Domain topology and domain switching kinetics in a hybrid improper ferroelectric

Abstract

Charged polar interfaces such as charged ferroelectric walls or heterostructured interfaces of ZnO/(Zn,Mg)O and LaAlO₃ /SrTiO₃ , across which the normal component of electric polarization changes suddenly, can host large two-dimensional conduction. Charged ferroelectric walls, which are energetically unfavourable in general, were found to be mysteriously abundant in hybrid improper ferroelectric (Ca,Sr)₃ Ti₂ O₇ crystals. From the exploration of antiphase boundaries in bilayer-perovskites, here we discover that each of four polarization-direction states is degenerate with two antiphase domains, and these eight structural variants form a Z₄ × Z₂ domain structure with Z₃ vortices and five distinct types of domain walls, whose topology is directly relevant to the presence of abundant charged walls. We also discover a zipper-like nature of antiphase boundaries, which are the reversible creation/annihilation centres of pairs of two types of ferroelectric walls (and also Z₃ -vortex pairs) in 90° and 180° polarization switching. Our results demonstrate the unexpectedly rich nature of hybrid improper ferroelectricity.

ARTICLE

Received 17 Dec 2015 | Accepted 12 Apr 2016 | Published 24 May 2016

F.-T. Huang1, F. Xue2, B. Gao1, L.H. Wang3, X. Luo3, W. Cai1,w, X.-Z. Lu4, J.M. Rondinelli4, L.Q. Chen2

& S.-W. Cheong1,3

Charged polar interfaces such as charged ferroelectric walls or heterostructured interfaces of ZnO/(Zn,Mg)O and LaAlO3/SrTiO3, across which the normal component of electric polarization changes suddenly, can host large two-dimensional conduction. Charged ferro-electric walls, which are energetically unfavourable in general, were found to be mysteriously abundant in hybrid improper ferroelectric (Ca,Sr)3Ti2O7 crystals. From the exploration of antiphase boundaries in bilayer-perovskites, here we discover that each of four polarization-direction states is degenerate with two antiphase domains, and these eight structural variants form a Z4 Z2 domain structure with Z3 vortices and ve distinct types of domain

walls, whose topology is directly relevant to the presence of abundant charged walls. We also discover a zipper-like nature of antiphase boundaries, which are the reversible creation/annihilation centres of pairs of two types of ferroelectric walls (and also Z3-vortex pairs) in 90 and 180 polarization switching. Our results demonstrate the unexpectedly rich nature of hybrid improper ferroelectricity.

DOI: 10.1038/ncomms11602 OPEN

Domain topology and domain switching kinetics in a hybrid improper ferroelectric

1 Rutgers Center for Emergent Materials, Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA. 2 Department of Materials Science and Engineering, Pennsylvania State University, University Park, Pennsylvania 16802, USA. 3 Laboratory for Pohang Emergent Materials, Max Plank POSTECH Center for Complex Phase Materials, Pohang University of Science and Technology, Pohang 790-784, Korea. 4 Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, USA. w Present address: Chongqing University of Science and Technology,

Chongqing 401331, China. Correspondence and requests for materials should be addressed to S.-W.C. (email: mailto:[email protected]

Web End [email protected] ).

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Over the last decade, two-dimensional (2D) conduction in heterostructured interfaces with polar discontinuity1,2 or compositionally homogeneous charged interfaces such as

charged ferroelectric domain walls (FE DWs)310 has attracted enormous attention for emergent phenomena and new material functionalities. However, undesirable chemical/structural complexity such as ionic diffusion, oxygen vacancies or structural/strain variations near the interface results in equivocal interpretation of the origin of 2D conduction1113. In parallel, signicant efforts have been launched to investigate the 2D conduction at charged FE DWs, which are well dened at the atomic scale. The conducting FE DWs were observed in chemically homogeneous thin lms, for example, Pb[ZrxTi1-x]O3 (ref. 14), BiFeO3 (ref. 10) and Bi0.9La0.1FeO3/

SrRuO3 heterostructure9 and bulk single crystals, for example, LiNbO3 (ref. 4), BaTiO3 (ref. 5) and Er(Ho)MnO3 (refs 6,7). These conducting FE DWs are intrinsically unstable because of large energy cost8,15, often pinned by chemical defects4 and sporadically5 and articially created with external voltage9. However, charged domain walls (DWs), some of which are highly conducting, were found to be abundant in the hybrid improper FE (Ca,Sr)3Ti2O7 (ref. 3).

Ordering phase transitions in condensed matter can be accompanied by directional variants and antiphase boundaries (APBs). Directional-variants result in domains with different directional order parameters. The role of APBs16,17 on materials functionalities has been well recognized1822. In particular, the discovery of strong interaction or interlocking nature of APBs with ferroic orders in diverse functional materials opens new grounds for material research. Examples include the ferromagnetic coupling in Heusler alloys23, the reduced spin polarization in half-metal magnetites24, the duality nature of DWs and topological defects in hexagonal manganites25, FE APBs in a nonpolar matrix16 and conducting and ferromagnetic walls of antiferromagnetic domains in pyrochlore iridates26.

Hybrid improper ferroelectricity (HIF), a phenomenon involving polarization induced by a hybridization of two non-polar lattice instabilities, offers great promise towards the realization of room-temperature multiferroism2731. The key idea is to design new materials in which ferroelectricity and (anti)ferromagnetism can be coupled by the same lattice instability, therefore providing an indirect but strong coupling between polarization and magnetism2729,31,32. Examples of compounds with HIF include the double-layered Ruddlesden-Popper perovskites with the chemical formula of A3B2O7

(Fig. 1, A2 alkali metal; B4 transition metal)3,27,32.

Unexpectedly, charged FE DWs, some of which are highly conducting, were also found to be mysteriously abundant in the recently discovered Ruddlesden-Popper-type HIF (Ca,Sr)3Ti2O7 crystals3.

