Abstract
Hybrid improper ferroelectricity (HIF) denotes a new class of polar instability by the mixture of two octahedral-distortion modes and can feature the coexistence of abundant head-to-head and tail-to-tail polar domains, of which the domain walls tend to be charged due to the respective screening charges with an opposite sign. However, no such coexisting carriers are available in the materials. Using group-theoretical, microscopic, and spectroscopic analyses, we establish the existence of a hidden antipolar order parameter in model HIF (Ca,Sr)3Ti2O7 by the condensation of a weak, previously unnoticed antipolar lattice instability, turning the order-parameter spaces to be multicomponent with the distinct polar-antipolar intertwining and accompanied formation of Néel-type twinlike antipolar domain walls (few nanometers) between the head-to-head and tail-to-tail domains. The finite-width Néel walls and correlated domain topology inherently lift the polar divergences between the domains, casting an emergent exemplification of charged domain-wall screening by an antipolar ingredient.
| Original language | English |
|---|---|
| Article number | 157601 |
| Journal | Physical Review Letters |
| Volume | 119 |
| Issue number | 15 |
| DOIs | |
| Publication status | Published - 2017 Oct 10 |
ASJC Scopus subject areas
- Physics and Astronomy(all)
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Hidden Antipolar Order Parameter and Entangled Néel-Type Charged Domain Walls in Hybrid Improper Ferroelectrics. / Lee, M. H.; Chang, C. P.; Huang, F. T.; Guo, G. Y.; Gao, B.; Chen, C. H.; Cheong, S. W.; Chu, M. W.
In: Physical Review Letters, Vol. 119, No. 15, 157601, 10.10.2017.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - Hidden Antipolar Order Parameter and Entangled Néel-Type Charged Domain Walls in Hybrid Improper Ferroelectrics
AU - Lee, M. H.
AU - Chang, C. P.
AU - Huang, F. T.
AU - Guo, G. Y.
AU - Gao, B.
AU - Chen, C. H.
AU - Cheong, S. W.
AU - Chu, M. W.
N1 - Funding Information: Lee M. H. 1 Chang C.-P. 1 Huang F.-T. 2 Guo G. Y. 3,4 Gao B. 2 Chen C. H. 1,2 Cheong S.-W. 2 Chu M.-W. 1 ,* Center for Condensed Matter Sciences, 1 National Taiwan University , Taipei 106, Taiwan Rutgers Center for Emergent Materials and Department of Physics and Astronomy, 2 Rutgers University , Piscataway, New Jersey 08854, USA Department of Physics, 3 National Taiwan University , Taipei 106, Taiwan Physics Division, 4 National Center for Theoretical Sciences , Hsinchu 300, Taiwan * Corresponding author. chumingwen@ntu.edu.tw 10 October 2017 13 October 2017 119 15 157601 28 February 2017 19 June 2017 © 2017 American Physical Society 2017 us American Physical Society Hybrid improper ferroelectricity (HIF) denotes a new class of polar instability by the mixture of two octahedral-distortion modes and can feature the coexistence of abundant head-to-head and tail-to-tail polar domains, of which the domain walls tend to be charged due to the respective screening charges with an opposite sign. However, no such coexisting carriers are available in the materials. Using group-theoretical, microscopic, and spectroscopic analyses, we establish the existence of a hidden antipolar order parameter in model HIF ( Ca , Sr ) 3 Ti 2 O 7 by the condensation of a weak, previously unnoticed antipolar lattice instability, turning the order-parameter spaces to be multicomponent with the distinct polar-antipolar intertwining and accompanied formation of Néel-type twinlike antipolar domain walls (few nanometers) between the head-to-head and tail-to-tail domains. The finite-width Néel walls and correlated domain topology inherently lift the polar divergences between the domains, casting an emergent exemplification of charged domain-wall screening by an antipolar ingredient. Gordon and Betty Moore Foundation http://dx.doi.org/10.13039/100000936 Gordon E. and Betty I. Moore Foundation http://sws.geonames.org/6252001/ GBMF4413 National Science Foundation http://dx.doi.org/10.13039/100000001 NSF http://sws.geonames.org/6252001/ NSF MRI-1532006 Ministry of Science and Technology, Taiwan http://dx.doi.org/10.13039/501100004663 Ministry of Science and Technology of Taiwan MOST http://sws.geonames.org/1668284/ National Taiwan University http://dx.doi.org/10.13039/501100006477 NTU http://sws.geonames.org/1668284/ Academia Sinica http://dx.doi.org/10.13039/501100001869 http://sws.geonames.org/1668284/ The macroscopic Landau theory of phase transitions depicts the grand fundamental of a plethora of phenomena ranging from ferroelectricity [1–3] to density waves [4] , with the ferroelectric (FE) transition being the textbook example for general structural phase transitions in solids [5,6] . In the corresponding group-theoretical context, proper FEs refers to a material with the spontaneous polarization as a primary order parameter, which transforms like a zone-center polar lattice instability, and improper FEs delineates ferroelectricity induced by an order parameter belonging to a zone-boundary nonpolar irreducible representation (irrep) with FE polarization being the secondary order parameter upon the transition [1,2,5–7] . In oxides, the zone-boundary instability can be linked to oxygen polyhedral distortions [7–9] . The general antiferrodistortive octahedral buckling in A B O 3 perovskites ( A and B , respectively, are 12- and sixfold coordinated cations; O is oxygen) is particularly intriguing considering the two ubiquitous, yet competing, order parameters of zone-center FE and zone-boundary octahedral instabilities in the bulks [6,10–12] . Further upon heterojunction, the translational symmetry generic to the bulks is broken across the interface, and the heterostructure can be subject to misfit strain, perturbing the existing order-parameter competition and likely mediating two-dimensional interfacial phenomena [13,14] . The rejuvenated FE instabilities in LaAlO 3 / SrTiO 3 heterojunctions ( LaAlO 3 and SrTiO 3 , nominally free from FE ordering) [13] and the improper ferroelectricity in PbTiO 3 / SrTiO 3 superlattices ( PbTiO 3 , originally proper FEs) [14] are exemplifications of such two-dimensional engineering. Indeed, Ruddlesden-Popper oxides, ( A O ) − ( A n B n O 3 n ) , naturally crystallize into two-dimensional perovskites ( n is the perovskite-unit number) [15] , with the rocksalt A O layer sectioning the three-dimensional corner-shared octahedra into two-dimensional perovskite slabs that nurture more octahedral degrees of freedom [15,16] . The Ruddlesden-Popper phases hence display rich octahedral distortions [15,16] , and the recently coined hybrid improper ferroelectricity (HIF) in n = 2 Ca 3 Ti 2 O 7 (CTO) and ( Ca , Sr ) 3 Ti 2 O 7 is particularly enlightening with the zone-center Γ -point ferroelectricity being driven by the hybrid condensation of two zone-boundary octahedral instabilities that transform like two-dimensional X -point irreps [17–22] . Macroscopically, the CTO and ( Ca , Sr ) 3 Ti 2 O 7 are distinguished from prototypical proper FE BaTiO 3 [23–25] and improper FE rare-earth molybdates [1–3,7–9] by the abundant head-to-head (HH) and tail-to-tail (TT) domains, where the FE dipoles point toward and away from each other across the respective domain walls (DWs) [18–20] . Accordingly, notable electrostatic divergences arise therein, and the HH and TT domains cannot be stable without the complementary screening charges at the DWs, while only electrons are available in n -type titanates [13,18,23–25] . The microscopic screening at the HH and TT DWs in CTO and ( Ca , Sr ) 3 Ti 2 O 7 is thus highly interesting and remains unsettled despite the proposal of topological protection by antiphase boundaries (APBs) [19,20] . Here, we report the atomic-scale observation of finite HH and TT DWs (few-nanometer width) with an unanticipated antipolar structure in model HIF Ca 2.5 Sr 0.5 Ti 2 O 7 (CSTO) and the correlated screening of the polar divergences using macroscopic group-theoretical analysis and microscopic structural and electronic investigations by (scanning) transmission electron microscopy [(S)TEM] and electron energy-loss spectroscopy (EELS). This work refines the understanding in physics of complex FE domains [19,20,26,27] . Figures 1(a) and 1(b) exhibit the FE ground-state structure (space group A 2 1 a m ) along respective b ’ and a ’ projections ( a ’ ∼ b ’ ∼ √ 2 a , c ′ ∼ c , thus c for simplicity; a and c are parent tetragonal lattice parameters) and the FE polarization (order parameter P ) along the a ′ axis [20] . Using the point-charge approximation for FE-dipole estimations [13] , we derived each atomistic contribution to P in an individual perovskite slab [gray region, Fig. 1(a) ] in Fig. 1(c) . Figure 1(d) represents the group-theoretical analysis of the symmetry tree [28] for transition pathways. 