Topological vortices with complex domains and domain walls exist in hexagonal manganites, which undergo a structural transition accompanying ferroelectric polarization and trimerization. We have systematically studied the origin of two different types (type-I and type-II) of vortex domains with controlled oxygen stoichiometry and found that the evolution between type-I and type-II vortex domains and the presence of charged walls between two different trimerization antiphase domains result from an oxygen vacancy gradient. We have also discovered a rare phenomenon of vortex core split, which appears to stem from the instability of charged ferroelectric walls between domains with the same trimerization antiphase.

Chemical composition variation is a critical factor for functionalities of a wide range of ferroelectrics and pyroelectrics, which are important for application as an active component in various electronics. This is because ions can provide surface charge compensation for electric polarization. For example, Li defect gradient results in abundant charged ferroelectric domain walls in LiNbO3,1–3 and a ferroelectric mono-domain can be reversibly induced by varying oxygen stoichiometry.4 Thus, controlling chemical composition can result in manipulation of domains and functionalities of ferroelectric and pyroelectric materials, including hexagonal manganites.

Hexagonal manganites (h-RMnO3: R = rare earths) exhibit improper ferroelectricity accompanying topological defects in a trimerized ferroelectric lattice, which coexists with magnetic order, i.e., becomes multiferroic, at low temperatures.5,6 The origin of trimerization is caused by the size mismatch between R and Mn-O layers, which leads to three trimerization antiphases (α, β, γ).7 Due to a subsequent ionic displacement with a net electric dipole moment, each trimerization phase can supply two different ferroelectric polarizations (+, −, meaning upward or downward along the c axis).8–12 These six trimerization antiphase and ferroelectric domains cycle around a merging point with alternating ferroelectric polarization and trimerization antiphases in two different domain configurations: (α+, β, γ+, α, β+, γ) or (α+, γ, β+, α, γ+, β), which can be viewed as a vortex and an anti-vortex. These vortices/antivortices are found to be associated with intriguing collective magnetism,13 electric conductance14,15 at domain walls, as well as large magnetoelectric coupling of domains,16 unveiled using magnetic force microscope, conductive-atomic force microscope, and magnetoelectric force microscope techniques.17 Landau theory with parameters determined from first-principles calculations indicates that the vortices are topological defects with emergence of Z2 × Z3 symmetry and the unique coupling between the ferroelectric and magnetic domain walls.18,19

A network of vortices and antivortices in h-RMnO3 can be neatly analyzed in terms of graph theory.20 The density of vortex network strongly varies depending on heat treatment conditions. When h-RMnO3 crystals are grown below the ferroelectric-trimerization transition temperature (Tc), they exhibit stripe domains. However, when a h-RMnO3 crystal with stripe domains is heated above and cooled down across Tc, vortex domains form everywhere in the crystal, and the density of vortices decreases with the decreasing cooling rate across Tc.21–23 It turns out that the zoo of Z2 × Z3 vortices is, in fact, a forest of thermally excited three-dimensional vortex lines spanning the entire crystal, which result from the emergent continuous U(1) symmetry near the critical temperature.24 It appears that the Kibble-Zurek mechanism,25–28 which is initially proposed to explain the early universe formation, is also responsible for the network formation of multiferroic vortices through a continuous phase transition.26,29

The networks of vortices are found to be in two different types: type-I domains with roughly equal fractions of upward and downward polarization domains as shown in Figs. 1(a) and 1(c), and type-II domains with one dominant polarization displayed in Figs. 1(b) and 1(d).20,30 An internal self-electric-poling effect was proposed to be responsible for the dominance of one polarization domains, which may be induced by oxygen off-stoichiometry near the surfaces.17 However, the detailed nature of this self-poling is still not well investigated. Here, we report experimental systematics of self-poling process with different heat treatments for varying oxygen content and also depth profiling of domain topology with varying degree of chemical etching. This paper is organized as follows: (1) First, we discuss how the oxygen vacancies influence domains structure on HoMnO3 (Tc ≈ 1050 °C) utilizing different annealing environments and the evolution between type-I and type-II domains in LuMnO3 (Tc ≈ 1400 °C). (2) Second, we discuss the connection between self-poling in YbMnO3 (Tc ≈ 1350 °C) with external electric field poling in YMnO3 (Tc ≈ 970 °C). (3) Then, we explain complex domain structures in YbMnO3, which are induced by different oxygen vacancy distributions. (4) Last but not least, we present an extreme self-poling effect in Y bMnO3, resulting in vortex core fragmentation.