To unveil the origin of these abundant charged FE DWs, we have explored the complete connectivity of DWs in Ca2.55Sr0.45-

Ti2O7 (CSTO; FE TcE790 K) and Ca3Mn1.9Ti0.1O7 (CMTO; FE TcE360 K) single crystals with in-plane polarization along the pseudo-tetragonal [110] directions3,30,33, particularly with mapping of APBs using transmission electron microscopy (TEM). Note that APBs are invisible in piezoresponse force microscopy (PFM)34, which is usually a good method to map out FE domain congurations. Phase-eld simulations35 were also conducted to understand the origin of domain congurations in CMTO and CSTO. Our results reveal that the formation of a unique Z4 Z2 domain topology with Z3 vortices is responsible

for the presence of abundant charged FE DWs in CSTO. In addition, we have also investigated the kinetics associated with polarization switching in CSTO, understanding of which is crucial for developing precise control of conducting FE walls.

ResultsZ4 Z2 domain structure with eight different states. Figure 1a

shows two characteristic lattice modes in A3B2O7: First, the BO6 octahedral in-phase rotations are either clockwise (the sign of the rotation is ) or anticlockwise ( ) about a [001]T direction

(denoted as a0a0c in the Glazer notation36 or the X2 mode), and second, the BO6 octahedral tilting occurs about two o1104T axes, that is, apical oxygen-motions displace towards the 1st to 4th quadrants (denoted as a a c0 or the X3 mode)

with respect to the high-symmetry tetragonal I4/mmm (T, space group #139) structure. Below the phase transition, the X3 mode adopts one of the four tilts (14) accompanying the X2 mode with or rotations into a combined distortion pattern of

a a c having eight degenerate states, which we label as 1, 2, 3 and 4 (the complete structures are shown in Fig. 1b,c).

1+

c +

+

aa

c +

++

2

1

P

aT

c

3

4

+

aT

aT

c

3 3+ 1

2+ 4 4+ 2

Figure 1 | Structural illustrations of the eight ferroelectric domains in A3B2O7. (a) An in-plane BO6 octahedral constituent with tilting along the o1104T directions and rotation around the [001]T direction. Plus ( ) and

minus ( ) represent clockwise and anticlockwise rotations. White arrows

indicate the displaced directions (1st to 4th quadrants) of the apical oxygen of the BO6 octahedron due to octahedral tilting. The red spheres represents

O ions. (b) The 1 domain state. The red arrow indicates the polarization

direction. The grey dotted lines depict the basic tetragonal framework constructed by B-site ions and the green dashed rectangle depicts the orthorhombic cell. The cross-sectional structure includes two bi-layers formed by orange and light green corner-sharing BO6 octahedra. Each domain state can be unambiguously identied by naming the distortions of a given octahedron (blue-circled) as the ve adjacent octahedra in each bi-layer are constrained to tilt and to rotate in opposite senses, and also the overall crystallographic symmetry (A21am) determines the distortions in the adjacent bi-layers. (c) The in-plane structural models of the 1 , 2, 3

and 4 domain states. Switching of the octahedral tilting pattern is involved between two domain states in, for example, 1 versus 3 , 1

versus 3 , 2 versus 4 and 2 versus 4 , and switching of the

octahedral rotation pattern is required between 1 versus 1 , 2 versus

2 , 3 versus 3 and 4 versus 4 . Antiphase domain relations can

be found between two domain states in, for example, 1 versus 3 ,

1 versus 3 , 2 versus 4 and 2 versus 4 . The corresponding

polarization direction in each domain state can be derived readily from our nomenclature; for example, the 1 domain state accompanies a

polarization towards the 2nd quadrantstarting from the 1st quadrant and rotating clockwise ( ) to the 4th quadrant that results in the nearest

A-site cation (and polarization) being displaced in the opposite direction to the 2nd quadrant. Note that the net in-plane dipole moment (G5 ) is caused by this A-site-cation displacement.

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Figure 1b shows the 1 state projected along the [001]T and

[010]T directions. For example, the apical oxygen of the blue-circled octahedron moves towards the 1st quadrant (white arrow) with a clockwise rotation (black curved arrow) to form a 1

state. A trilinear coupling among the X2 mode, X3 mode and the polar G5 mode (A-site displacement) yields four FE polarizations parallel or antiparallel to the two o1104T tilting axes3,27. We emphasize that each polarization direction is associated with two degenerate states, for example, the 1 and

3 polarizations point in the same direction (red and light-red

arrows in Fig. 1b,c), a consequence of both nonpolar order parameters (X3 and X2 ) changing signs. These four polarization directional variants with twofold degeneracy form the basis of the

Z4 Z2 domain structures in the HIF A3B2O7. Figure 2a shows a

structural model of a APB (green line) between the 1 and 3

states, at which the orthorhombic unit cells labelled by green dotted lines illustrate the discontinuation of octahedral tilting (white arrows) and rotation ( and ) at the wall. APBs might

exist in A3B2O7, but behave hidden in the PFM images as the two domains give the same piezo-response3.

Z3 vortices in the Z4 Z2 domain structures of (Ca,Sr)3Ti2O7.

