Domain walls of ferroelectric BaTiO3 within the Ginzburg-Landau-Devonshire phenomenological model

Mechanically compatible and electrically neutral domain walls in tetragonal, orthorhombic and rhombohedral ferroelectric phases of BaTiO3 are systematically investigated in the framework of the phenomenological Ginzburg-Landau-Devonshire (GLD) model with parameters of Ref. [Hlinka and Marton, Phys. Rev. 74, 104104 (2006)]. Polarization and strain profiles within domain walls are calculated numerically and within an approximation leading to the quasi-one-dimensional analytic solutions applied previously to the ferroelectric walls of the tetragonal phase [W. Cao and L.E. Cross, Phys. Rev. 44, 5 (1991)]. Domain wall thicknesses and energy densities are estimated for all mechanically compatible and electrically neutral domain wall species in the entire temperature range of ferroelectric phases. The model suggests that the lowest energy walls in the orthorhombic phase of BaTiO3 are the 90-degree and 60-degree walls. In the rhombohedral phase, the lowest energy walls are the 71-degree and 109-degree walls. All these ferroelastic walls have thickness below 1 nm except for the 90-degree wall in the tetragonal phase and the 60-degree S-wall in the orthorhombic phase, for which the larger thickness of the order of 5 nm was found. The antiparallel walls of the rhombohedral phase have largest energy and thus they are unlikely to occur. The calculation indicates that the lowest energy structure of the 109-degree wall and few other domain walls in the orthorhombic and rhombohedral phases resemble Bloch-like walls known from magnetism.Comment: 12 pages, 9 figure

Comment on ``Elastic Stabilization of a Single-Domain Ferroelectric State in Nanoscale Capacitors and Tunnel Junctions" [N.A. Pertsev and H. Kohlstedt, Phys. Rev. Lett. 98, 257603 (2007).]

In a recent Letter [N.A. Pertsev and H. Kohlstedt, Phys. Rev. Lett. 98, 257603 (2007)] the authors claim that "even nanoscale capacitors and tunnel junctions may have out of plane polarization sufficient for memory applications." Here we show in an elementary way that this conclusion is not substantiated by their calculations and that they should have come to the opposite conclusion within their approximations.Comment: 2 pages, no figure

Correlation Between Structure And C-Afm Contrast Of 180-Degree Domain Walls In Rhombohedral Bati03

Using Landau-Ginzburg-Devonshire theory we describe 180-degree domain wall structure, intrinsic energy and carrier accumulation in rhombohedral phase of BaTiO3 as a function of the wall orientation and flexoelectric coupling strength. Two types of domain wall structures (phases of the wall) exist depending on the wall orientation. The low-energy 'achiral' phase occurs in the vicinity of the {110} wall orientation and has odd polarization profile invariant with respect to inversion about the wall center. The second 'chiral' phase occurs around {211} wall orientations and corresponds to mixed parity domain walls that may be of left-handed or right-handed chirality. The transformation between the phases is abrupt, accompanied with 20-30% change of the domain wall thickness and can happen at fixed wall orientation with temperature change. We suggest that the phase transition may be detected through domain wall thickness change or by c-AFM. The structure of the domain wall is correlated to its conductivity through polarization component normal to the domain wall, which causes free carriers accumulation. Depending on the temperature and flexoelectric coupling strength relative conductivity of the wall becomes at least one order of magnitude higher than in the single-domain region, creating c-AFM contrast enhancement pronounced and detectable.Comment: 31 pages, 10 figures, Supplementary material

Landau-Ginzburg-Devonshire theory for electromechanical hysteresis loop formation in piezoresponse force microscopy of thin films

Electromechanical hysteresis loop formation in piezoresponse force microscopy of thin ferroelectric films is studied with special emphasis on the effects of tip size and film thickness, as well as dependence on the tip voltage frequency. Here, we use a combination of Landau-Ginzburg-Devonshire (LGD) theory for the description of the local polarization reversal with decoupling approximation for the calculation of the local piezoresponse loops shape, coercive voltages and amplitude. LGD approach enables addressing both thermodynamics and kinetics of hysteresis loop formation. In contrast to the "rigid" ferroelectric approximation, this approach allows for the piezoelectric tensor components dependence on the ferroelectric polarization and dielectric permittivity. This model rationalizes the non-classical shape of the dynamic piezoelectric force microscopy (PFM) loops.Comment: 23 pages, 5 figures, 1 appendix,to be submitted to J. Appl. Phy

