Effective piezoelectric response of twin walls in ferroelectrics

Abstract

The effective piezoelectric coefficients of twin walls in tetragonal ferroelectric are calculated in the framework of decoupling approximation and Landau-Ginzburg-Devonshire theory allowing for polarization gradient terms, electrostriction and flexoelectric coupling. Using an example of piezoelectric response of a 1 -a 2 twins to a homogeneous electric field, we show that the response is almost independent on the flexoelectric coupling, but is very sensitive to the values of polarization gradient coefficients. This behavior originates from the strong coupling between local dielectric susceptibility and the gradient coefficients. The enhancement of piezoelectric response from 10% up to a factor of 10 3 times is predicted. The local electromechanical response of the domain walls can thus provide information on the gradient terms in GLD expansion and pinning mechanisms of the ferroelectric domain walls. The observability of these effects by the piezoresponse force microscopy of electroded structures and impact on the functional properties of the systems with dense domain structures is analyzed.* morozo@i.com.ua † sergei2@ornl.gov 2

Stationary domain wall contribution to enhanced ferroelectric susceptibility

“…(B670), the calculated intrinsic dielectric permittivity (B245) and by assuming the domain wall width to be (conservatively) 1-10 nm [39][40][41][42]47 , one can estimate e dw to be 1,500-19,000, which is 6-78 times larger than the expected intrinsic response within a domain. As noted above, recent theoretical work using a decoupling approximation and GLD modelling suggests the possibility of up to a thousandfold enhancement of the dielectric susceptibility and piezoelectric response across 90°domains walls in tetragonal ferroelectrics (like those found in our samples) due to structural and polarization inhomogeneities within the domain wall region 22 . Our work, in turn, experimentally demonstrates that high-density, stationary 90°domain walls could provide significantly enhanced dielectric response in the epitaxial thin films, particularly at large domain wall densities.…”

“…Such models suggested that 180°d omain walls in BaTiO 3 could possess permittivity almost an order of magnitude larger than the bulk of the domains. More recently, advanced Ginzburg-Landau-Devonshire (GLD) models have probed the role of polarization gradients near 90°domain walls in BaTiO 3 to suggest that such domain walls could give rise to an enhancement of susceptibilities between 1.1 and 1,000 times larger than the bulk 22 . Despite these predictions as to the potential importance of such stationary contributions, it has proven difficult to quantitatively measure and isolate the stationary contribution (possibly because of the small relative volume associated with domain walls in most samples).…”

“…The second is the so-called extrinsic contribution, which refers to the contribution that arises due to the motion of domain walls under an applied stimulus [10][11][12][13][14][15][16][17][18] . Beyond the motional extrinsic contribution from domain walls, various reports have highlighted the potential importance of what has been alternatively called a stationary or frozen contribution that arises from the response of the volume of the ferroelectric material within the finite width of the domain walls to an applied stimulus irrespective of any lateral displacements or deformations of the wall [19][20][21][22] .…”

Preface to Special Topic: Selected Papers from the Piezoresponse Force Microscopy Workshop Series: Part of the Joint ISAF-ECAPD-PFM 2012 Conference

“…Theoretical model of SPM tip electrostatic field has been developed, effective piezoelectric response of twin walls has been analyzed, 79 and resolving ferroelectric nanostructures by PFM has been attempted. 80 In particular, Morozovska et al have calculated the effective piezoelectric response of twin domain walls using decoupling approximation and Landau-GinzburgDevonshire theory.…”

“…The strong dependence of the piezocoefficients on the polarization gradient was predicted. 79 The exact solution to the coupled problem of indentation of the punch, subjected to either heat or chemical substance distribution at its base, into three-dimensional semi-infinite transversely isotropic material is presented, 58 which can be used to understand the image formation mechanisms in techniques such as thermal SPM and ESM. In their contribution, Pan et al numerically studied PFM resolution for different kinds of domain walls, in particular, tilted domain wall.…”