Polarized optical microscope images on CSTO and CMTO crystals both clearly exhibit orthorhombic twins, that is, orthorhombically distorted ferroelastic (FA) domains. In addition, in-plane PFM studies show the intriguing FE domains comprising abundant meandering head-to-head and tail-to-tail charged DWs3 (Supplementary Fig. 1). Compared with PFM, dark-eld TEM (DF-TEM) under systematic controlled diffraction conditions allows us to light up domains induced directly by local structural deformations37. Figure 2bd shows a series of DFTEM images taken along the [001]T direction using superlattice

peaks g1 3/2(1, 1, 0)T parallel to the polar axis within a

single FA domain. Three domains (iiii) in Fig. 2bd, in which domains i and ii reveal the same domain contrast but opposite to domain iii in contrast, show the existence of antiphase domains i and ii, and an APB between them. Three FE domains including two antiphase domains merging at one vertex point are well illustrated in Fig. 2bd. As a sense of rotation along the merging three domains is dened in the phase space (see below), their intersection can be called a Z3 vortex. Note that the relative polar aorth directions can be identied from the related electron diffraction patterns but the absolute polarization direction cannot be. Thus, once the polarization direction is chosen for one domain, then the polarization directions in other domains can be fully assigned without ambiguity. Evidently, the existence of APBs remains unchanged even if the assignment of the polarization direction is reversed. Figure 2e depicts one possible assignment with 1 and 3 antiphase domains. The APB between these

1 and 3 domains accompanies the sign change of both

rotation and tilting (Fig. 2a). The presence of an APB and a Z3 vortex also suggests the existence of pure rotation (a0a0c )-driven DWs and pure tilting (a a c0)-driven DWs. We dene a tilting-type FEt DW (rotation-type FEr DW) as the wall between adjacent FE domains having opposite a a c0 tilting (a0a0c rotation) but identical a0a0c rotation (a a c0 tilting). The structural details of FEt and FEr DWs are shown in Supplementary Figs 2 and 3. Note that the Z3 vortex in Fig. 2e consists of three distinct walls: FEr (red-dotted), FEt DWs (red-solid) and APB (green line).

Figure 3a shows a mosaic of DF-TEM images covering three FA (that is, orthorhombic twin; FA(i) and FA(ii)) regions in a CSTO crystal. In the DF-TEM image obtained using orthorhombic superlattice peaks g1 contributed from the FA(i) domain marked by red and blue circles in Fig. 3b, the neighbouring FA(ii)

a

APB

P(1+)=P(3)

1+ 3

aT

+

+

+

aT

b c d e

APB

ii

3

ii i ii

iii

1+

i

i

FEr

3+

iii

iii

FEt

Figure 2 | Antiphase boundary (APB) in a CSTO crystal. (a) The local distortions near an [110]T-oriented APB (green line) between the 1 and

3 states, which are identical in polarization direction but differ in structure with respect to rotation (black curved arrows) and tilting (white arrows) by

180. (b) A ab-plane DF-TEM image taken using superlattice g1 3/2(1, 1, 0)Tspot. (c) A DF-TEM image taken using superlattice g1 3/2( 1, 1, 0)T

spot. A reversed contrast in b,c demonstrates the characteristic of 180-type FE domains. (d) A DF-TEM image taken using g1 spot at a large tilting angle to tune contrast by enhancing excitation error. A clear boundary interference fringe can then be observed between domains ii and iii, implying an inclined nature and a strong strain gradient expected in rotation-driven FEr DWs. (e) The schematic domain conguration obtained from bd demonstrates a typical

Z3 vortex pattern within a FA domain, composed of three 180-FE domains and three DWs: FEr (red-dotted), FEt (red-solid) DWs and APB (green-solid). White arrows denote the polarization directions in FE domains. Scale bar, 500 nm.

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a

b

[001]T

e

f

FA(ii) FA(i)

FA(ii)

FA(i)

c

FA(ii)

100 nm

g

1+

3+

h

3+

3 FAt

d

3 2+

2

FEt

FEr

3

1

3

3+

APB

1+

aT

3+

4+

aT

500 nm

FAtr

50 m

Figure 3 | The Z3-vortex patterns in Ca2.55Sr0.45Ti2O7 and Ca3Mn1.9Ti0.1O7 crystals. (a) A 2.2 3.9 mm2 mosaic of DF-TEM images were taken using the

superlattice g1 spot (red-circled) of domain FA(i) in a CSTO crystal along [001]T. The coloured arrows represent polarization directions within the domain. (b) The electron diffraction pattern was taken by covering regions FA(i) and FA(ii) showing a 90-crystallographic-twin relation. The red/blue circled spots were contributed from the orthorhombic distortions of the FA(i) region and the green/yellow ones were from the FA(ii) area. The colour-circled spot located in each DF image is the selected superlattice Bragg spot to light up the corresponding domains at a given orientation. (c) A DF-TEM image of the white rectangular box region was taken using the blue circled superlattice g1 spot. (d) A proposed domain conguration of c. (e,f) DF-TEM images taken using (e) red circle and (f) yellow circle spots corresponding to superlattice g1 spots in a CMTO crystal. A Z3-vortex network appears, with three DWs meeting at one point and with irregular shaped FE/FA domains. (g) A proposed domain conguration of e. Two types of FA DWs, FAt (blue-dotted) and FAtr (blue-solid), were identied. (h) Polarized optical image of a CMTO crystal showing irregular twin (that is, FA) domains in a hundreds micrometre scale.

Table 1 | DFT calculated coefcients for the Landau polynomial.

Coefcient a33 a3333 b11 b1111 b1122 c11 t3311 d

Unit eV f.u. 1 2 eV f.u. 1 4 eV f.u. 1 2 eV f.u. 1 4 eV f.u. 1 4 eV f.u. 1 2 eV f.u. 1 4 eV f.u. 1 3

Value 0.3505 0.1868 0.2024 0.0527 0.0176 0.0188 0.1464 0.1701

DFT, density functional theory.

regions exhibit a dark contrast (Fig. 3a). Aside from the major contrast between FA(i) and FA(ii), a self-organized Z3-vortex network is clearly visible within the FA(i) region.