FIG. 1.

Optical microscope images of HoMnO3 after chemical etching: (a) the specimen is annealed above Tc in Ar flow, showing type-I vortex network. (b) Another piece annealed above Tc in Ar flow is re-annealed at 700 °C in air, showing type-II vortex network. The corresponding schematics for the boxed regions are displayed in (c) and (d), respectively.

FIG. 1.

Optical microscope images of HoMnO3 after chemical etching: (a) the specimen is annealed above Tc in Ar flow, showing type-I vortex network. (b) Another piece annealed above Tc in Ar flow is re-annealed at 700 °C in air, showing type-II vortex network. The corresponding schematics for the boxed regions are displayed in (c) and (d), respectively.

Close modal

All h-RMnO3 crystal specimens were grown by a flux method: 10 mol. % RMnO3 polycrystalline powders with 90 mol. % Bi2O3 powders as flux were heated to 1250 °C and then cooled slowly to 800 °C in a platinum crucible. Plates-like crystals can be found with a center meter size in the a-b plane and hundreds microns thickness along the c axis. In order to visualize domain patterns, crystal specimens were etched chemically in phosphoric acid at 150 °C. The domain patterns of chemically etched crystals are observable using topography-sensitive techniques such as an optical microscopy (Zeiss Microscope) and an atomic force microscopy, AFM (Nanoscope IIIA, Veeco with WSXM software),31 as phosphoric acid preferentially etches the surface of upward-polarization domains.

When a h − RMnO3 crystal is heated to high temperatures above, for example, 1000 °C, due to sufficient thermal energy and large ionic diffusion, the crystal tends to have rather uniform oxygen vacancies throughout the entire crystal. However, during cooling process in atmosphere with sufficient oxygen, around a 700 °C range, oxygen diffusion into the crystal occurs, but is limited in the surface area due to a limited diffusion length, unless the cooling rate is unrealistically slow. Thus, it is natural to have an oxygen vacancy gradient from the surface to inside of a crystal; in other words, surface is more-or-less oxygen stoichiometric, but significant oxygen vacancies may exist inside of the crystal. In order to explore the effect of oxygen off-stoichiometry on domain networks, we annealed two HoMnO3 single crystals together above Tc in Ar atmosphere and slowly cooled to ∼1000 °C in 2 h. Afterwards, they were quickly cooled down to room temperature to avoid any surface oxidation at lower temperatures. After this heat treatment, one crystal was chemically etched, and its optical microscope image is shown in Fig. 1(a). The crystals after this heat treatment are expected to have uniform oxygen vacancies throughout the entire crystals. Indeed, Fig. 1(a) exhibits type-I domain network with roughly half-half distribution of upward and downward polarization domains in the entire surface. In other words, there is no preference between upward and downward polarization domains after this heat treatment. The second crystal was re-annealed in air at 700 °C for 5 h, and then followed by furnace cooling. This re-annealing in air is expected to result in oxidation of only near surfaces of the crystal due to limited oxygen diffusion length. As shown in Fig. 1(b), the crystal surface after this re-annealing, indeed, shows type-II domains with narrow downward polarization domains and broad upward polarization domains. The large gradient of oxygen vacancies with less oxygen vacancies near surfaces results in an effective upward internal electric field, which results in the energetic preference of upward polarization domains.

Type-II domains near the surface induced by oxygen vacancy gradient change into type-I domains inside of the crystal. The evolution of ferroelectric domain configuration along the c axis was investigated with sequential etching. One LuMnO3 crystal was heat-treated at 1450 °C in air, and then followed by furnace cooling to room temperature. The crystal was minimally etched for 10 min to reveal the domain pattern on the crystal surface. Its optical microscope image shown in Fig. 2(a) reveals clearly type-II domains on the crystal surface. However, the identical area after additional 30 min etching unveils type-I domains inside of the crystal as shown in Fig. 2(b). The schematics in Fig. 3(c) for the boxed areas in Figs. 3(a) and 3(b) show type-II domains (top) at the surface and inside type-I domains (middle). In fact, the combined cartoon (bottom) with both type-I and type-II domains corresponds to the image in Fig. 3(b).

