The amplitudes of electric-field-induced translational vibrations of 90 ± domain walls formed in a tetragonal ferroelectric thin film grown on a cubic substrate are calculated theoretically. The domain wall contribution to the dielectric response of an epitaxial film is evaluated and shown to be important in common heterostructures. In some special film/substrate systems this contribution must increase rapidly with decreasing film thickness, which may result in a giant dielectric anomaly. PACS numbers: 77.80.Dj, 77.22.Ch, 77.55.+f Considerable current interest in ferroelectric thin films is due to their numerous potential applications in electronic devices, which utilize the unique dielectric, pyroelectric, piezoelectric, and electro-optic properties of ferroelectric materials. For many applications, such as dynamic random access memory with very large scale integration, highfrequency transducers, thermistors, and electroluminescent displays, the fabrication of thin films with large electric permittivities is especially important.Recent experimental studies [1][2][3][4][5] have found that, in tetragonal ferroelectric thin films epitaxially grown on cubic substrate, elastic domains (twins) may form during the preparation of heterostructures. The 90 ± domain structure of an epitaxial film has a strong impact on the hysteretic polarization behavior of a ferroelectric layer [4,6]. It may be expected that the formation of 90 ± domain walls in the epitaxial film can also increase markedly its electric permittivity because of the field-induced translational displacements of the walls. Indeed these ferroelastic domain walls, in contrast to the purely ferroelectric 180 ± walls, have a thickness much larger than the unit cell size (about 100 Å in BaTiO 3 [7]) so that the lattice potential barriers hindering their translational motion must be negligible. This supposition is strongly supported by the dielectric measurements on bulk BaTiO 3 single crystals with a laminar 90 ± domain structure [8], which clearly demonstrate that displacements of the 90 ± wall can be induced even by a weak measuring field E ϳ 1 kV͞m. In addition, it has been shown [9-13] that the vibrational motion of 90 ± walls must contribute considerably to the dielectric response of tetragonal ferroelectric ceramics.The above considerations motivated us to perform the first theoretical analysis of the domain wall vibrations in epitaxial ferroelectric thin films. In this Letter, we show that very large permittivities e ϳ 10 5 may arise from these vibrations in the heterostructures involving ultrathin films and pairs of materials having lattice misfits near some special value.Consider a thin tetragonal ferroelectric film epitaxially grown on a cubic substrate with the (001) plane parallel to the surface. Three variants of elastic domains can ex-ist in such a film: c domains with the tetragonal c axis perpendicular to the film surface and a 1 and a 2 domains in which the c axes are parallel to the [100] and [010] axes of the substrate, respectively. In acco...