1 10.1103/PhysRevLett.119.157601.f1 FIG. 1. (a),(b) The FE - A 2 1 a m crystal structures along b ’ and a ′ projections, respectively. The crystallographic sites are indicated (gray, Ca / Sr ; cyan, Ti; red, oxygen). White arrows in (a), the antiparallel Ca 1 / Sr 1 and Ca 2 / Sr 2 displacements (black arrow, P ). Gray arrows in (b), the antipolar Ca 2 / Sr 2 displacements. Dashed gray lines in (a) and (b), guides for the off-center Ca / Sr displacements. (c) The a ′ -oriented polarization (black) of an individual perovskite slab in (a) and the atomistic contribution of each crystallographic site. (d) Group-theoretical analysis of the symmetry tree, with the black label indicating the space group. The symbols in parentheses depict the primary order-parameter directions. Solid (dashed) lines, reported (otherwise) transition pathways. Compared to the paraelectric parent phase ( I 4 / m m m ), the antiferrodistortive octahedral tilting (order parameter T ) in a ′ b ′ plane in Figs. 1(a) and 1(b) originates from the lattice instability against the X 3 − irrep, and the order parameter of octahedral rotation ( R ) along the c axis represents the X 2 + -irrep distortion mode, altogether known as the hybrid condensation of the two X -point irreps [17–22] . This cooperative transition lifts any single direct route to A 2 1 a m , with the polar P addressed by the zone-center Γ 5 − irrep [Fig. 1(d) ] [17,21,29] . It is noted that the zone-boundary Z 4 link for the pathway from Γ 5 − -induced F 2 m m to A 2 1 a m [Fig. 1(d) ] renders the resultant A 2 1 a m nonferroic [5] , ruling out the FE ground state as a child group of the Γ 5 − irrep. This latter feature confirms the HIF notion of P as the product of R and T [17,21] , and the ferroelectricity in CSTO was readily ascribed to the Γ 5 − -induced antiparallel Ca 1 / Sr 1 and Ca 2 / Sr 2 displacements along the a ′ axis [white arrows, Fig. 1(a) ] [18–20,30] . The atomistic decomposition of P [Fig. 1(c) ], however, unveils that all Γ 5 − -related Ca / Sr , Ti, and O displacements along a ′ are involved [21,22] . The thus-derived P of ∼ 2.14 μ C / cm 2 for a perovskite slab, i.e., ∼ 4.28 for an unit cell (uc), is compatible with the measured ∼ 2.97 μ C / cm 2 in single crystals [18] . Figure 1(c) hence suggests that the formed crystallographic opinions on the HIF [17,18,29,30] deserve further elaborations. Figure 2(a) shows the b ’ -projected STEM high-angle annular dark-field (HAADF) image of HH domains. Figure 2(b) exhibits one set of STEM-EELS chemical maps [13,31] . Figure 2(c) depicts the characteristic HAADF imaging along the a ′ projection. The b ’ -projected DF TEM imaging of different specimen regions is shown in Fig. 2(d) . Figure 2(e) represents the TT counterpart to Fig. 2(a) . Each panel in Fig. 2 was acquired in crystalline areas well away from any twin boundaries and thus denotes the inherent structural characteristics. 2 10.1103/PhysRevLett.119.157601.f2 FIG. 2. (a) The HAADF imaging of HH domains revealing a different feature in the DW (yellow). Ca 1 / Sr 1 , red rectangle. (b) The STEM-EELS chemical mapping. Gray (white) circles, Ca / Sr (Ti) omitting the off-center distortions. (c) The a ′ -projected HAADF image. Lower-bottom inset, an uc enlargement showing the accentuated antipolar Ca 1 / Sr 1 (white-margined) and Ca 2 / Sr 2 (red-margined arrows) displacements. Dashed white lines, guides for the eyes. (d) The various DF images (red, blue, and green) with the contrast reversal in each set unveiling the domain polarity. (e) The HAADF imaging of TT domains, with the DW structure (yellow) mimicking (a) and (c). P in the DWs and (c), pointing in or out. White rectangles, projected uc. Compared to pristine CTO, the Sr substitution increases the domain density by accompanied reduction in the a ′ b ′ -orthogonality and related ferroelastic-strain cost, rendering DW investigations convenient with various DW angles [18–20,31] . The larger, heavier Sr preferentially occupies the spacious perovskite A site [Fig. 2(b) ; Sr map, blue] compared to the ninefold rocksalt A site (Ca map, red), without introducing additional distortion to the CTO [15,18] and accounting for the enhanced Ca 1 / Sr 1 contrasts in the HAADF imaging [red rectangles, Fig. 2(a) ]. A careful examination of Fig. 2(a) unveils that the HH DW (yellow) shows a different structure from that in the neighboring domains. Surprisingly, the DW structure mimics the a ′ -projected CSTO [Fig. 2(c) ], with the b ’ -oriented antipolar Ca 2 / Sr 2 displacements in Fig. 1(b) being attenuated (red-margined arrows, bottom-left inset) and the nominally quenched Ca 1 / Sr 1 rejuvenated and exhibiting antipolar distortions (white-margined arrows). These accentuated b ’ -oriented antipolar Ca / Sr displacements lead to the previously unnoticed distortion of hourglass- and barrel-like perovskite units along c stacking [Fig. 2(c) ]. The TT DW [yellow, Fig. 2(e) ] shows the same distortion pattern of hourglass-barrel stacking as the HH counterpart [yellow, Fig. 2(a) ] and a ′ -projected CSTO [Fig. 2(c) ]. Figure 2(d) reveals that the HH and TT domains are equally populated. In Fig. 3 , we scrutinize the antipolar displacements as the hidden order parameter. 