Wall thickness dependence of the scaling law for ferroic stripe domains

Catalán, Gustau; Scott, J. F.; Schilling, A.; Gregg, J. M.; Street, Downing

doi:10.1088/0953-8984/19/2/022201

Cited by 82 publications

(81 citation statements)

References 34 publications

(62 reference statements)

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“…This equation is also useful in that it can be used in reverse in order to estimate the domain wall thickness of any ferroic with well-defined boundary conditions (Catalan et al, 2007a). Indirect versions of it have been calculated for the specific case of ferroelectrics (Lines and Glass, 2004;De Guerville et al, 2005), but in fact Eq.…”

Section: Wall Thickness and Universality Of Kittel's Lawmentioning

confidence: 99%

Domain wall nanoelectronics

et al. 2012

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Domains in ferroelectrics were considered to be well understood by the middle of the last century: They were generally rectilinear, and their walls were Ising-like. Their simplicity stood in stark contrast to the more complex Bloch walls or Néel walls in magnets. Only within the past decade and with the introduction of atomic-resolution studies via transmission electron microscopy, electron holography, and atomic force microscopy with polarization sensitivity has their real complexity been revealed. Additional phenomena appear in recent studies, especially of magnetoelectric materials, where functional properties inside domain walls are being directly measured. In this paper these studies are reviewed, focusing attention on ferroelectrics and multiferroics but making comparisons where possible with magnetic domains and domain walls. An important part of this review will concern device applications, with the spotlight on a new paradigm of ferroic devices where the domain walls, rather than the domains, are the active element. Here magnetic wall microelectronics is already in full swing, owing largely to the work of Cowburn and of Parkin and their colleagues. These devices exploit the high domain wall mobilities in magnets and their resulting high velocities, which can be supersonic, as shown by Kreines' and co-workers 30 years ago. By comparison, nanoelectronic devices employing ferroelectric domain walls often have slower domain wall speeds, but may exploit their smaller size as well as their different functional properties. These include domain wall conductivity (metallic or even superconducting in bulk insulating or semiconducting oxides) and the fact that domain walls can be ferromagnetic while the surrounding domains are not.

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Section: Wall Thickness and Universality Of Kittel's Lawmentioning

confidence: 99%

Domain wall nanoelectronics

et al. 2012

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“…S10). ω should scale with the total crystal thickness along its polar axis, D, as ω = a · D γ , where a is a prefactor that depends on the domain-wall thickness and γ is theoretically 0.5 (42,43) and empirically between ∼0.4 and 0.6 (67)(68)(69). By relating ω to D from several single crystals (without grain boundaries; SI Appendix, Fig.…”

Section: Applied Physical Sciencesmentioning

confidence: 99%

Tetragonal CH ₃ NH ₃ PbI ₃ is ferroelectric

Rakita

Bar-Elli

Meirzadeh

et al. 2017

Proc. Natl. Acad. Sci. U.S.A.