FIG. 2.

Evolution from type-II to type-I domains with sequential etching. (a) Optical microscope image of a LuMnO3 crystal surface after 10 min chemical etching, showing type-II domains on the surface. (b) Optical microscope image on the identical region after additional 30 min etching. Type-I domains appear in addition to the original type-II domains. (c) Top: cartoon of blue-boxed region of the surface type-II domains. Middle: cartoon of inside type-I domains. Bottom: combination of type-I and type-II domains, corresponding to the red-boxed region in (b). White lines depict the surface type-II domain walls.

FIG. 2.

Evolution from type-II to type-I domains with sequential etching. (a) Optical microscope image of a LuMnO3 crystal surface after 10 min chemical etching, showing type-II domains on the surface. (b) Optical microscope image on the identical region after additional 30 min etching. Type-I domains appear in addition to the original type-II domains. (c) Top: cartoon of blue-boxed region of the surface type-II domains. Middle: cartoon of inside type-I domains. Bottom: combination of type-I and type-II domains, corresponding to the red-boxed region in (b). White lines depict the surface type-II domain walls.

Close modal
FIG. 3.

Comparison between self-poling due to an oxygen vacancy gradient and external electric polings. Optical microscope image of Ar-flow annealed Y bMnO3 after chemical etching shown in (a) exhibits type-I domains, but that of another Y bMnO3 crystal annealed in air shown in (b) demonstrates a self-poling effect near the surface. (c) is the corresponding 3-dimensional image. (d) and (e) indicate the schematics of oxygen vacancy distributions. Cross-sectional cartoons are shown of polarization domains along the green lines in (a) and (b), respectively. Note that in oxygen vacancy distribution cartoons, the y axes are depth in nanometers and the x axes are oxygen vacancy concentration δ of RMnO3-δ. (f) displays an AFM scanning image across an electric poling boundary, and the blue boxed region is enlarged in (g), demonstrating that electric poling changes type-I domains to type-II domains.

FIG. 3.

Comparison between self-poling due to an oxygen vacancy gradient and external electric polings. Optical microscope image of Ar-flow annealed Y bMnO3 after chemical etching shown in (a) exhibits type-I domains, but that of another Y bMnO3 crystal annealed in air shown in (b) demonstrates a self-poling effect near the surface. (c) is the corresponding 3-dimensional image. (d) and (e) indicate the schematics of oxygen vacancy distributions. Cross-sectional cartoons are shown of polarization domains along the green lines in (a) and (b), respectively. Note that in oxygen vacancy distribution cartoons, the y axes are depth in nanometers and the x axes are oxygen vacancy concentration δ of RMnO3-δ. (f) displays an AFM scanning image across an electric poling boundary, and the blue boxed region is enlarged in (g), demonstrating that electric poling changes type-I domains to type-II domains.

Close modal

This chemistry driven self-poling was also found in Y bMnO3. Fig. 3(a) displays the type-I domain network of a Y bMnO3 crystal, which is annealed at 1350 °C, followed by furnace cooling to 1180 °C, and then quenched to room temperature in Ar flow. This type-I domain network is due to no self-poling effect (i.e., no oxygen vacancy gradient). In contrast, another Y bMnO3 crystal was annealed at 1350 °C, and then furnace cooled in air. Due to oxygen absorption only near surfaces during cooling process, an oxygen vacancy gradient from the crystal surface to interior exists in the crystal. This leads to a self-poling effect and type-II domains near surface, which results in the bright narrow lines in the AFM scanning image in Fig. 3(b). However, inside of the crystal where oxidation during cooling did not occur due to oxygen diffusion limit, the surface type-II domains becomes type-I domains that appear as dark and middle-contrast domains in Fig. 3(b). Thus, the plateau of the middle-contrast domains exhibits the boundary between the uniformly oxygen-vacant interior and oxidized surface region. In other words, the height of the narrow bright domains reflects more-or-less the length of oxygen diffusion during cooling process in air. We emphasize that the AFM image seems to indicate nine domains merging at one point, but is, in fact, due to type-II domains on surface and inside type-I domains. The evolution of domain configuration is better shown in Fig. 3(c), which is the 3-dimensional image of Fig. 3(b). The corresponding schematics for the oxygen vacancy distribution and cartoons for cross-sectional polarization along the green line in Figs. 3(a) and 3(b) are displayed in Figs. 3(d) and 3(e), respectively. Note that during chemical etching, domains with upward polarization are etched faster than domains with downward polarization.