3 10.1103/PhysRevLett.119.157601.f3 FIG. 3. (a) The calculated phonon dispersion of CTO with identical antipolar distortion to the CSTO (inset, a ′ -projected HAADF of CTO). (b)–(d) The CBED patterns along respective b ’ , a ′ , and c projections with the BF (gray margined) embedded in the center of the WP. m , mirror. The symmetry characteristics in (b) and (c) refer to the point group 2 m m of A 2 1 a m . In (d), the 2 m m BF and twofold WP (guiding white, red arrows) symmetries suggest point-group 222-type distortion at the P 5 irrep. 4 10.1103/PhysRevLett.119.157601.f4 FIG. 4. (a)–(c) Γ 5 − , X 2 + , and X 3 − irreps with respective primary order parameters of P (black arrows), R (red), and T (blue) along ( a , a ), (0, a ), and (0, a ), forming four-domain topologies by the degeneracy labeled on edges. u (dashed lines), secondary order parameter of ferroelastic strain at the DWs. Gray (black) uc, c -projected parent (FE) lattice. (d) P 5 with effective ( 0 , 0 , b , b ). Green arrow, primary order parameter of antipolar Ca / Sr displacements ( A , double-headed). The eight domains (labels on edges) form a four-domain topology upon a b degeneracy. (e) Domain topology (upper panel) upon Γ 5 − -, X 2 + -, X 3 − -, and P 5 -irrep condensations. P and A , intertwined macroscopic order parameters in the four domains (1–4; eight domains upon P reversals). (f) The HH and TT domains with a generically sandwiched antipolar- A , Néel-type DW by the inherent domain topology such as 1-2-3 or 1-4-3 in (e). (g) A cross-sectional view of the coexisting HH and TT domains in (f). (h) The experimental HAADF evidence for (g), with the n = 3 defect also showing P 5 - type antipolar distortion within the DW (yellow). Figure 3(a) shows the calculated phonon dispersion of CTO that exhibits an identical antipolar distortion pattern (inset) to CSTO [31] . The negative frequency and local minimum at a given reciprocal lattice point indicate the uc instability against the irrep [13,38] . Figure 3(a) thus reveals the existence of Γ -, X -, and P -point soft phonons [1–3,6–8,16,38] , with the N - and Z -point saddles arising from the proximity to Γ - and P -point instabilities considering their incompatibility with the symmetry tree [Fig. 1(d) ] [5,32,39] . The pronounced X - and P -point dips in Fig. 3(a) signify their important roles in the ground-state structure [38] , and the shallower Γ -point phonon is consistent with the HIF by X -point instabilities [17,22] . Notably, P -point instability is undocumented in the earlier theoretical [17,22,29,30] and powder diffraction studies [15,20,21] while admissible for Ruddlesden-Popper phases [16] . The thermal diffused scattering in convergent-beam electron diffraction (CBED), owing to electron-phonon interaction, is a fundamental map of symmetry elements within the phonon spectrum [40] . CBED is then complementary to powder diffractions when probing intricate structural distortions is limited by the diffraction peak-intensity and -overlap subtleties [15,20,21,46] . Figures 3(b)–3(d) show the b ’ -, a ′ -, and c -projected CBED patterns of CSTO, showing Bragg-scattered disks with dynamical-interference fringes in the bright field (BF; center, transmitted disk) and striped thermal-diffused Kikuchi bands in the whole pattern (WP). A careful examination of the BF in Fig. 3(b) reveals the characteristic absence of a mirror perpendicular to a ’ * , and the Kikuchi bands in the WP (green stripes) map the 2 m m point-group symmetry of A 2 1 a m by the two perpendicular mirrors (white) [15] . Likewise, the BF - 2 m m and WP - 2 m m symmetries in Fig. 3(c) agree with the a ′ -projected 2 m m point group of A 2 1 a m [15] . Surprisingly, the c -projected Fig. 3(d) shows 2 m m BF and twofold WP considering the absent mirror operation between group-1 Kikuchi bands and group-2 and -4 ones (blue stripes; guiding white, red arrows) and the twofold operation for groups 1 and 3. This BF-WP symmetry combination leads to the 2 m R m R diffraction group that refers to the 222 point group [47] . Figures 3(b)–3(d) thus suggest that there exists a weak 222-type distortion. An investigation of the