Figure 3c shows a reversed contrast within the white rectangular box taken using a g1 spot (blue-circled) and the schematic (Fig. 3d) shows a pair of Z3 vortices is linked by an APB (green line). Boundaries between the 3 (pink) and 3 (blue) domains

form broad contrast walls, identied as FEr DWs (red-dotted lines of Fig. 3d). By comparing the domain contrasts (Fig. 3c), wall features and the neighbouring FA domains obtained from our DF-TEM images, we completely assign all domain states and wall types appearing in Fig. 3a (see the Methods for details).

Domain topology of Ca3(Mn,Ti)2O7. We also grew high-quality CMTO single crystals and conrmed the presence of polar domains in the same polar space group (A21am) as Ca3Ti2O7 at 300 K. Figure 3h shows a polarized optical microscopy image of surprisingly irregular FA DWs on the cleaved (001)T surface, distinct from the prototypical straight FA DWs (that is, orthorhombic twin walls) in CSTO. Our DF-TEM images (Fig. 3e,f) demonstrate consistently the presence of irregular twin patterns. The FA(i) domain is excited when the red-circled g1 spot was used for imaging (Fig. 3e), and it turns to deep-dark contrast when the orthogonal yellow-circled spot was excited (Fig. 3f). Inside each FA domain, there exist 180-type FE domains; for

example, bright and grey contrast domains in Fig. 3e,f and Supplementary Fig. 4. The domain conguration shown in Fig. 3g displays the presence of Z3 vortices with three domains merging at the vortex cores, which exist within a FA domain, as well as at boundaries between FA domains. Thus, the conguration of Z3-

vortex domains seems universal in the HIF A3B2O7, despite the existence of eight possible structural variants. Note that there exist two types of FA DWs: ferroelastic tilting DWs (FAt DW)

between states in the same rotation, for example, the 1 and 2

or 3 and 2 (blue-dotted lines in Fig. 3d and Supplementary

Fig. 2), and FA tilting rotation (FAtr) DWs between, for

example, the 2 and the 3 states (blue lines in Fig. 3d and

Supplementary Fig. 2). A single tilting of either a a0c0 or a0a c0 type may occur at FAt and FAtr DWs (white arrows in Supplementary Fig. 2). FAtr DWs seem naturally accompanied with a complete octahedral-rotation frustration at the walls, implying a higher energy of FAtr DWs than that of FAt DWs (Supplementary Fig. 3).

Phase-eld simulations. We also employed the phase-eld method (Methods and Tables 13)35 to investigate the domain structure of HIF A3B2O7, as shown in Fig. 4a,b. The details of the simulations are given in the Methods. The eight states are represented by different colours. Ca3Ti2O7 exhibits straight FA

DWs (Fig. 4a), consistent with the experimental observation3

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(Supplementary Fig. 1). Across the FA DWs, a dark colour tends to become another dark colour, for example, a red (1 ) colour

tends to change to a green (2 ) colour, rather than to a light

green (4 ) colour (Fig. 4a, circle ii). Similarly, two light colours

tend to be close with each other across the FA DWs (Fig. 4a, circleiii). These indicate that the rotation order parameter tends to be unchanged across the FA DWs38, which is consistent with the previous discussion on the low energy of FAt, compared with FAtr

DWs. Supplementary Fig. 3 shows the oxygen positions of the eight states relative to the tetragonal position. With the assumption that a wall going through a tetragonal-like state with zero polarization costs more energy, the energy hierarchy among the ve DWs can be estimated to be FAtrFErrFEtrFAtrrAPB. The statistics of DW lengths obtained from phase-led simulation results give a ratio of

FEr:FAt:FEt:APB:FAtr 34:28:28:8:2 in Ca3Ti2O7 (Fig. 4a) and

FAt:FEr:FAtr:FEt:APB 52:22:12:7:7 in Ca3Mn2O7 (Fig. 4b). A

comparably large population of FEt, FEr and FAt walls, especially in Ca3Ti2O7, suggests that APB and FAtr walls belong to the higher energy set than others. Experimentally, within a limited number of DWs that we have observed, CSTO exhibits an 82% population of the lower energy set (FEr, FEt and FAt walls), whereas CMTO shows a 64% population. The low population in CMTO is likely related with the existence of irregular FA domains in CMTO. Note that although an energy hierarchy may exist, we do observe experimentally and theoretically all ve kinds of DWs.

The energy diagram for the HIF A3B2O7 such as Fig. 4c can be constructed with all eight states (vertices) and all ve kinds of walls (edges connecting two vertices). Note that in Fig. 4c, only a small part of edges are shown, and each vertex is connected to all of the rest vertices through edges in the full energy diagram. The i, ii and iii loops in Fig. 4c correspond to Z3 vortices in the

Fig. 4a,b, respectively. The presence of only Z3 vortices indicates that the energy difference among ve types of DWs is not large, so the lowest-energy vortex defect is always Z3-type. Note that if, for example, APB is associated with much higher energy than others, then APB will be fully avoided, and Z4-type vortex defects such as 1 /3 /3 /1 /1 can occur, but we observe only

Z3-type vortices. In low-magnication TEM images, we

Table 2 | DFT calculated elastic stiffness tensor coefcients.

Coefcient C11 C12 C13 C33 C44 C66

Value 315 77.6 98.0 297 81.6 83.1

DFT, density functional theory.

All values are given in units of GPa.

Table 3 | Normalized gradient energy coefcients.

Coefcient j1111 j1122 j1122 d1111 d1122 d1212 g1111 g1122 g1212

Value 0.88 8.8 8.8 0.88 8.8 8.8 0.50 0.088 0.088

All values are normalized with respect to g 2.2 eV f.u.

