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Bratkovsky and Levanyuk Reply:The main new result of our paper [1] is that the ferroelectric (FE) with the dead layer of thickness d is always split into domains, no matter how thin the layer is. We have found that the width of the domains a depends exponentially on d 22 when the dead layer is thin. We have also evaluated the response of the structure to external field (Fig. 2 in [1], and Ref. [2]). In the Comment [3] Tagantsev has tried to interpret our approximate Eq. (14), which he misrepresented as the main result of the Letter, within the "capacitors in series" model, by assuming that the dielectric constant of the FE is infinite, e f `.However, Tagantsev has failed to notice that e f , as found in the "capacitor" model, is not infinite, but finite and actually negative. Indeed, a simple calculation in the capacitor model gives [2]

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We study the domain structure in ferroelectric thin films with a 'passive' layer (material with damaged ferroelectric properties) at the interface between the film and electrodes within a continuous medium approximation. An abrupt transition from a monodomain to a polydomain state has been found with the increase of the 'passive' layer thickness d. The domain width changes very quickly at the transition (exponentially with d −2 ). We have estimated the dielectric response dP/dE (the slope of the hysteresis loop) in the 'fatigued' multidomain state and found that it is in agreement with experiment, assuming realistic parameters of the layer. We derive a simple universal relation for the dielectric response, which scales as 1/d, involving only the properties of the passive layer. This relation qualitatively reproduces the evolution of the hysteresis loop in fatigued samples and it could be tested with controlled experiments. It is expected that the coercive field should increase with decreasing lateral size of the film. We believe that specific properties of the domain structure under bias voltage in ferroelectrics with a passive layer can resolve the long-standing 'paradox of the coercive field 77.80.Dj, 84.32.Tt, 85.50.+k Recent studies of thin ferroelectric films have revived interest in properties of the ferroelectric domain structures. It became clear that some basic aspects of these properties remain unexplored, whereas they are of key importance for applications. For instance, the progressive loss of switchable polarization after repeated switching cycles, i.e. polarization fatigue, is a serious problem in device applications of ferroelectrics. In spite of extensive studies, the physics of the fatigue remains poorly understood. Various mechanisms were considered over the years [1][2][3][4][5][6][7][8]. 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 ferroelectric-electrode interface [1,3,6], or to the pinning of domain walls by defects [2,4]. In this paper, we study the effects of a passive layer (material with damaged ferroelectric properties). We assume an ideal infinite ferroelectric film and treat it within the continuous medium approximation. The model exhibits very interesting properties relevant for real systems.The passive layer leads to the appearance of a depolarizing field in the ferroelectric, so that the system would tend to transform to a polydomain state in order to reduce the field. There is, therefore, a transition between the monodomain state, when the thickness d of the passive layer is zero, to a polydomain state otherwise. What is the nature of this transition? This is the main theoretical question we address in this paper.For a short-circuited infinite ferroelectric plate, as we shall show, the domain structure exists for any value of the passive layer thickness, in disagreement with some earlier results [9]. A surprising feature of the ...