isotropy subgroups of I 4 / m m m reveals that point-group 222 is bound to the P -point irrep of P 5 , with the P 5 -irrep F 222 [Fig. 1(d) ] allowing the b ’ -oriented antipolar Ca 1 / Sr 1 and Ca 2 / Sr 2 displacements in Figs. 2 and 3(a) (inset) [5,39] . The condensation of P -point instability [Fig. 3(a) ] is unambiguously correlated with the P 5 -irrep antipolar distortion, establishing the group-theoretical footing of the antipolar displacements as a hidden order parameter [31] . In effect, the P 5 irrep [Fig. 1(d) ] is composed by two primary order parameters along respective ( a , a ) and ( b , b ) directions and two secondary order parameters to be addressed in Fig. 4 [5,16,28,39] . The order-parameter direction of P 5 is thus denoted as ( a , a , b , b ) [5,39] , suggesting that the b ’ -oriented antipolar order parameter, i.e., ( b , b ), shall have an a ′ -degenerate counterpart and the physics of CSTO is composed by novel multicomponent order-parameter spaces of P 5 , Γ 5 − , X 2 + , and X 3 − (one primary and one secondary order parameter for the latter three two-dimensional irreps). In Figs. 4(a)–4(c) , we illustrate the primary P , R , and T order-parameter directions in respective Γ 5 − , X 2 + , and X 3 − and the corresponding four-domain topology [5,39] . Taking Fig. 4(a) , for instance, P points along ( a , a ), i.e., a ′ in A 2 1 a m (black square), and is fourfold degenerate with ( a , a ), ( − a , a ), ( − a , − a ), and ( a , − a ) due to the a b degeneracy in I 4 / m m m , casting four domains with the ferroelastic strain ( u ) at DWs (dashed lines) as a secondary order parameter [5,28,39] . The in-plane octahedral rotation R in Fig. 4(b) (red arrows) and out-of-plane tilting T in Fig. 4(c) (blue) can be understood likewise [5,30,39] . In P 5 [Fig. 4(d) ], an ( a , a )-oriented antipolar order parameter A would nonetheless coincide with P [Fig. 4(a) ] and is readily suppressed due to the absent antipolar distortion along the a ′ axis (Figs. 1 and 2 ). The P 5 irrep effectively becomes ( 0 , 0 , b , b ), with one survived primary order parameter A along b ’ , two secondary order parameters of u and P [Fig. 4(e) ], and four-domain topology considering the reduction from eight by the a b degeneracy [5,39] . Upon the hybrid condensation of R and T , P turns out to be the macroscopic order parameter in the phenomenological domain topology [35,36,48] as well as A considering its accompanied observations in Figs. 2(a) and 2(e) . The symmetry essences in Figs. 4(a)–4(d) are then summarized into Fig. 4(e) , with the P and A forming the macroscopic order parameters and being generically intertwined in the four-domain topology (otherwise, eight domains upon P -direction reversals [18–20,30] ). Through this P - A pairing, antipolar- A twins spontaneously appear between the HH and TT domains [Fig. 4(f) , plane view; sandwiched P , double headed for arbitrary reversals] by the topology of 1-2-3, 1-4-3, or inherent combination of any three domains in Fig. 4(e) , with the HH and TT sharing equal probability [indeed observed in Fig. 2(d) ] and the twinlike DWs mimicking the FE Néel walls characterized by an in-plane 90° rotation of the dipole and a finite width [Fig. 4(f) ] [35,36,48,49] . Figure 4(g) represents a schematic cross-sectional view of the Néel walls [Fig. 4(f) ] and is affirmed by Fig. 4(h) . It has been theoretically suggested that the emergence of FE Néel walls with finite widths refers to the existence of an additional order parameter within the walls, which can be allowed only in FEs featuring multicomponent order-parameter spaces and is rare in matter [48,49] . This surprising exemplification in CSTO [Figs. 2(a) , 2(e) , and 4(h) ] corresponds to this notion by the distinct P - A intertwining and accompanied order-parameter spaces (Fig. 4 ). On either side of the Néel walls [Figs. 4(g) and 4(h) ], the readily formed 180°-domain configuration along c leads to coexisting depolarization fields with opposite signs and naturally mitigates the electrostatic divergence thereby, similar to the function of 180° domains in proper FEs [23,35,36,48] . The finite wall width is also helpful in smearing out any residual electrostatic divergence in the a ′ b ′ plane. Accordingly, the HH and TT DWs are not electrostatically divergent and do not require screening charges (Fig. S1) [31] . These FE Néel walls impose a structural screening on the primitively charged DWs and discount the proposed APB-DW characteristics [19,20] considering an APB-based a ′ / 2 or c / 2 translation