Magnetic Moment Softening and Domain Wall Resistance in Ni Nanowires

Magnetic moments in atomic scale domain walls formed in nanoconstrictions and nanowires are softened which affects dramatically the domain wall resistance. We perform ab initio calculations of the electronic structure and conductance of atomic-size Ni nanowires with domain walls only a few atomic lattice constants wide. We show that the hybridization between noncollinear spin states leads to a reduction of the magnetic moments in the domain wall. This magnetic moment softening strongly enhances the domain wall resistance due to scattering produced by the local perturbation of the electronic potential.Comment: 4 pages, 5 figure

Domain wall conduction in multiaxial ferroelectrics

The conductance of domain wall structures consisting of either stripes or cylindrical domains in multi-axial ferroelectric-semiconductors is analyzed. The effects of the domain size, wall tilt and curvature, on charge accumulation, are analyzed using the Landau-Ginsburg Devonshire (LGD) theory for polarization combined with Poisson equation for charge distributions. Both the classical ferroelectric parameters including expansion coefficients in 2-4-6 Landau potential and gradient terms, as well as flexoelectric coupling, inhomogeneous elastic strains and electrostriction are included in the present analysis. Spatial distributions of the ionized donors, free electrons and holes were found self-consistently using the effective mass approximation for the respective densities of states. The proximity and size effect of the electron and donor accumulation/depletion by thin stripe domains and cylindrical nanodomains are revealed. In contrast to thick domain stripes and thicker cylindrical domains, in which the carrier accumulation (and so the static conductivity) sharply increases at the domain walls only, small nanodomains of radius less then 5-10 correlation length appeared conducting across entire cross-section. Implications of such conductive nanosized channels may be promising for nanoelectronics.Comment: 39 pages, 11 figures, 3 tables, 4 appendice

Thermodynamics of nanodomain formation and breakdown in Scanning Probe Microscopy: Landau-Ginzburg-Devonshire approach

Thermodynamics of tip-induced nanodomain formation in scanning probe microscopy of ferroelectric films and crystals is studied using the Landau-Ginzburg-Devonshire phenomenological approach. The local redistribution of polarization induced by the biased probe apex is analyzed including the effects of polarization gradients, field dependence of dielectric properties, intrinsic domain wall width, and film thickness. The polarization distribution inside subcritical nucleus of the domain preceding the nucleation event is very smooth and localized below the probe, and the electrostatic field distribution is dominated by the tip. In contrast, polarization distribution inside the stable domain is rectangular-like, and the associated electrostatic fields clearly illustrate the presence of tip-induced and depolarization field components. The calculated coercive biases of domain formation are in a good agreement with available experimental results for typical ferroelectric materials. The microscopic origin of the observed domain tip elongation in the region where the probe electric field is much smaller than the intrinsic coercive field is the positive depolarization field in front of the moving counter domain wall. For infinitely thin domain walls local domain breakdown through the sample depth appears. The results obtained here are complementary to the Landauer-Molotskii energetic approach.Comment: 35 pages, 8 figures, suplementary attached, to be submitted to Phys. Rev.

The Interaction of an 180 degree Ferroelectric Domain Wall with a Biased Scanning Probe Microscopy Tip: Effective Wall Geometry and Thermodynamics in Ginzburg-Landau-Devonshire Theory

The interaction of ferroelectric 180 degree domain wall with a strongly inhomogeneous electric field of biased Scanning Probe Microscope tip is analyzed within continuous Landau-Ginzburg-Devonshire theory. Equilibrium shape of the initially flat domain wall boundary bends, attracts or repulses from the probe apex, depending on the sign and value of the applied bias. For large tip-wall separations, the probe-induced domain nucleation is possible. The approximate analytical expressions for the polarization distribution are derived using direct variational method. The expressions provide insight how the equilibrium polarization distribution depends on the wall finite-width, correlation and depolarization effects, electrostatic potential distribution of the probe and ferroelectric material parameters.Comment: 37 pages, 9 figures, 4 Appendices, to be submitted to Phys. Rev.