Since this self-poling effect is induced by an oxygen vacancy gradient, which produces an effective electric field along the c axis in h-RMnO3, applying a large external electric field should be able to result in switching type-I domains to type-II domains. The result of our electric field experiment is displayed in Fig. 3(f). External electric poling experiment was performed on an YMnO3 crystal with two Ag electrodes on the top and bottom a-b surfaces. We applied an external electric field of 200 kV/cm, which is larger than the coercive field of YMnO3. After electric field poling at 77 K, the Ag electrodes were removed mechanically. After chemical etching of the poled crystal, AFM scanning experiment was performed across the boundary (white dashed line) between the poled region and un-poled region. The un-poled region (the left side of white dashed line) exhibits type-I domains with roughly half and half distribution of upward and downward polarization domains, but the negative electric poled region (the left side of white dashed line) shows more-or-less type-II domains (dominant dark domains with upward polarization and narrow bright domains with downward polarization). The blue boxed region in Fig. 3(f) is enlarged in Fig. 3(g), where type-II domains seem evident in the electric poled region. We emphasize that compared with self-poling, a part of un-favored bright domains in type-II domains after poling is still somewhat broad, which demonstrates that electric poling is not very uniform unlike chemistry driven self-poling. By assuming the effective electric field induced by oxygen vacancy gradient same with that in the electric poling experiment (200 kV/cm) and the oxygen content of the oxidized surface exactly 3, and using the dielectric constant of ErMnO3,32 we estimate the oxygen vacancy concentration of the bulk RMnO3-δ crystal to be δ = 0.02. Note that this bulk oxygen content is very close to 3, and the oxidized surface region is very thin (on the order of 100 nm), so it is impractical to measure the oxygen vacancy concentration experimentally.

A similar behavior is also found in LuMnO3. A LuMnO3 crystal was heated to 1410 °C, and then furnace-cooled down to room temperature in air. After chemical etching, optical microscope image was taken on the crystal surface and is displayed in Fig. 4(a). AFM scanning experiments were performed on the red boxed and blue boxed regions, of which AFM images are displayed in Figs. 4(b) and 4(c), respectively. Line-scan profiles of both images along the green lines clearly show the surface type-II domains with un-favored narrow domains and the deep-inside type-II domains. A 3-dimensional cartoon in Fig. 4(d), constructed from the AFM images of Fig. 4(b) after chemical etching, displays the distribution of corresponding domains before chemical etching. Note that the sharp change from type-II to type-I domains induces the plateaus of middle-contrast domains, which defines charged tail-to-tail domain walls with different trimerization antiphase domains, flat along the a-b plane.

FIG. 4.

Optical microscope image of air-annealed LuMnO3 after chemical etching is shown in (a). (b) and (c) are AFM scanning images of the red and blue boxed regions in Fig. 4(a), respectively, and the line-scan profiles along the green lines. (d) 3-dimensional cartoon of domains before chemical etching, corresponding to (b).

FIG. 4.

Optical microscope image of air-annealed LuMnO3 after chemical etching is shown in (a). (b) and (c) are AFM scanning images of the red and blue boxed regions in Fig. 4(a), respectively, and the line-scan profiles along the green lines. (d) 3-dimensional cartoon of domains before chemical etching, corresponding to (b).

Close modal

One Y bMnO3 crystal, embedded in polycrystalline powders, was annealed at 1350 °C, slowly cooled to 1320 °C with 30 °C/h, and then fast cooled to room temperature in air. Due to oxygen trapped in powders and slow cooling across Tc, even more complex oxygen vacancy distribution occurs in the crystal and is responsible for domain patterns in Fig. 5. Wavy type-II domains on the crystal surface are due to fast cooling in the oxygen absorption temperature range such as 650 °C-800 °C, but smooth type-II domains are found inside of the crystal, as shown in the AFM image of Fig. 5(a). These inside type-II domains are due to a non-uniform oxygen vacancy distribution inside of the crystal. The corresponding schematic for the oxygen vacancy distribution and line-scan profile along the green line are displayed in Fig. 5(b). Schematics for domains near the surface and inside of the crystal are shown in the top and bottom of Fig. 5(c), respectively. Note that the surface domains and the inside domains share identical vortex cores, consistent with the notion that the density of vortex cores mostly depends on the cooling rate cross Tc.