unable to result in the observed hourglass-barrel-like antipolar DW structure. The HH and TT DWs adherent to the sixfold FE vortices in improper-FE hexagonal manganites represent the first systematically studied domain topology [26,27,34,50] and arise from Z 6 topological defects by the trimerized polyhedral tilting characteristic of K 3 instability (locked into three phase angles of 0, 2 π / 3 , and 4 π / 3 , i.e., topological Z 3 symmetry; accompanied Γ 2 − FE degeneracy, Z 2 ; Z 3 × Z 2 = Z 6 ) [51,52] , with the HH and TT DWs being atomically sharp [52–56] and to be electrostatically screened [27,34] . By analogy, the HH and TT DWs in CSTO have been ascribed to Z 4 × Z 2 topological defects [ Z 4 , fourfold degenerate R and T ; Z 2 , FE degeneracy; Figs. 4(a)–4(d) ] [19,20] , of which the entangled electrostatic screening [27,34] is, however, discarded (Fig. S1) and the characteristic DWs are rather few-nanometer wide and Néel type [Figs. 2(a) , 2(e) , and 4(h) ]. We then performed a group-theoretical analysis on the K 3 instability in the manganites, leading to the order-parameter directions of ( a , 0), ( − a / 2 , √ 3 a / 2 ), and ( − a / 2 , − √ 3 a / 2 ), equivalent to the respective Z 3 angles of 0, 2 π / 3 , and 4 π / 3 and being twofold degenerate with ( − a , 0), ( a / 2 , − √ 3 a / 2 ), and ( a / 2 , √ 3 a / 2 ) like Z 2 [39,57] . The analysis also allows domain permutations along the out-of-plane directions as the Z 6 topological defects [39,57] , altogether suggesting that our phenomenological methodology can be an explicit simple solution to complex domain topologies [48,57] , though largely unnoticed before. Future topological-defect elaborations [51,52] by incorporating the P - A intertwining shall lead to the same Néel-DW topology as ours while a dedicated issue on its own. In summary, the b ’ -oriented antipolar Ca / Sr displacements arise from a hidden antipolar order parameter by the condensation of P 5 instability. The accepted notion on the ferroelectricity and domains in the HIF has been argued over Γ 5 − , X 2 + , and X 3 − irreps while insufficient for addressing the antipolar distortion and coexisting HH and TT domains. With the P 5 irrep, the order-parameter spaces become multicomponent, and the domain topology constitutes intertwined polar and antipolar characteristics, with the sandwiched antipolar Néel-type DWs screening the HH and TT dipoles. The HIF represents a vivid example that structural screening can be an alternative to the conventional electrostatic screening of HH and TT domains. This work could stimulate further studies of structurally mediated screening in pursuit of new discoveries by thorough group-theoretical explorations in all plausible order-parameter spaces. The authors thank Professor M. S. Senn and the funding in Taiwan by Ministry of Science and Technology (Taiwan), National Taiwan University, and Academia Sinica (Taiwan), and at Rutgers by the Gordon and Betty Moore Foundation’s EPiQS Initiative through Grant No. GBMF4413 to the Rutgers Center for Emergent Materials. The crystal growth at Rutgers was supported by the NSF MRI Grant No. MRI-1532006. [1] 1 A. P. Levanyuk and D. G. Sannikov , Sov. Phys. Usp. 17 , 199 ( 1974 ). SOPUAP 0038-5670 10.1070/PU1974v017n02ABEH004336 [2] 2 V. Dvorak , Ferroelectrics 7 , 1 ( 1974 ). FEROA8 0015-0193 10.1080/00150197408237942 [3] 3 G. Venkataraman , Bull. Mater. Sci. 1 , 129 ( 1979 ). BUMSDW 0250-4707 10.1007/BF02743964 [4] 4 G. Grüner , Density Waves in Solids ( Perseus , Cambridge, MA, 1994 ). [5] 5 H. T. Stokes and D. M. Hatch , Isotropy Subgroups of the 230 Crystallographic Space Groups ( World Scientific , Singapore, 1988 ). [6] 6 Structural Phase Transitions I , edited by K. A. Müller and H. Thomas ( Springer-Verlag , Berlin, 1981 ). [7] 7 J. D. Axe , B. Dorner , and G. Shirane , Phys. Rev. Lett. 26 , 519 ( 1971 ). PRLTAO 0031-9007 10.1103/PhysRevLett.26.519 [8] 8 B. Dorner , J. D. Axe , and G. Shirane , Phys. Rev. B 6 , 1950 ( 1972 ). PLRBAQ 0556-2805 10.1103/PhysRevB.6.1950 [9] 9 J. M. Perez-Mato , D. Orobengoa , and M. I. Aroyo , Acta Crystallogr. Sect. A 66 , 558 ( 2010 ). ACACEQ 0108-7673 10.1107/S0108767310016247 [10] 10 K. A. Müller , W. Berlinger , and F. Waldner , Phys. Rev. Lett. 21 , 814 ( 1968 ). PRLTAO 0031-9007 10.1103/PhysRevLett.21.814 [11] 11 J. D. Axe , G. Shirane , and K. A. Müller , Phys. Rev. 183 , 820 ( 1969 ). PHRVAO 0031-899X 10.1103/PhysRev.183.820 [12] 12 W. Zhong and D. Vanderbilt , Phys. Rev. Lett. 74 , 2587 ( 1995 ). PRLTAO 0031-9007 10.1103/PhysRevLett.74.2587 [13] 13 P. W. Lee , V. N. Singh , G. Y. Guo , H.