We report on the thickness dependence of the ferroelastic domains of PbTiO 3 films grown on (110)-DyScO 3 with low thicknesses (up to 240 nm), which fall outside the validity range of the square root law proposed by Roytburd. For slow-grown films, the data reveal the linear thickness dependence predicted by Pertsev and Zembilgotov, using a complete elastic description, while a 2/3 scaling exponent is found for fast-grown films. Extremely long domains running all through the samples have been observed in the latter case, compared to the short domains observed in slow-grown films. These differences are ascribed to the in-plane anisotropy for domain wall nucleation, which is likely caused by the anisotropic elastic modulus of the substrate. V C 2013 AIP Publishing LLC.[http://dx.doi.org/10.1063/1.4823536]The response of domains and domain walls crucially affects (and often determines) the dielectric properties and switching behavior of ferroelectrics. This is particularly important in thin films where the ferroelectric (180 ) and ferroelastic (non-180 ) domain walls are formed in order to comply with the stringent electrical (large depolarizing field) and mechanical (substrate mismatch strain and clamping) boundary conditions.The size of the domains increases with increasing film thickness as a result of the balance between the depolarizing field energy (for 180 domains) 1 or elastic strain energy (for non-180 domains) 2 and the domain wall formation energy. Thus, the thinner the films, the larger the domain wall density and the greater the influence of the walls on the ferroelectric properties. Moreover, domain walls break spatial symmetry and could add functionalities to the films when present in large amounts. 3 It is therefore most relevant to have good control of the domain formation and the density of domain walls. 4 Domain formation in ferroelectrics has been largely studied. 2,3,[5][6][7][8][9][10][11][12][13][14][15] In order to adapt to the substrate and to locally minimize the mismatch strain or the depolarizing field, the domains form in a periodic manner. 6,7 It is known that there is a quadratic dependence, W / d 1=2 , of the domain width (W) with the crystal thickness (b). In ferroelastic domains (typically 90 domains), this b 1=2 dependence is an approximation in the regime of d ) W. 2 For smaller thicknesses, a linear dependence has been predicted by Pertsev and Zembilgotov (P&Z), 8 but it has not been experimentally confirmed yet.In this paper we investigate the thickness dependence of the periodicity of ferroelastic 90 domains (a/c twins) in the lower thickness regime using PbTiO 3 films grown on DyScO 3 substrates. This combination is chosen because there is a very small lattice mismatch between film and substrate at the growth temperature. This minimizes the formation of defects during growth. As the films are cooled down strain develops and can be relaxed by forming a/c domains. The absence of defects allows these domains to form in a very periodic fashion. 13,16 Interestingly, when the films...