1.

a

c

g

aT

4

1

aT

iii

3

(1) APB

FEr FEt

1+

3+

2

3

ii

1+

i

ii

iii

i

APB :

4+ FAtr : FAt :

(2) (3)

(5)

(4) FAtr FAtr

FAtr

FEt

APB

FAtr FAt

iii

11+++

3 -

33+++

1

44+++

Ca3Ti2O7

Ca3Mn2O7

FEt :

4+

b

3+

2+

2+

1+

4

3

FEr :

f

1

1+

3

3+

22+++

4

2

-

-

-

d e

FAt

1+ FAt

i

ii

1+

2

2

1+

FEr

1 FAt

3+ FEt

Figure 4 | Z4 Z2 domain with Z3 vortices in Ca3Ti2O7 and Ca3Mn2O7. (a,b) In-plane domain structures of Ca3Ti2O7 and Ca3Mn2O7 from phase-eld

simulations. The eight colours denote the eight domain variants as listed. Z3 vortices corresponding to loops iiii are denoted by black circles in spite of different nature of FA domains in Ca3Ti2O7 and Ca3Mn2O7. (c) Schematic of the energy diagram in A3B2O7 compounds with eight vertices, representing eight domain variants. Each vertex is connected to seven edges that correspond to one of ve types of DWs as shown in the right side. Loops iiii depict possible vortex domains and domain walls (in fact, Z3 vortices). Note that non Z3-type vortex domains corresponding to loops connecting, for example, (1 , 3 , 3 , 1 , 1 ) or (1 , 2 , 3 , 3 , 1 ) have not been observed experimentally. (df) Experimental DF-TEM images demonstrate two Z3

vortices at a very short interval of 50 nm in a Ca3Ti2O7 crystal. Scale bar, 100 nm. (d) Image was taken under a Friedels-pair-breaking condition to reveal 180-type domain contrast. Polarization directions were shown by white arrows. (e) Image was taken under a larger tilting angle to reveal boundary interference fringes clearly. The width of bent fringes indicates a broad DW interrupting the connection of 1 (red) and 3 (pink) domains. (f) Image

shows a schematic of the corresponding domain conguration. (g) Five possible Z3-vortex congurations derived from the energy diagram. The indicated domain states are examples. Type 1, the only Z3-vortex conguration appearing within a single orthorhombic twin. Type 2, the most common Z3 vortex across the orthorhombic twin boundaries. Type 3, Z3 vortex accompanying 90 ferroelectric switching at APB. Type 4, Z3 vortex accompanying ferroelectric switching in the absence of APB. Type 5, the least favoured Z3 vortex with two high energy FAtr walls.

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sometimes observe vortices looking like Z4-type. However, all these likely Z4-type vortices turn out to be pairs of closely linked Z3 vortices with inclined broad DWs, as shown in Fig. 4df. The energy diagram (Fig. 4c) is, in fact, a hyper-tetrahedron in seven dimensions, which has eight vertices and only triangular faces. Each triangular face in this hyper-tetrahedron corresponds to a Z3 vortex. All possible congurations of Z3 vortex derived from the energy diagram (Fig. 4c) are shown in Fig. 4g and have been observed experimentally. The conguration of Z3 vortex domains seems universally adopted in HIF A3B2O7 compounds. Note that FA DWs in Ca3Ti2O7, nucleated from a high-temperature tetragonal phase (I4/mmm)33,39, tend to be straight, whereas FA

DWs in Ca3Mn2O7, nucleated from the Acaa (space group #68) phase30 below B360 K, are irregular (Supplementary Fig 4). A phase-eld simulation for the nucleation and growth of the FE A21am domains from the Acaa matrix is shown in

Supplementary Movie 1.

Domain switching kinetics. In-situ poling results on CSTO using a DF-TEM technique unveil intriguing domain switching kinetics, which can be understood in terms of the creation and annihilation of Z3 vortex-antivortex (V-VA) pairs. In-situ poling is achieved utilizing fast positive charging40,41 induced by focusing the electron beam (B300 nm in diameter) of the TEM at a thin and local area, and the slow reduction of effective electric elds, because of charge dissipation, occurs after removing the focused beam. Thus, in order to observe the in-situ poling process, DF-TEM images are obtained immediately after defocusing the electron beam, before the charges are completely dissipated (on the order of 30 min). Figure 5ae shows a Z3 V-VA pair (cyan

and blue circles) within one FA domain behaving coherently with in-situ poling. In-situ poling at a 5 oclock position near the crystal edge induces a direct 180 polarization reversal of a 4

(light green) domain to a 4 (yellow) domain (Fig. 5c), which is

accompanied by the creation of a V-AV pair. The induced 4

domain shrinks slowly after defocusing the electron beam (from Fig. 5ce). Eventually, the induced 4 domain disappears, and at

the same time, the V-AV pair annihilates. This result demonstrates a 180 polarization reversal associated with the creation or annihilation of a Z3 V-AV pair. Furthermore, the results in Fig. 5ae reveal that APBs act as nucleation reservoirs for the Z3 V-AV pair creation and annihilation (Supplementary

Fig. 5 and Supplementary Movie 2 for more details). Figure 5f illustrates that in a Z3 V-AV pair creation process, a segment of a

APB becomes two FE DWs (one FEr DW and the other FEt DW); FEt DWs with a larger energy than that of FEr tend to be pinned at the original APB location, whereas FEr DWs tend to be mobile. This observation is in accordance with the energy hierarchy of FErrFEtrAPB discussed earlier.