-J. Liu , J.-C. Lin , Y.-H. Chu , C. H. Chen , and M.-W. Chu , Nat. Commun. 7 , 12773 ( 2016 ). NCAOBW 2041-1723 10.1038/ncomms12773 [14] 14 E. Bousquet , M. Dawber , N. Stucki , C. Lichtensteiger , P. Hermet , S. Gariglio , J.-M. Triscone , and P. Ghosez , Nature (London) 452 , 732 ( 2008 ). NATUAS 0028-0836 10.1038/nature06817 [15] 15 M. M. Elcombe , E. H. Kisi , K. D. Hawkins , T. J. White , P. Goodman , and S. Matheson , Acta Crystallogr. Sect. B 47 , 305 ( 1991 ). ASBSDK 0108-7681 10.1107/S0108768190013416 [16] 16 D. M. Hatch and H. T. Stokes , Phys. Rev. B 35 , 8509 ( 1987 ). PRBMDO 0163-1829 10.1103/PhysRevB.35.8509 [17] 17 N. A. Benedek and C. J. Fennie , Phys. Rev. Lett. 106 , 107204 ( 2011 ). PRLTAO 0031-9007 10.1103/PhysRevLett.106.107204 [18] 18 Y. S. Oh , X. Luo , F.-T. Huang , Y. Wang , and S.-W. Cheong , Nat. Mater. 14 , 407 ( 2015 ). NMAACR 1476-1122 10.1038/nmat4168 [19] 19 F.-T. Huang , F. Xue , B. Gao , L.H. Wang , X. Luo , W. Cai , X.-Z. Lu , J. M. Rondinelli , L. Q. Chen , and S.-W. Cheong , Nat. Commun. 7 , 11602 ( 2016 ). NCAOBW 2041-1723 10.1038/ncomms11602 [20] 20 F.-T. Huang , B. Gao , J.-W. Kim , X. Luo , Y. Wang , M.-W. Chu , C.-K. Chang , H.-S. Sheu , and S.-W. Cheong , npj Quantum Mater. 1 , 16017 ( 2016 ). 2397-4648 10.1038/npjquantmats.2016.17 [21] 21 M. S. Senn, A. Bombardi , C. A. Murray , C. Vecchini , A. Scherillo , X. Luo , and S. W. Cheong , Phys. Rev. Lett. 114 , 035701 ( 2015 ). PRLTAO 0031-9007 10.1103/PhysRevLett.114.035701 [22] 22 X.-Z. Lu and J. M. Rondinelli , Nat. Mater. 15 , 951 ( 2016 ). NMAACR 1476-1122 10.1038/nmat4664 [23] 23 M. Y. Gureev , A. K. Tagantsev , and N. Setter , Phys. Rev. B 83 , 184104 ( 2011 ). PRBMDO 1098-0121 10.1103/PhysRevB.83.184104 [24] 24 T. Sluka , A. K. Tagantsev , D. Damjanovic , M. Gureev , and N. Setter , Nat. Commun. 3 , 748 ( 2012 ). NCAOBW 2041-1723 10.1038/ncomms1751 [25] 25 T. Sluka , A. K. Tagantsev , P. Bednyakov , and N. Setter , Nat. Commun. 4 , 1808 ( 2013 ). NCAOBW 2041-1723 10.1038/ncomms2839 [26] 26 T. Choi , Y. Horibe , H. T. Yi , Y. J. Choi , W. Wu , and S.-W. Cheong , Nat. Mater. 9 , 253 ( 2010 ). NMAACR 1476-1122 10.1038/nmat2632 [27] 27 W. Wu , Y. Horibe , N. Lee , S.-W. Cheong , and J. R. Guest , Phys. Rev. Lett. 108 , 077203 ( 2012 ). PRLTAO 0031-9007 10.1103/PhysRevLett.108.077203 [28] 28 B. J. Campbell , H. T. Stokes , D. E. Tanner , and D. M. Hatch , J. Appl. Crystallogr. 39 , 607 ( 2006 ). JACGAR 0021-8898 10.1107/S0021889806014075 [29] 29 A. B. Harris , Phys. Rev. B 84 , 064116 ( 2011 ). PRBMDO 1098-0121 10.1103/PhysRevB.84.064116 [30] 30 E. A. Nowadnick and C. J. Fennie , Phys. Rev. B 94 , 104105 ( 2016 ). PRBMDO 2469-9950 10.1103/PhysRevB.94.104105 [31] 31 See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevLett.119.157601 for the detail, which includes Refs. [32–45]. [32] 32 M.-W. Chu , S. K. Lee , D. Hesse , and U. Gösele , Appl. Phys. Lett. 85 , 2029 ( 2004 ). APPLAB 0003-6951 10.1063/1.1788879 [33] 33 C.-P. Chang , M.-W. Chu , H. T. Jeng , S.-L. Cheng , J. G. Lin , J.-R. Yang , and C. H. Chen , Nat. Commun. 5 , 3522 ( 2014 ). NCAOBW 2041-1723 10.1038/ncomms4522 [34] 34 D. Meier , J. Seidel , A. Cano , K. Delaney , Y. Kumagai , M. Mostovoy , N. A. Spaldin , R. Ramesh , and M. Fiebig , Nat. Mater. 11 , 284 ( 2012 ). NMAACR 1476-1122 10.1038/nmat3249 [35] 35 P. Marton , I. Rychetsky , and J. Hlinka , Phys. Rev. B 81 , 144125 ( 2010 ). PRBMDO 1098-0121 10.1103/PhysRevB.81.144125 [36] 36 J. Hlinka , V. Stepkova , P. Marton , and P. Ondrejkovic , Topological Structures in Ferroic Materials, edited by J. Seidel ( Springer International , Switzerland, 2016 ). [37] 37 Y. Shimakawa, Y. Kubo , Y. Nakagawa , S. Goto , T. Kamiyama , H. Asano , and F. Izumi , Phys. Rev. B 61 , 6559 ( 2000 ). PRBMDO 0163-1829 10.1103/PhysRevB.61.6559 [38] 38 J. M. Perez-Mato , M. Aroyo , A. Garcia , P. Blaha , K. Schwarz , J. Schweifer , and K. Parlinski , Phys. Rev. B 70 , 214111 ( 2004 ). PRBMDO 1098-0121 10.1103/PhysRevB.70.214111 [39] 39 H. T. Stokes and D. M. Hatch , ISODISTORT Software , http://stokes.byu.edu/isotropy.html . [40] 40 L. Reimer , Transmission Electron Microscopy: Physics of Image Formation and Microanalysis , 4th ed. ( Springer-Verlag , Berlin, 1984 ). [41] 41 P. Giannozzi , S. de Gironcoli , P. Pavone , and S. Baroni , Phys. Rev. B 43 , 7231 ( 1991 ). PRBMDO 0163-1829 10.1103/PhysRevB.43.7231 [42] 42 J. P. Perdew , Electronic Structure of Solids ’91 , edited by P. Ziesche and H. Eschrig ( Akademie Verlag , Berlin, 1991 ). [43] 