fie

s calculatio e first-princ using the V escribed usi

gradient a ly until the utoff is set tion is calc Elastic Ba r both the b ate, as sugg

one, severa hase are esta by the cNEB ergy upon th is the energ ric state) as hing takes

eld E

c

vs. film ferroelec

n & polariz iples calcul Vienna Ab- ng PBEsol approximatio Hellman-F

to 500 eV.

culated usi and (cNEB bulk and thi

ested in ear al initiating ablished by B method. T he switching gy of one op the referen the two-ste

6

m thickness ctric hystere

zation swit lations base -initio Simu

(Perdew-B on (GGA) eynman for V. The Monk

ing the Ber B) method

⁷

in film, we rlier work.

g structures y the linear The switchi g coordinat ptimization nce. It is see ep path. Fo

s t with erro esis loops.

tching d on the pro ulation Pac Burke-Ernze method.

⁵

T rces are con

khorst-Pack rry phase

7

to compu adopt the n

s of transiti interpolatio ng path ene te for bulk c n structure w

en that this or the Pbcn

or bars evalu

ojected augm ckage (VAS erhof-revise The atomic nverged to le k k-point m

approach.

⁶

ute the tw non-polarize

ion states b on method a ergy is then crystal, as s with respect

is a triple-w as the inte

uated from

mented wav SP).

^2,3

The ed)

⁴

parame

positions a ess than 5.0 mesh is 4×4 Here, we wo-step pola ed Pbcn stru

between the and these st n calculated shown in Fi ct to the init

well profile ermediate s

the

ve (PAW) electron etrization are fully 0 meV/Å.

4×1. The use the arization ucture as

e A2

₁

am

tructures

together

g. S6, in

tial state

e and the

state, the

(13)

7

barrier for switching is slightly lower than that of the other switching path (~ 34 meV/Ti in our result, not shown) where the Pnam structure is chosen as the intermediate state, as proposed in previous calculation.

⁸

This is the reason why the Pbcn structure is chosen as the intermediate state, allowing kinetically more favorable switching.

We then discuss the CTO thin films. We fix a and c lattice constants to the in-plane lattices of (110)STO, allowing the relaxation of lattice constant b and internal atoms. In the optimizations of the transition states, the lattice constants are fixed to the original value determined by the linear interpolation method, and the internal atomic degrees of freedom are relaxed. The energy profile along the switching path is also plotted in Fig. S6, while the triple-well profile is exhibited once more.

Fig. S6. The calculated energy barrier for polarization switching between two A2

₁

am ferroelectric phases (P) across the Pca2

1

-Pbcn-Pca2

1

path for bulk crystal lattice and slightly

strained thin film lattice. See text for details.

0 1 2 3 4

0 10 20 30 40 50

En e rgy (me V /Ti )

A 21am Pca2

1 Pbcn Pca2

1 A 2

1am +P N P -P

Sw itching Coordinate film

bulk

(14)

8

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8