We also studied electron beam-induced poling in different directions. The switching process depends signicantly on the electric eld orientation (Supplementary Fig. 5). For example, Fig. 5g shows another region with two antiphase 4 (yellow) and

2 (light yellow) domains with slightly different bright contrasts

located next to an APB (green line). Interestingly, when the electron beam is focused on the specimen edge away from FA DWs (blue lines) and an electric eld (red/white arrow in Fig. 5h) perpendicular to the original polar axis is induced, a 90 polarization switching from a bright 2 (light yellow) to dark

3 (pink) triangular domain is observed. The induced 3

domain returns slowly to the initial 2 state with charge

a

c

f i

g

FEr

2

4 2+ 4+

FAt

2+

4+

APB

FEt

APB

FAt APB

V FEr

4+

4

V

FAtr

E

E

E

d

FEt

b

AV

AV

FAtr

h

2

2+

4+

4

APB

APB

APB FEr+FEt

APB FAt+FAtr

e

3 4+

1+

+

aT

E

E

+

aT

Figure 5 | The domain switching kinetics under e beam-induced poling. In-plane DF-TEM images and schematics of domain structures in a CSTO crystal under different directions of induced electric eld indicated by red arrows. Coloured arrows and domains represent polarization directions and FE domain states, respectively. Scale bar, 200 nm. (ae) Image sequences showing a Z3 vortex-antivortex (V-AV) pair evolution during in-situ poling within a single ferroelastic domain. (a,b) The initial state. (c,d) The states during the charge dissipation process after defocusing electron beam. (e) The nal state. With a focused electron beam at the sample edge, a direct 180 polarization reversal is observed (4 -4 ) via V-AV pair creation (ac), and the created

domain disappears slowly with charge dissipation, which accompanies V-AV pair annihilation (ce). Cyan and blue circles denote Z3 vortices and antivortices, respectively. A black arrowhead is the location marker. (f) Schematic showing the 180 ferroelectric polarization switching via splitting or coalescence of a APB into two ferroelectric walls: APB (green line)-FEt (red-solid) FEr (red-dotted) DWs. (g,h) Image sequences and schematics

showing 90 ferroelectric domain switching near a APB (green line). (g) The initial state. (h) The immediate image after electron beam focused at the sample edge away from the FA boundary (solid blue line). Only 90 poled domains (dark contrast) are observed (2 -3 and 4 -1 ). The 90

poled domains are assigned with the rotation order parameter same with those of the initial domains, which is consistent with the low-energy nature of FAt DW. The induced 3 (pink) and 1 (red) domains return slowly to the initial 2 (light yellow) and 4 (yellow) states with charge dissipation. (i)

Schematic showing a 90 ferroelectric polarization switching within a FA domain via splitting or coalescence of a APB into two ferroelastic walls: APB -FAtr (blue-solid) FAt (blue-dotted) DWs. Emphasize that there is no hint of the presence of any intermediate states corresponding to 90polarization

reversal during this process.

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NATURE COMMUNICATIONS | DOI: 10.1038/ncomms11602 ARTICLE

dissipation. This process is involved with the splitting or coalescence of an APB to two FA DWs; one FAtr DW and the

other FAt DW (Fig. 5i). The created FAtr DW with high energy stays at the original APB location, whereas the created FAt DW

with low energy tends to be mobile.

DiscussionWe observe a direct 180 (90) polarization switching, instead of going through an intermediate 90 (180) polarization state in the in-situ poling process. We emphasize that the coherent DW network of Z4 Z2 domains with Z3 vortices and some highly

curved walls (Fig. 3) leads to the presence of charged DWs and APBs. The presence of Z3-vortices instead of the formation of antiparallel domains separated by neutral walls also indicates that a moderate energy difference among ve types of DWs. In particular, those APBs serve as primary nucleation centres for 180 and 90 polarization switching, and the presence of mobile n-type charge carriers, screening the polar discontinuity at charged DWs, are responsible for the large conduction of head-to-head DWs3. Note that the APBs with the discontinuity of both octahedral tilting (t) and rotation (r) costs more energy and one ABB splits into two FE/FA walls under an external electric eld, so an APB becomes a nucleation centre of a new poled domain (Fig. 5). This can also happen in high-energy FAtr DWs as shown in the Fig. 6. This zipper-like splitting of high-energy DWs accompanies the emergence of Z3 V-AV pairs. The high-energy

APB and FAtr DWs dominate the nucleation controlled kinetics

of polarization ipping, while the low-energy FEr and FAt DWs tend to move steadily with an external electric eld, which can be responsible for the DWs motion kinetics. Emphasize that unlike expected minor roles of APBs with just translation phase shift, APBs dominate the FE polarization switching in hybrid improper FE (Ca,Sr)3Ti2O7. These unexpected discoveries of the role of

APBs and the domain topology relevant to the presentence of abundant conducting DWs should be further investigated for deeper understanding and nano-engineering of the domains and DWs in hybrid improper FEs.

Methods

Sample preparation. Single-crystalline CSTO and CMTO were grown by using optical oating zone methods. For polycrystalline Ca3-xSrxTi2O7 (Ca3Mn2-xTixO7)

feed rods, stoichiometric CaCO3, SrCO3 and TiO2 (MnO2) were mixed, ground, pelletized and sintered at 1,3501,550 C for 30 h. Substituting Sr into the Ca site in Ca3Ti2O7 induces the reduced size of FA domains suitable for TEM studies. It was very difcult to grow high-quality single crystals of pure Ca3Mn2O7, but the slight substitution of Ti into the Mn site of Ca3Mn2O7 stabilizes crystal growth without changing the relevant physics of Ca3Mn2O7. Crystals are highly cleavable, and were cleaved in air for optical microscopy observation. Transparent amber coloured CSTO single crystals and non-transparent dark blue coloured CMTO present a similar polar orthorhombic symmetry (space group #36, A21am)3,30,33. Crystal structure and lattice parameters were examined by X-ray diffraction with a Philips XPert powder diffractometer and the general structure analysis system program. CMTO possesses a one and half larger FA distortion (that is, orthorhombicity dened by (a b)/(a b)*100%, B0.08 %) than Ca3Ti2O7 (B0.05 %). Cycling the

CMTO sample temperature through Tc leads to a completely different irregular FA pattern, indicating that the domain formation is not simply due to pinning by disorder such as chemical defects or dislocations.