43 The Quantum Espresso project (2015), http://www.quantum-espresso.org/ . [44] 44 P. E. Blöchl , Phys. Rev. B 50 , 17953 ( 1994 ). PRBMDO 0163-1829 10.1103/PhysRevB.50.17953 [45] 45 The VASP team ( 2009 ), https://www.vasp.at/ . [46] 46 M. H. Lee, C. H. Chen , C. M. Tseng , C. S. Lue , Y. K. Kuo , H. D. Yang , and M. W. Chu , Phys. Rev. B 89 , 195142 ( 2014 ). PRBMDO 1098-0121 10.1103/PhysRevB.89.195142 [47] 47 D. B. Williams and C. B. Carter , Transmission Electron Microscopy ( Plenum , New York, 1996 ). [48] 48 A. K. Tagantsev , L. E. Cross , and J. Fousek , Domains in Ferroic Crystals and Thin Films ( Springer New York, 2010 ). [49] 49 A. K. Tagantsev , E. Courtens , and L. Arzel , Phys. Rev. B 64 , 224107 ( 2001 ). PRBMDO 0163-1829 10.1103/PhysRevB.64.224107 [50] 50 T. Jungk , A. Hoffmann , M. Fiebig , and E. Soergel , Appl. Phys. Lett. 97 , 012904 ( 2010 ). APPLAB 0003-6951 10.1063/1.3460286 [51] 51 S. M. Griffin, M. Lilienblum , K. T. Delaney , Y. Kumagai , M. Fiebig , and N. A. Spaldin , Phys. Rev. X 2 , 041022 ( 2012 ). PRXHAE 2160-3308 10.1103/PhysRevX.2.041022 [52] 52 S. Artyukhin , K. T. Delaney , N. A. Spaldin , and M. Mostovoy , Nat. Mater. 13 , 42 ( 2014 ). NMAACR 1476-1122 10.1038/nmat3786 [53] 53 T. Matsumoto , R. Ishikawa , T. Tohei , H. Kimura , Q. Yao , H. Zhao , X. Wang , D. Chen , Z. Cheng , N. Shibata , and Y. Ikuhara , Nano Lett. 13 , 4594 ( 2013 ). NALEFD 1530-6984 10.1021/nl402158c [54] 54 J. Li , F.-K. Chiang , Z. Chen , C. Ma , M.-W. Chu , C.-H. Chen , H. Tian , H. Yang , and J. Li , Sci. Rep. 6 , 28047 ( 2016 ). SRCEC3 2045-2322 10.1038/srep28047 [55] 55 Z. Chen , X. Wang , S. P. Ringer , and X. Liao , Phys. Rev. Lett. 117 , 027601 ( 2016 ). PRLTAO 0031-9007 10.1103/PhysRevLett.117.027601 [56] 56 S. Cheng, J. Li , M. G. Han , S. Deng , G. Tan , X. Zhang , J. Zhu , and Y. Zhu , Phys. Rev. Lett. 118 , 145501 ( 2017 ). PRLTAO 0031-9007 10.1103/PhysRevLett.118.145501 [57] 57 P. Tolédano , M. Guennou , and J. Kreisel , Phys. Rev. B 89 , 134104 ( 2014 ). PRBMDO 1098-0121 10.1103/PhysRevB.89.134104
PY - 2017/10/10
Y1 - 2017/10/10
N2 - Hybrid improper ferroelectricity (HIF) denotes a new class of polar instability by the mixture of two octahedral-distortion modes and can feature the coexistence of abundant head-to-head and tail-to-tail polar domains, of which the domain walls tend to be charged due to the respective screening charges with an opposite sign. However, no such coexisting carriers are available in the materials. Using group-theoretical, microscopic, and spectroscopic analyses, we establish the existence of a hidden antipolar order parameter in model HIF (Ca,Sr)3Ti2O7 by the condensation of a weak, previously unnoticed antipolar lattice instability, turning the order-parameter spaces to be multicomponent with the distinct polar-antipolar intertwining and accompanied formation of Néel-type twinlike antipolar domain walls (few nanometers) between the head-to-head and tail-to-tail domains. The finite-width Néel walls and correlated domain topology inherently lift the polar divergences between the domains, casting an emergent exemplification of charged domain-wall screening by an antipolar ingredient.
AB - Hybrid improper ferroelectricity (HIF) denotes a new class of polar instability by the mixture of two octahedral-distortion modes and can feature the coexistence of abundant head-to-head and tail-to-tail polar domains, of which the domain walls tend to be charged due to the respective screening charges with an opposite sign. However, no such coexisting carriers are available in the materials. Using group-theoretical, microscopic, and spectroscopic analyses, we establish the existence of a hidden antipolar order parameter in model HIF (Ca,Sr)3Ti2O7 by the condensation of a weak, previously unnoticed antipolar lattice instability, turning the order-parameter spaces to be multicomponent with the distinct polar-antipolar intertwining and accompanied formation of Néel-type twinlike antipolar domain walls (few nanometers) between the head-to-head and tail-to-tail domains. The finite-width Néel walls and correlated domain topology inherently lift the polar divergences between the domains, casting an emergent exemplification of charged domain-wall screening by an antipolar ingredient.
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U2 - 10.1103/PhysRevLett.119.157601
DO - 10.1103/PhysRevLett.119.157601
M3 - Article
C2 - 29077441
AN - SCOPUS:85031315310
VL - 119
JO - Physical Review Letters
JF - Physical Review Letters
SN - 0031-9007
IS - 15
M1 - 157601
ER -