FIG. 5.

AFM scanning image of one vortex-antivortex pair in Y bMnO3 is displayed in (a). The corresponding schematic for the oxygen vacancy distribution and line-scan profile along the green line are displayed in Fig. 5(b). Note that in the oxygen vacancy distribution cartoon in (b), the y axis is depth in nanometers and the x axis is oxygen vacancy concentration of RMnO3-δ. Schematics for domains near the surface and inside are displayed in the top and bottom of Fig. 5(c), respectively.

FIG. 5.

AFM scanning image of one vortex-antivortex pair in Y bMnO3 is displayed in (a). The corresponding schematic for the oxygen vacancy distribution and line-scan profile along the green line are displayed in Fig. 5(b). Note that in the oxygen vacancy distribution cartoon in (b), the y axis is depth in nanometers and the x axis is oxygen vacancy concentration of RMnO3-δ. Schematics for domains near the surface and inside are displayed in the top and bottom of Fig. 5(c), respectively.

Close modal

As we have explored numerous self-poling cases in h-RMnO3, we have discovered a rare self-poling phenomenon, as displayed in Fig. 6. One Y bMnO3 crystal was annealed in a manner similar with that for the Y bMnO3 crystal discussed above. This crystal was polished only one side and was ion-milled only at the polished surface, so the final specimen is mostly the un-polished virgin surface region. Fig. 6(a) shows a 7.5 × 3.5 μm large-range superlattice dark-field transmission electron microscope (DF-TEM) image performed with transmission electron microscope (JEOL-2010F) using a superlattice spot g + = 1/3(116). Bright and dark contrasts originates from the Friedel’s pair breaking due to the presence of 180° ferroelectric domains. The red, blue, and green-boxed areas in Fig. 6(a) exhibit broken vortex cores. This vortex core split is clearly visible in the magnified images in Figs. 6(b)6(d). One pair of type-I vortex and antivortex, where six domains merge at each core, can be found at the right-hand-side top of Fig. 6(a). However, most of vortex or antivortex cores are fragmented. Fig. 6(e) shows the schematic of all trimerization and ferroelectric domains. Not that the nature of trimerization antiphase and ferroelectric polarization of all domains is un-ambiguously identified using the Z2 × Z3–coloring rules.9,20–22

FIG. 6.

(a) A large-range superlattice dark-field TEM image shows vortex core split. This image is a mosaic of many dark-field TEM images taken using a g + = 1/3(116) spot. (b)–(d) are enlarged images for the red, blue, and green boxed regions, respectively. (e) displays the schematic of trimerization and ferroelectric domains.

FIG. 6.

(a) A large-range superlattice dark-field TEM image shows vortex core split. This image is a mosaic of many dark-field TEM images taken using a g + = 1/3(116) spot. (b)–(d) are enlarged images for the red, blue, and green boxed regions, respectively. (e) displays the schematic of trimerization and ferroelectric domains.

Close modal

We propose that the vortex core fragmentation originates from strong domain wall pinning and the high energy cost of charged head-to-head domain walls with the identical trimerization antiphase. In Fig. 7(a), six domain walls around one vortex core on a crystal surface are shown as blue dashed lines, and inside six domain walls with a tilted vortex core are displayed as red dashed lines. The domains at the surface and inside of the crystal are labeled with black and gray (α+, β, γ+, α, β+, γ) letters, respectively. This tilted vortex core results in a charged head-to-head domain wall with one trimerization antiphase, as shown in the purple region of Fig. 7(a). Fig. 7(b) displays a cross-sectional cartoon for the tilted vortex core and the charged head-to-head wall of γ domains. This wall between the top γ domain and bottom γ+ domain costs large domain wall energy, and extremely unstable, as evident in the free energy landscape shown in Fig. 7(d). In the Mexican-hat-type energy landscape, the energy barrier between, for example, two neighboring β and α+ domains (black dashed-line) is small, but the energy barrier between γ and γ+ domains (pink dashed curve) is much larger.18,33 This positively charged domain wall between γ and γ+ domains can be readily removed by upward effective electric field due to oxygen vacancy gradient. As schematically shown in Fig. 7(c), this effect combined with strong pinning of domain walls at the surface, probably due to impurities at the surface, results in expansion of γ+ domain to γ domain regions at the surface and also the vortex core split. This scenario is in accordance with our DF-TEM results, as shown in Figs. 7(e) and 7(f). Note that in most cases of self-poling, we observed the evolution from type-I to type-II domains without any change of vortex cores, which corresponds to vortex core pinning. However, in this particular sample, we suspect that the vortex cores are highly tilted away from the c axis and domain wall pinning is particularly strong at the surface, leading to the vortex core fragmentation.