Dark-eld TEM measurement. Specimens for DF-TEM studies were fabricated on Ca3Ti2O7 (CTO), Ca2.55Sr0.45Ti2O7 (CSTO) and Ca3Mn1.9Ti0.1O7 (CMTO)

single crystals (B1 2 0.1 mm3 in size) by mechanical polishing, followed by

Ar-ion milling and studied using a JEOL-2010F TEM. Note that one TEM specimen can include up-to-a-hundred FA domains for observations, and we have examined two CSTO, one CTO and two CMTO TEM specimens. Although the width of FA domains varies, our conclusion on the Z4 Z2 domain structure with

Z3 vortex patterns and ve types of DWs is universal in all specimens that we have

a

1+

2-

FA (i)

FA (ii)

1+

2-

FA (i)

FA (ii)

a

b

APB :

FAtr :

FAt :

FEt : FEr :

3

3

b

FAtr FAt+FEr

1

3 1

1+

2

FAt

c

1+

3

1+

2-

E

FAtr

2+

FAtr

4

V

AV

1

aT

1

3

3

4+

FEr

aT

3+

1+ 1

1

2

4

Figure 6 | Domain switching kinetics in the absence of APBs in CSTO. (a) In-plane DF-TEM images show two ferroelastic (FA(i) and FA(ii)) regions. Domain states 2 (light yellow arrow) and 1 (red arrow) are

assigned based on diffraction patterns and the assumption of a non-charged head-to-tail wall. (b) Polarization domain evolutions across a FAtr

boundary. Election beam focused at the end of a FA boundary close to the sample edge induces an electric eld indicated by a red/white arrow. A polarization switching (dark grey contrast) from 1 - 2 in FA(i) and

2 -2 in FA(ii) is observed. The right-side cartoon shows a schematic

of the domain switching via a splitting/merging of FAtr - FAt FEr DWs. A high energy FAtr DW becomes two DWs with lower energies; one ferroelectric FEr DW and the other ferroelastic FAt DW, which is consistent with our energy hierarchy. Both FAt and FEr DWs tend to be mobile and highly curved, which is again consistent the low energy nature of FAt and

FEr DWs in our energy hierarchy. Cyan and blue circles denote Z3 vortex(V) and antivortex (AV), respectively. Scale bar, 500 nm.

g2+

4+

1+

3

3+

2+

Figure 7 | A full assignment of domain states and wall types in CSTO. (a) A 2 2.9 mm2 mosaic of DF-TEM images were taken using the

superlattice g2 3/2( 1, 1, 2)T spot of domain FA(i) in a CSTO crystal

along [111]T, showing only part of DWs in this condition. Neither domain contrast nor curved and broad FEr DWs can be visualized under this condition. A tilting (1st or 3rd quadrants) conguration are depicted. Scale bar, 500 nm. (b) A DF-TEM image taken using another superlattice g1

spot (yellow circle), 90 relative to the one for FA(i), within the white rectangular box. The bright contrast corresponds to the other four types of 180 FE domains (2 , 2 , 4 and 4 ) inside the FA(ii) region. (c) A

schematic domain and domain wall conguration for the area in a, including various FE domains and ve types of DWs.

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ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms11602

observed. We also found that the FA domain size depends little on various heat treatment conditions in both CSTO and CMTO. We observed vortex domains by DF-TEM imaging taking two diffraction vectors: (i) superlattice g1 3/2(1, 1,

0)T (3, 0, 0)orth spots, parallel to the polar axis in [001]T zone and (ii)

superlattice g2 3/2( 1, 1, 2)T (0, 3, 3)orth spots, perpendicular to the

polar axis in [1, 1, 1]T zone, 15 tilting from c-axis. Figure 7a shows DF-TEM

images taken at the same area as Fig. 3a using the superlattice g2 spot. Non-FE structural boundaries can be visualized under this condition as the g2 vector is perpendicular to the polar aorth-axis and the FE contribution is minimized. To avoid confusion with APBs, those boundaries observed in this condition without considering the polarization effect are named as B-boundaries. The appearance of B-boundaries is a result of symmetry breaking through the tetragonal-toorthorhombic phase transition. They tend to show step-like features along the o1004T direction. Based on the domain switching kinetics shown in Fig. 5, we argue that those B-boundaries are either APBs or FEt DWs, so APBs and FEt DWs tend to be o1004T-oriented. Contrarily, FEr DWs show wavy features with no preferred orientation, because of the so-called rotational compatibility conditions38. The role of B-boundaries is further discussed in Supplementary Fig. 5. Figure 7b shows DF-TEM image taken using the superlattice g1 spot, showing the domain contrast of neighbouring FA(ii) region. A full assignment of domain states and DW types in a CSTO crystal is shown in Fig. 7c based on the domain contrast shown in Figs 3a and 7b and wall features associated with local distortions discussed below.

Local structural distortions at FE and FA DWs. Supplementary Fig. 2a shows a (110)T-oriented FEt DW between two neighbouring 1 and 3 domains, where

the octahedral tilting (a a c0) may be fully suppressed if octahedral tilting changes across the DW by passing through the tetragonal central position (Supplementary Fig. 3). On the other hand, Supplementary Fig. 2b shows a FEr

