Bratkovsky and Levanyuk Reply:

Bratkovsky, A. M.; Levanyuk, A. P.

doi:10.1103/physrevlett.87.179703

Cited by 159 publications

(370 citation statements)

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“…In very thin films the interaction between the two opposite surfaces [35], dead layers [36,37] or ferroelastic effects [38][39][40] can induce a departure from LLK, often in the form of a divergence in domain size for very small thickness. On the other hand, experimentally, for perovskite ferroelectrics the LLK holds down to smaller thickness than those studied here (Fig.…”

Section: -2 Value Ofmentioning

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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Section: -2 Value Ofmentioning

confidence: 99%

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

et al. 2008

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“…21 , 22 Formation and stability of 90° domain structures in epitaxial films of ferroelectricinsipient ferroelastic under the misfit strain influence were considered by different groups, with special attention to the period and conditions of existence 23,24,25 and transition between monodomain and polydomain structures. 26 However, the details of domain walls structure were not considered in these studies. Domain walls structure in proper ferroelastic was considered by Salje et al 27 , 28 , 29 It was found 28 that nonzero internal stress exists at a domain wall due to coupling between primary order parameter (shear strain) and dilatation strains there.…”

Section: Introductionmentioning

confidence: 99%

“…Consequently, polarization and/or elastic strain in the multidomain state are typically considered using harmonic function approximation, 2,13,26 which is indeed reasonable near the phase transition point, but this approximation could not allow one to grasp the domain walls details for the case of developed domain structure. In contrast, in the paper we derive the domain wall profile near the surface self-consistently using perturbation theory.…”

Section: Introductionmentioning

confidence: 99%

Surface effect on domain wall width in ferroelectrics

Eliseev

Morozovska

Kalinin

et al. 2009

Journal of Applied Physics

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We study the effect of depolarization field related with inhomogeneous polarization distribution, strain and surface energy parameters on a domain wall profile near the surface of a ferroelectric film within the framework of Landau-Ginzburg-Devonshire phenomenology. Both inhomogeneous elastic stress and positive surface energy lead to the wall broadening at electrically screened surface. For ferroelectrics with weak piezoelectric coupling, the extrapolation length that defines surface energy parameter, affects the wall broadening more strongly than inhomogeneous elastic stress. Unexpectedly, the domain wall profile follows a long-range power law when approaching the surface, while it saturates exponentially in the bulk.In materials with high piezoelectric coupling and negligibly small surface energy (i.e. high extrapolation length) inhomogeneous elastic stress effect dominates.

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“…In this case the linear response of 180 0 domain structure without pinning is not affected by intimate contact between the ferroelectric and the dead layer (excluding mere renormalization of materials constants by homogeneous stresses). Note that this is invalid in the case of 90 o domains [8] or a linear coupling between the strain and the polarization [9]. Here we address the anomalous behavior of the dielectric constant ǫ ef f in detail.…”

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confidence: 99%

Very large dielectric response of thin ferroelectric films with the dead layers

2001

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We study the dielectric response of ferroelectric (FE) thin films with "dead" dielectric layer at the interface with electrodes. The domain structure inevitably forms in the FE film in presence of the dead layer. As a result, the effective dielectric constant of the capacitor ǫ ef f increases abruptly when the dead layer is thin and, consequently, the pattern of 180-degree domains becomes "soft". We compare the exact results for this problem with the description in terms of a popular "capacitor" model, which is shown to give qualitatively incorrect results. We relate the present results to fatigue observed in thin ferroelectric films. 77.22.Ch, 77.80.Dj, 84.32.Tt, 85.50.+k We have shown recently that the dead layer forming at the interface between ferroelectric (FE) thin film and electrodes has drastic effect on the electric response of a capacitor [1]. It has direct bearing on fatigue observed in FE capacitors since in many cases the deterioration of the switching behavior, like the loss of the coercive force and of the squareness of hysteresis loop, were attributed to the growth of a "passive layer" at the ferroelectricelectrode interface [2][3][4][5]. It is of principal importance that the presence of a dead layer, no matter how thin in comparison with thickness of the ferroelectric layer, triggers a formation of the domain structure in FE film [1]. We have shown that when the thickness of the dead layer d is not very small, the apparent (net) polarization P a of the ferroelectric with 180−degree domain walls follows an approximate relation dP a /dE ∝ ǫ g /d, which is in good correspondence with available experimental data (see e.g. [6,7] and references therein). Importantly, the response of this structure to an external bias voltage becomes more rigid when d increases, i.e. when the dead layer grows, even in the absence of pinning by defects.The implication for real systems is that with the growth of the passive layer the hysteresis loop very quickly deteriorates and looses its squareness, as observed. The approximate 1/d dependence of the response suggests that the effective dielectric constant of the capacitormay become very large when the layer is thin. Here C is the capacitance of the electroded FE film of area A, with L the separation between electrodes. Indeed, when the dead layer is thin, the domain width a becomes very large, it grows exponentially with 1/d 2 [1]. The response of this domain structure is very soft, and this should translate into very abrupt increase of the dielectric constant ǫ ef f of the capacitor. It is easy to show that in the present case (180 o domains) the linear response is not changed by electromechanical effect, the change in ǫ ef f only appearing in quadratic terms in external field, but here we are interested in zero-field value of ǫ ef f only. We have assumed a quadratic coupling between the elastic strains and the polarization (as in perovskites). In this case the linear response of 180 0 domain structure without pinning is not affected by intimate contact between th...

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Bratkovsky and Levanyuk Reply:

Cited by 159 publications

References 4 publications

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

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

Surface effect on domain wall width in ferroelectrics

Very large dielectric response of thin ferroelectric films with the dead layers

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