FIG. 7.

Schematics showing the planar view (a) and side view (b) of a highly tilted vortex core away from the c axis. Blue and red dashed lines represent the surface and inside vortex domains, respectively. The presence of positively charged walls (purple region in (a)) of γ domains is evident in (a) and (b). (c) Schematic diagram showing a vortex core split after removing positively charged walls of γ domains. Newly formed domain walls after vortex core split are displayed with the green lines. (d) Mexican-hat-type free energy landscape for six trimerization and ferroelectric phases in h-RMnO3.18 Black dashed line represents a small energy barrier between two neighboring phases, and the pink dashed curve indicates a high energy route between γ+ and γ phases. (e) Schematic for the red boxed area in Fig. 6(a) displays trimerization and ferroelectric phases, vortex core split, and expansion of γ+ into γ domains. (f) DF-TEM image taken using a g − = 1/3(1 1 6) spot shows opposite contrast to Fig. 6(b) with identified trimerization and ferroelectric phases. Green lines display the newly formed domain walls after vortex core split.

FIG. 7.

Schematics showing the planar view (a) and side view (b) of a highly tilted vortex core away from the c axis. Blue and red dashed lines represent the surface and inside vortex domains, respectively. The presence of positively charged walls (purple region in (a)) of γ domains is evident in (a) and (b). (c) Schematic diagram showing a vortex core split after removing positively charged walls of γ domains. Newly formed domain walls after vortex core split are displayed with the green lines. (d) Mexican-hat-type free energy landscape for six trimerization and ferroelectric phases in h-RMnO3.18 Black dashed line represents a small energy barrier between two neighboring phases, and the pink dashed curve indicates a high energy route between γ+ and γ phases. (e) Schematic for the red boxed area in Fig. 6(a) displays trimerization and ferroelectric phases, vortex core split, and expansion of γ+ into γ domains. (f) DF-TEM image taken using a g − = 1/3(1 1 6) spot shows opposite contrast to Fig. 6(b) with identified trimerization and ferroelectric phases. Green lines display the newly formed domain walls after vortex core split.

Close modal

In summary, we have clarified the origin of two types of topological vortex domains in bulk crystals of hexagonal manganites, one of which is induced by self-poling due to oxygen off-stoichiometry. From comprehensive exploration of a large number of well-controlled crystal specimens, we found that the nature of self-poling is much richer than that ever reported: the change from type-II domains at the surface into bulk type-I domains induced by oxygen vacancy gradient, the change between two different type-II domains with opposite preferred polarization directions induced by non-monotonic oxygen vacancy distribution, and the presence of charged walls between two different trimerization antiphase domains associated with these domain configuration changes. These domain configuration changes are usually accompanied by strong vortex core pinning. However, we have also observed an extreme self-poling effect with strong vortex domain wall pinning, resulting in vortex core fragmentation. This vortex core fragmentation appears to stem from the high instability of charged ferroelectric domain walls with the same trimerization phase. Our findings unveil the rich self-poling characteristics in hexagonal manganites and provide new insights into manipulating domains in complex ferroelectrics and polar materials by controlling chemistry.

We thank Yoichi Horibe and Seung Chul Chae for stimulating discussion. This work is supported by the Gordon and Betty Moore Foundation’s EPiQS Initiative through Grant No. GBMF4413 to the Rutgers Center for Emergent Materials. F.F. is also supported by China Scholarship Council.

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