DW between neighbouring 1 and 1 domains, where neither of the two lattice

modes becomes zero. Thus, FEr DW may accompany a lower energy than FEt DW does (Supplementary Fig. 3). Given that the oxygen octahedra in A3B2O7 are

connected by sharing the oxygen atom in their corner, at those DWs, some shift of equatorial oxygens (indicated by red spheres in black circles in Supplementary Fig. 2a,b) that locate between Ti sites (cyan spheres) is expected. Enlarged views of the octahedra across the DWs (Supplementary Fig. 2a,b upper panels) clearly show a larger octahedral mismatch at the FEr DW than that at the FEt DW when observed along the [100]T axis. Experimentally, APBs can be identied from the domain contrast without ambiguity (Fig. 2bd). Although DWs can deviate from typical orientations to minimize the wall energy in the thin foil-type geometry of TEM specimens, we constantly observe a narrow sharp-contrast wall and a relatively broad wall with clear interference fringes near a Z3 vortex core. As strain provides the main diffraction contrast change in our DF-TEM images, we associate the narrow sharp-contrast lines with a less octahedral mismatch to FEt DWs in the ab-plane projection. This is, indeed, the case for a sharper wall between domain i and iii shown in Fig. 2d and between domains 1 and 3 or domains 1 and

3 shown in Fig. 4d,e, which we therefore assign as FEt DWs. A clear interference

fringes or wavy features can be observed between domains ii and iii (Fig. 2d) and domains 1 and 1 or domains 3 and 3 (Fig. 4d,e), suggesting an inclined

nature and a strong strain gradient as expected in FEr DWs.

Phase-eld modeling. To describe the distortion relative to the high symmetry phase with space group I4/mmm, three sets of order parameters are used, that is, ji(i 3) for the oxygen octahedral rotation around the x3 axis, and yi(i 1,2) and

Pi(i 1,2) for the octahedral tilt and polarization component along the xi(i 1,2)

pseudocubic axis, respectively23,42. The total free energy density can be expressed by

f aijjijj aijkljijjjkjl bijyiyj bijklyiyjykyl

tijkljijjykyl dj3y1P1 y2P2 gijPiPj

kijkl

@ji

@xj

1

where aij, aijkl, bij, bijkl, tijkl, d and gij are the coefcients of Landau polynomial, kijkl, dijkl and gijkl are gradient energy coefcients, cijkl is the elastic stiffness tensor, eij and e0kl are the total strain and eigen strain, and Ei is the electric eld given by

Ei j,i with j the electrostatic potential. Note that gij40, and the term

dj3(y1P1 y2P2) determines that (P1,P2,0) and (y1,y2,0) are parallel or antiparallel,

dependent on the sign of j3. The eigen strain is related to the order parameters through e0ij lijkljkjl hijklykyl, where lijkl and hijkl are coupling coefcients.

Here the coupling between polarization and strain is ignored, as the secondary order parameter polarization is always parallel or antiparallel to the octahedral tilt order parameter. The Landau polynomial is expanded based on group theory analysis42, and the related coefcients are obtained by rst-principles calculations38,4348 (Tables 13). Anisotropic properties are assumed in gradient energy coefcients kijkl and dijkl, that is, kiiii5kijij, diiii5dijij (ref. 38). The phase-

eld equations are solved with the initial condition of zero plus a small random

noise for the order parameter components49. Periodic boundary conditions are employed along the three directions. The system size is 1,024Dx 1,024Dx 1Dx,

and the grid spacing is Dx 0.30 nm.

Coefcients of Ca3Ti2O7 used in the phase-eld simulations. Total energy calculations based on density functional theory within the generalized-gradient approximation given by the revised PerdewBeckeErzenhof parameterization for solids43 using the projector augmented wave method4445 implemented in the Vienna Ab initio Simulation Package4647 are used to obtain the coefcients found in the Landau polynomial (Methods, Equation (1)). A plane-wave cutoff of 600 eV and a 4 4 1 k-point mesh with Gaussian smearing (0.10 eV width) is used for

the Brillouin-zone integrations. The calcium 3s, 3p and 4s electrons, Ti 3p, 3d and 4s electrons, and O 2s and 2p electrons are treated as valence states.

The coefcients for the Landau polynomial are obtained by tting the calculated total energies as a function of magnitude of the order parameters for the congurations corresponding to displacement patterns for each individual mode or combination of modes. The values for the relevant coefcients are given in Table 1. In all total energy calculations, the lattice constants are xed at the calculated equilibrium values for the high-symmetry I4/mmm structure (parent clamping approximation). The total elastic stiffness tensor, including the contributions for distortions with rigid ions and the contributions from relaxed ions, is also obtained by calculating the strainstress relations48 in the I4/mmm structure (Table 2). The gradient energy coefcients kijkl, dijkl and gijkl are estimated based on the gradient

energy coefcients of BiFeO3 (ref. 38) as both the two systems show the coexistence of oxygen octahedral tilt and polarization, and are listed in Table 3. Note that the domain structures are determined by the relative magnitude of different gradient energy coefcients, and will be hardly affected by the specic values.

Data availability. The authors declare that all source data supporting the ndings of this study are available within the article and the Supplementary Information File.

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Acknowledgements

The work at Rutgers was supported by the Gordon and Betty Moore Foundations EPiQS Initiative through Grant GBMF4413 to the Rutgers Center for Emergent Materials, and the work at Postech was supported by the Max Planck POSTECH/KOREA Research Initiative Program [Grant No. 2011-0031558] through NRF of Korea funded by MSIP. F.X., X.-Z.L., J.M.R., and L.Q.C. were supported by the National Science Foundation (NSF) through the Pennsylvania State University MRSEC under award number DMR-1420620. DFT calculations were performed on the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by NSF (ACI-1053575).

Author contributions

F.-T. H. conducted the TEM experiments and wrote the paper. F.X., X.-Z.L., J.M.R. andL.Q.C. performed the modelling, B.G., L.H.W. and X.L. synthesized single crystals, and W.C. performed the IP-PFM. S.-W.C. initiated and supervised the research.

Additional information

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How to cite this article: Huang, F.-T. et al. Domain topology and domain switching kinetics in a hybrid improper ferroelectric. Nat. Commun. 7:11602 doi: 10.1038/ncomms11602 (2016).

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