255

221

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Halide perovskite (HaP) semiconductors are revolutionizing photovoltaic (PV) solar energy conversion by showing remarkable performance of solar cells made with HaPs, especially tetragonal methylammonium lead triiodide (MAPbI 3 ). In particular, the low voltage loss of these cells implies a remarkably low recombination rate of photogenerated carriers. It was suggested that low recombination can be due to the spatial separation of electrons and holes, a possibility if MAPbI 3 is a semiconducting ferroelectric, which, however, requires clear experimental evidence. As a first step, we show that, in operando, MAPbI 3 (unlike MAPbBr 3 ) is pyroelectric, which implies it can be ferroelectric. The next step, proving it is (not) ferroelectric, is challenging, because of the material's relatively high electrical conductance (a consequence of an optical band gap suitable for PV conversion) and low stability under high applied bias voltage. This excludes normal measurements of a ferroelectric hysteresis loop, to prove ferroelectricity's hallmark switchable polarization. By adopting an approach suitable for electrically leaky materials as MAPbI 3 , we show here ferroelectric hysteresis from well-characterized single crystals at low temperature (still within the tetragonal phase, which is stable at room temperature). By chemical etching, we also can image the structural fingerprint for ferroelectricity, polar domains, periodically stacked along the polar axis of the crystal, which, as predicted by theory, scale with the overall crystal size. We also succeeded in detecting clear second harmonic generation, direct evidence for the material's noncentrosymmetry. We note that the material's ferroelectric nature, can, but need not be important in a PV cell at room temperature.halide perovskites | photovoltaics | semiconductors | ferroelectricity | pyroelectricity N ew optoelectronic materials are of interest for producing solar cells with higher power and voltage efficiencies, lower costs, and improved long-term reliability. A very recent entry is the family of halide perovskites (HaPs), in particular those based on methylammonium (MA) lead iodide (MAPbI 3 ), MAPbBr 3 , and its inorganic analog CsPbBr 3 . Devices based on these perform remarkably well as solar cells (1, 2), as well as in other optoelectronic applications, such as LEDs and electromagnetic radiation detectors (3-5). Understanding possible unique characteristics of HaPs may show the way to other materials with similar key features.The ABX 3 (X = I, Br, Cl) HaP semiconductors (SCs), that is, with perovskite or perovskite-like structures, reach, via a steep absorption edge, a high optical absorption coefficient (∼10 5 cm −1 ) (6, 7), long charge carrier lifetimes (∼0.1-1 μs) (8), and reasonable carrier mobilities (less than or equal to ∼100 cm 2 ·V −1 ·s −1 ) (9), and have a low exciton binding energy (10). With these characteristics, the thickness of the optical absorber layer can be ≤0.5 μm, which allows the charge carriers (separated electrons and holes) to diffuse/d...

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“…For comparison, equivalent data for domains in other ferroic systems (ferroelectric or ferromagnetic) are included. Ferroelectric domains are generally smaller than ferromagnetic domains [18][19][20][21], but the ferroelectric domains in BFO are noticeably bigger, and close to the domain size of magnetic Co. This suggests a higher energy cost of the domain walls [21,22], consistent with a strong magnetoelectric coupling at the wall [6].…”

mentioning

confidence: 99%

“…Ferroelectric domains are generally smaller than ferromagnetic domains [18][19][20][21], but the ferroelectric domains in BFO are noticeably bigger, and close to the domain size of magnetic Co. This suggests a higher energy cost of the domain walls [21,22], consistent with a strong magnetoelectric coupling at the wall [6]. This contrasts with the apparently low intrinsic magnetoelectric coupling of the bulk material [23], and underlines the interest of domain walls as multiferroic entities in their own right [24].…”

mentioning

confidence: 99%

Fractal Dimension and Size Scaling of Domains in Thin Films of MultiferroicBiFeO3

et al. 2008

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Domains in ferroelectric films are usually smooth, stripelike, very thin compared with magnetic ones, and satisfy the Landau-Lifshitz-Kittel scaling law (width proportional to square root of film thickness). However, the ferroelectric domains in very thin films of multiferroic BiFeO 3 have irregular domain walls characterized by a roughness exponent 0.5-0.6 and in-plane fractal Hausdorff dimension H jj 1:4 0:1, and the domain size scales with an exponent 0:59 0:08 rather than 1 2 . The domains are significantly larger than those of other ferroelectrics of the same thickness, and closer in size to those of magnetic materials, which is consistent with a strong magnetoelectric coupling at the walls. A general model is proposed for ferroelectrics, ferroelastics or ferromagnetic domains which relates the fractal dimension of the walls to domain size scaling.

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Wall thickness dependence of the scaling law for ferroic stripe domains

Cited by 82 publications

References 34 publications

Domain wall nanoelectronics

Domain wall nanoelectronics

Tetragonal CH ₃ NH ₃ PbI ₃ is ferroelectric

Fractal Dimension and Size Scaling of Domains in Thin Films of MultiferroicBiFeO3

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Wall thickness dependence of the scaling law for ferroic stripe domains

Cited by 82 publications

References 34 publications

Domain wall nanoelectronics

Domain wall nanoelectronics

Tetragonal CH 3 NH 3 PbI 3 is ferroelectric

Fractal Dimension and Size Scaling of Domains in Thin Films of MultiferroicBiFeO3

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Tetragonal CH ₃ NH ₃ PbI ₃ is ferroelectric